Nanofluids: Thermophysical Analysis and Heat Transfer ...530636/FULLTEXT01.pdf · Nanofluids: Thermophysical analysis and heat transfer performance Joan Iborra Approved Examiner Björn

Nanofluids: Thermophysical Analysis and

Heat Transfer Performance

JOAN IBORRA RUBIO

Master of Science Thesis

KTH School of Industrial Engineering and Management

Energy Technology EGI-2012-018MSC

Division of Applied Thermodynamics

SE-100 44 STOCKHOLM

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Master of Science Thesis EGI 2012-018MSC

Nanofluids: Thermophysical analysis and heat transfer

performance

Joan Iborra

Approved

Examiner

Björn Palm

Supervisor

Ehsan Bitaraf Haghighi

Commissioner

Contact person

Abstract

Nanofluids can be described as colloidal suspensions of solid particles smaller than 100 nm

diluted in a base fluid. According to the literature nanofluids have better thermophysical

properties and might achieve better cooling performance compared to conventional liquids.

The current Master Thesis is divided into two main sections; the first part consists of the

analysis of thermal conductivity and viscosity of nanofluids, while the second part is about the

performance of forced convective heat transfer in laminar flow with nanofluids.

For the evaluation of thermal conductivity and viscosity, which are the main two important

thermo-physical properties, different nanoparticles were tested, such as Al2O3 (with 3-50 w%),

TiO2 (with 3-40 w%), SiO2 (with 3-45 w%) and CeO2 (with 3-20 w%); all of them dispersed in

distilled water. The results have been compared with the results provided by the Chemical

Department of University of Birmingham for validation/comparison. Moreover, temperature

effect on viscosity and thermal conductivity has been studied as well. Furthermore, some

theoretical models have been used in order to understand the behavior of thermal

conductivity and viscosity.

For the second part, several nanofluids have been tested to evaluate heat transfer coefficient

in a horizontal open micro-tube test section under laminar flow regime. The test section had

an inner diameter of 0.50 mm and 30 cm length made of stainless steel. Along the pipe, seven

thermocouples were unevenly attached on the outer surface in order to measure the local wall

temperatures. Furthermore, two more thermocouples were used to measure inlet and outlet

temperatures. A differential pressure transducer was used to measure pressure drop, and a DC

power supply was used to apply constant heat flux along the test section; moreover, a double

syringe pump were used to inject nanofluids inside the microtube.

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Acknowledgements

First of all, I would like to thank my supervisor Ehsan for his guidance and help during the

development of this Thesis. Furthermore, I would like to thank Mr. Björn Palm for accept to be

my tutor at KTH and also José Miguel Corberán from UPV, who recommend me for doing this

Thesis. Moreover, I cannot forget my laboratory partners Simon Ströder, Zahid Anwar, Seyed

Aliakbar Mirmohammadi and Mohammadreza Behi, since we have lived in a great working

climate every moment, and also for their help every time I needed; in this way, I also want to

thank Benny Sjoberg and Peter Hill for their technical support.

I thank also all Erasmus students I have met here at Sweden, first when I was living at Norrtälje

and then at Kista. All the moments we spent together will be kept on my mind for the rest of

my life.

On the other hand, I have to express my greatest gratitude to my family, especially my parents

Mariví and Joan, because of their unconditional love and support, and also for our never-

ending Skype sessions twice or more per week.

Finally, I would like to thank everyone who has come to visit me here at Stockholm, my parents

and their friends, my best friends from my village, my brother and my cousin, and my special

friend Maria, who is really important for me and whose visit I will never forget. Moreover, I

have to say that the fact of being away from home has been easier because of my endless

night talks with Jose and Maria, we never cared about the time and this made me feeling near

to home.

Tack s mycket! Thank you very much! Moltes gràcies!

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Contents

List of Figures

List of Tables

Nomenclature

1 Introduction 19

1.1 Nanofluid concept ............................................................................................ 20

1.2 Characteristic parameters ................................................................................ 21

1.3 Production methods......................................................................................... 23

1.3.1 Two steps process .............................................................................. 24

1.3.2 One step process ................................................................................ 24

1.3.3 Other processes ................................................................................. 25

1.4 Applications ...................................................................................................... 26

1.4.1 Electronic cooling applications ........................................................... 27

1.4.2 Other applications .............................................................................. 28

1.5 Literature survey .............................................................................................. 30

2 Measurement instrumentation and results 33

2.1 Thermal conductivity instrument ..................................................................... 33

2.2 Viscosity instrument ......................................................................................... 34

2.3 Results .............................................................................................................. 36

2.3.1 Weight concentration effect .............................................................. 36

2.3.1.1 Al2O3 Evonik .................................................................................. 42

2.3.1.2 ITN-Al2O3-13 .................................................................................. 47

2.3.1.3 TiO2 Evonik .................................................................................... 53

2.3.1.4 ITN-TiO2-10 .................................................................................... 58

2.3.1.5 SiO2 Levasil .................................................................................... 62

2.3.1.6 Al2O3 Alfa Aesar ............................................................................. 67

2.3.1.7 CeO2 Alfa Aesar ............................................................................. 70

2.3.2 Temperature effect ............................................................................ 73

2.3.2.1 Al2O3 Evonik 9 w% ......................................................................... 77

2.3.2.2 ITN-Al2O3-13 9 w%......................................................................... 80

2.3.2.3 TiO2 Evonik 9 w%. .......................................................................... 83

2.3.2.4 ITN-TiO2-10 9 w% .......................................................................... 86

2.3.2.5 SiO2 Levasil 9 w% ........................................................................... 89

2.3.2.6 Al2O3 Alfa Aesar 9 w% ................................................................... 91

2.3.2.7 CeO2 Alfa Aesar 9 w%º .................................................................. 94

2.3.3 Comparisons ....................................................................................... 97

2.3.4 Sensitivity analysis for TPS method.................................................. 107

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3 Test section 109

3.1 Design ............................................................................................................. 109

3.2 Operation ....................................................................................................... 112

3.3 Calculation procedure .................................................................................... 114

3.3.1 Thermophysical properties of nanofluids ........................................ 117

3.3.2 Global value’s calculation ................................................................. 119

3.3.3 Local value’s calculation ................................................................... 122

3.3.4 Average value’s calculation .............................................................. 123

3.3.5 Friction factor calculation ................................................................ 124

3.4 Error analysis .................................................................................................. 125

3.5 Results and discussions .................................................................................. 136

4 Conclusions 164

Bibliography 166

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List of Figures

1. Number of publications studying nanofluids during last years ..................................... 30

2. Thermal conductivity instrument ................................................................................... 33

3. Sample holder of termal conductivity instrument inside water bath ............................ 34

4. Viscosity instrument ....................................................................................................... 35

5. Sample holder of viscosity instrument ........................................................................... 35

6. Size particle distribution (Al2O3 – Evonik ....................................................................... 42

7. Relative thermal conductivity vs weight concentration (Al2O3 - Evonik).

Are shown both KTH and UBHAM experimental data and Maxwell prediction,

with an acceptance range of ± 5% ................................................................................. 43

8. Effective thermal conductivity vs weight concentration (Al2O3 - Evonik).

Is shown KTH data and Prasher prediction, with an acceptance range of ± 10% .......... 44

9. KTH data against other research groups. Relative thermal conductivity is plotted

versus volume percentage ............................................................................................. 44

10. Relative viscosity vs weight concentration (Al2O3 - Evonik). Einstein, Nielsen,

Maiga, and Krieger-Dougherty models are used in order to compare against

KTH and UBHAM experimental data .............................................................................. 45

11. KTH data against other research groups. Absolute viscosity is represented


12. Absolute viscosity vs shear rate (Al2O3 - Evonik) ............................................................ 47

13. Size particle distribution (ITN - Al2O3 – 13) .................................................................... 48

14. Relative thermal conductivity vs weight concentration (ITN - Al2O3 - 13) ..................... 48

15. Effective thermal conductivity vs weight concentration (ITN - Al2O3 - 13).




17. Relative viscosity vs weight concentration (ITN - Al2O3 - 13). Einstein, Nielsen,

Maiga, and Krieger-Dougherty models are used in order to compare against

KTH and UBHAM experimental data .............................................................................. 51



19. Absolute viscosity vs shear rate (ITN - Al2O3 - 13) .......................................................... 52

20. Size particle distribution (ITN - Al2O3 – 13) ................................................................... 53

21. Relative thermal conductivity vs weight concentration (TiO2 - Evonik) ........................ 53

22. Effective thermal conductivity vs weight concentration (TiO2 - Evonik).




24. Relative viscosity vs weight concentration (TiO2 - Evonik) ............................................ 56



26. Absolute viscosity vs shear rate (TiO2 – Evonik)............................................................. 57

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27. Size particle distribution (ITN – TiO2 - 10) ...................................................................... 58

28. Relative thermal conductivity vs weight concentration (ITN - TiO2 - 10) ....................... 58

29. Effective thermal conductivity vs weight concentration (ITN - TiO2 - 10).




31. Relative viscosity vs weight concentration (ITN - TiO2 - 10)........................................... 61

32. data against other research groups. Absolute viscosity is represented versus

volume percentage ........................................................................................................ 61

33. Absolute viscosity vs shear rate (ITN - TiO2 - 10) ........................................................... 62

34. Size particle distribution (SiO2 - LEV) .............................................................................. 62

35. Relative thermal conductivity vs weight concentration (SiO2 - LEV) ............................. 63

36. Effective thermal conductivity vs weight concentration (SiO2 - LEV).




38. Relative viscosity vs weight concentration (SiO2 - Levasil) ............................................ 65



40. Absolute viscosity vs shear rate (SiO2 - Levasil) ............................................................. 66

41. Size particle distribution (Al2O3 – Alfa Aesar)................................................................. 67

42. Relative thermal conductivity vs weight concentration (Al2O3 – Alfa Aesar) ................ 67

43. Effective thermal conductivity vs weight concentration (Al2O3 – Alfa Aesar).


44. Relative viscosity vs weight concentration (Al2O3 – Alfa Aesar) .................................... 69

45. Absolute viscosity vs shear rate (Al2O3 – Alfa Aesar) ..................................................... 70

46. Size particle distribution (CeO2 – Alfa Aesar) ................................................................. 70

47. Effective thermal conductivity vs weight concentration (CeO2 – Alfa Aesar).


48. Relative thermal conductivity vs weight concentration (CeO2 – Alfa Aesar) ................. 71

49. Relative viscosity vs weight concentration (CeO2 – Alfa Aesar) ..................................... 72

50. Absolute viscosity vs shear rate (CeO2 – Alfa Aesar) ...................................................... 73

51. Absolute thermal conductivity vs temperature (Al2O3 – Evonik – 9 w%).

Also an own-made prediction is plotted, with an acceptance range of ± 5% ................ 77

52. Relative thermal conductivity vs temperature (Al2O3 – Evonik – 9 w%).

Are shown experimental data and Maxwell prediction, with an acceptance

range of ± 5%.................................................................................................................. 78

53. Absolute viscsosity vs temperature (Al2O3 – Evonik – 9 w%).

Also an own-made prediction is plotted, with an acceptance range of ± 12% .............. 79

54. Relative viscosity vs temperature (Al2O3 – Evonik – 9 w%) ............................................ 79

55. Absolute viscosity vs shear rate (Al2O3 – Evonik – 9 w%) .............................................. 80

56. Absolute thermal conductivity vs temperature (ITN - Al2O3 – 13 – 9 w%).


57. Relative thermal conductivity vs temperature (ITN - Al2O3 – 13 – 9 w%).


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range of ± 5%................................................................................................................. .81

58. Absolute viscosity vs temperature (ITN - Al2O3 – 13 – 9 w%).


59. Relative viscosity vs temperature (ITN - Al2O3 – 13 – 9 w%) .......................................... 82

60. Absolute viscosity vs shear rate (ITN - Al2O3 – 13 – 9 w%) ............................................. 83

61. Absolute thermal conductivity vs temperature (TiO2 – Evonik – 9 w%).


62. Relative thermal conductivity vs temperature (TiO2 – Evonik – 9 w%).


range of ± 5%.................................................................................................................. 84

63. Absolute viscosity vs temperature (TiO2 – Evonik – 9 w%).


64. Relative viscosity vs temperature (TiO2 – Evonik – 9 w% .............................................. 85

65. Absolute viscosity vs shear rate (TiO2 – Evonik – 9 w%) ................................................ 85

66. Absolute thermal conductivity vs temperature (ITN - TiO2 – 10 – 9 w%).


67. Relative thermal conductivity vs temperature (ITN - TiO2 – 10 – 9 w%).


range of ± 5%.................................................................................................................. 87

68. Absolute viscosity vs temperature (ITN - TiO2 – 10 – 9 w%).


69. Relative viscosity vs temperature (ITN - TiO2 – 10 – 9 w%) ........................................... 88

70. Absolute viscosity vs shear rate (ITN - TiO2 – 10 – 9 w%) .............................................. 88

71. Absolute thermal conductivity vs temperature (SiO2 – Levasil – 9 w%).


72. Relative thermal conductivity vs temperature (SiO2 – Levasil – 9 w%).


range of ± 5%.................................................................................................................. 89

73. Absolute viscosity vs temperature (SiO2 – Levasil – 9 w%).


74. Relative viscosity vs temperature (SiO2 – Levasil – 9 w%) ............................................. 90

75. Absolute viscosity vs shear rate (SiO2 – Levasil – 9 w%) ................................................ 91

76. Absolute thermal conductivity vs temperature (Al2O3 – Alfa Aesar - 9 w%).


77. Relative thermal conductivity vs temperature (Al2O3 – Alfa Aesar - 9 w%).


range of ± 5%.................................................................................................................. 92

78. Absolute viscosity vs temperature (Al2O3 – Alfa Aesar - 9 w%).


79. Relative viscosity vs temperature (Al2O3 – Alfa Aesar - 9 w%) ....................................... 93

80. Absolute viscosity vs shear rate (Al2O3 – Alfa Aesar - 9 w%) ......................................... 94

81. Absolute thermal conductivity vs temperature (CeO2 – Alfa Aesar - 9 w%).


82. Relative thermal conductivity vs temperature (CeO2 – Alfa Aesar - 9 w%).


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range of ± 5%.................................................................................................................. 95

83. Absolute viscosity vs temperature (CeO2 – Alfa Aesar - 9 w%).


84. Relative viscosity vs temperature (CeO2 – Alfa Aesar - 9 w%) ....................................... 96

85. Absolute viscosity vs shear rate (CeO2 – Alfa Aesar - 9 w%) .......................................... 97

86. Relative thermal conductivity vs weight concentration.

Are shown experimental data from KTH and UBHAM for Al2O3 nanofluids

belonging to Evonik, ITN and Alfa Aesar ........................................................................ 98

87. Relative thermal conductivity vs temperature. Are shown experimental

data from KTH for Al2O3 nanofluids belonging to Evonik, ITN and Alfa Aesar ............... 98

88. Relative viscosity vs weight concentration. Are shown experimental

data from KTH and UBHAM for Al2O3 nanofluids belonging to Evonik,

ITN and Alfa Aesar .......................................................................................................... 99

89. Relative viscosity vs temperature. Are shown experimental data from

UBHAM for Al2O3 nanofluids belonging to Evonik, ITN and Alfa Aesar ......................... 99

90. Relative viscosity vs weight concentration. Are shown experimental data

from KTH and UBHAM for TiO2 nanofluids belonging to Evonik and ITN .................... 100

91. Relative thermal conductivity vs temperature. Are shown experimental

data from KTH for TiO2 nanofluids belonging to Evonik and ITN ................................. 100

92. Relative viscosity vs weight concentration. Are shown experimental

data from KTH and UBHAM for TiO2 nanofluids belonging to Evonik and ITN ............ 101

93. Relative viscosity vs temperature. Are shown experimental data from

UBHAM for TiO2 nanofluids belonging to Evonik and ITN ........................................... 101

94. Experimental data vs Maxwell equation. Are also plotted ± 5% and ± 10%

deviation ranges from prediction. Points correspond to weight concentration

analysis, so are represented nanofluids at different w% ............................................. 103

95. Experimental data vs Krieger equation. Are also plotted ± 5%, ± 10% and

± 15% deviation ranges from prediction. Points correspond to weight

concentration analysis, so are represented nanofluids at different w% ..................... 104

96. Experimental data vs Joan equation. Are also plotted ± 2,5% and ± 5%

deviation ranges from prediction. Points correspond to temperature analysis,

so are represented nanofluids at different temperatures ........................................... 105

97. Experimental data vs Joan equation. Are also plotted ± 5%, ± 10% and

± 15% deviation ranges from prediction. Points correspond to temperature

analysis, so are represented nanofluids at different temperatures ............................ 106

98. Thermal conductivity analysis with specific heat (in volumetric units) variations ...... 107

99. Thermal conductivity analysis with specific heat variations ........................................ 107

100. Thermal conductivity analysis with specific heat variations ........................................ 108

101. Schematic representation of the experimental set-up ................................................ 109

102. Experimental set-up .................................................................................................... 110

103. Thermocouples used to measure temperatures along the test section ...................... 110

104. Injecting pump consisting of two syringes ................................................................... 111

105. Insulated test section ................................................................................................... 112

106. Distribtion of thermocouples on test section .............................................................. 113

107. Experimental set-up in 3D. Source:

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http://www.kth.se/itm/inst/energiteknik/forskning/ett/projekt/nanohex/measuremen

ts/htc/setup-1-1.291042 .............................................................................................. 114

108. Schematic calculation procedure ................................................................................. 116

109. Ubication of used temperatures from micro-pipe.1 .................................................... 120

110. Convective heat transfer coefficient vs volumetric flow rate. Nanogap-Ag ................ 137

111. Convective heat transfer coefficient vs mass flow rate. Nanogap-Ag ......................... 137

112. Convective heat transfer coefficient vs velocity. Nanogap-Ag .................................... 138

113. Convective heat transfer coefficient vs pressure drop. Nanogap-Ag .......................... 138

114. Convective heat transfer coefficient vs pumping power. Nanogap-Ag ....................... 138

115. Convective heat transfer coefficient vs Reynolds number. Nanogap-Ag..................... 139

116. Nusselt number vs Reynolds number. Nanogap-Ag ..................................................... 139

117. Nusselt number vs Reynolds number (with theoretical Shah and Stephan

predictions). Nanogap-Ag ............................................................................................. 140

118. Local Nusselt number vs non-dimensional length (Shah prediction

is included). Nanogap-Ag, 19 mL/min test ................................................................... 140


is included). Nanogap-Ag, 21 mL/min test ................................................................... 140

120. Friction factor vs Reynolds number (Darcy-Weisbach equation is included

in order to modeling data). Nanogap-Ag ..................................................................... 141

121. Convective heat transfer coefficient vs volumetric flow rate. ITN-Al-13-9w% ............ 142

122. Convective heat transfer coefficient vs mass flow rate. ITN-Al-13-9w% ..................... 142

123. Convective heat transfer coefficient vs velocity. ITN-Al-13-9w% ................................ 142

124. Convective heat transfer coefficient vs pressure drop. ITN-Al-13-9w% ...................... 143

125. Convective heat transfer coefficient vs pumping power. ITN-Al-13-9w% ................... 143

126. Convective heat transfer coefficient vs Reynolds number. ITN-Al-13-9w% ................ 143

127. Nusselt number vs Reynolds number. ITN-Al-13-9w% ................................................ 144


predictions). ITN-Al-13-9w% ........................................................................................ 144

129. Local Nusselt number vs non-dimensional length (Shah prediction is

included). ITN-Al-13-9w%, 9 mL/min test ................................................................... 145


included). ITN-Al-13-9w%, 11 mL/min test .................................................................. 145


in order to modeling data). ITN-Al-13-9w% ................................................................. 145

132. Convective heat transfer coefficient vs volumetric flow rate. SiC-DW-9%-UBHAM .... 146

133. Convective heat transfer coefficient vs mass flow rate. SiC-DW-9%-UBHAM ............. 146

134. Convective heat transfer coefficient vs velocity. SiC-DW-9%-UBHAM ........................ 147

135. Convective heat transfer coefficient vs pressure drop. SiC-DW-9%-UBHAM .............. 147

136. Convective heat transfer coefficient vs pressure drop. SiC-DW-9%-UBHAM .............. 147

137. Convective heat transfer coefficient vs Reynolds number. SiC-DW-9%-UBHAM ........ 148

138. Nusselt number vs Reynolds number. SiC-DW-9%-UBHAM ........................................ 148


predictions). SiC-DW-9%-UBHAM ................................................................................ 149

140. Local Nusselt number vs non-dimensional length (Shah prediction is included).

SiC-DW-9%-UBHAM, 11 mL/min test .......................................................................... 149

http://www.kth.se/itm/inst/energiteknik/forskning/ett/projekt/nanohex/measurements/htc/setup-1-1.291042


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SiC-DW-9%-UBHAM, 13 mL/min test .......................................................................... 149

142. Friction factor vs Reynolds number (Darcy-Weisbach equation is included in

order to modeling data). SiC-DW-9%-UBHAM ............................................................. 150

143. Convective heat transfer coefficient vs volumetric flow rate. CeO2-Antaria ............... 151

144. Convective heat transfer coefficient vs mass flow rate. CeO2-Antaria ........................ 151

145. Convective heat transfer coefficient vs velocity. CeO2-Antaria ................................... 151

146. Convective heat transfer coefficient vs pressure drop. CeO2-Antaria ......................... 152

147. Convective heat transfer coefficient vs pumping power. CeO2-Antaria ...................... 152

148. Nusselt number vs Reynolds number. CeO2-Antaria ................................................... 153


predictions). CeO2-Antaria ........................................................................................... 153


included). CeO2-Antaria, 9 mL/min test ...................................................................... 153


included). CeO2-Antaria, 11 mL/min test ..................................................................... 154

152. Friction factor vs Reynolds number (Darcy-Weisbach equation is

included in order to modeling data). CeO2-Antaria ..................................................... 154

153. Convective heat transfer coefficient vs volumetric flow rate ...................................... 155

154. Convective heat transfer coefficient vs mass flow rate ............................................... 155

155. Convective heat transfer coefficient vs velocity .......................................................... 155

156. Convective heat transfer coefficient vs pressure drop ................................................ 156

157. Convective heat transfer coefficient vs pumping power ............................................. 156

158. Convective heat transfer coefficient vs Reynolds number .......................................... 156

159. Nusselt number vs Reynolds number .......................................................................... 157


predictions) .................................................................................................................. 157


is included). Surfactant analysis, 13 mL/min test ......................................................... 158


included). Surfactant analysis, 15 mL/min test ............................................................ 158


in order to modeling data). Surfactant analysis ........................................................... 159



166. Convective heat transfer coefficient vs velocity .......................................................... 160

167. Convective heat transfer coefficient vs pressure drop ................................................ 160

168. Convective heat transfer coefficient vs pumping power ............................................. 161

169. Convective heat transfer coefficient vs Reynolds number .......................................... 161

170. Nusselt number vs Reynolds number .......................................................................... 162


predictions) .................................................................................................................. 162

172. Local Nusselt number vs non-dimensional length (Shah prediction is included)

SiC-ANL, 9 mL/min test ................................................................................................. 162


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SiC-ANL, 9 mL/min test ................................................................................................ 163

174. Friction factor vs Reynolds number (Darcy-Weisbach equation is included in

order to modeling data). Surfactant analysis ............................................................... 163

List of Tables

1. Conductivity values for different solids and liquids (metallic and non-metallic) ........... 21

2. Thermal conductivity and viscosity values versus concentrations. Results are

obtained from KTH and UBHAM. Difference percentage has been calculated

regarding to UBHAM values ........................................................................................... 41

3. Thermal conductivity and viscosity values versus concentrations.

Difference percentage has not been calculated because weight

concentration of samples belonging to KTH and UBHAM are not the same ................. 42

4. Values for theoretical comparisons (Al2O3 - Evonik) ...................................................... 45

5. Values for theoretical comparisons for (ITN - Al2O3 - 13) ............................................... 51

6. Values for theoretical comparisons for (TiO2 - Evonik) .................................................. 56

7. Values for theoretical comparisons for (ITN – TiO2 - 10) ............................................... 60

8. Values for theoretical comparisons for (SiO2 - Evonik) .................................................. 65

9. Values for theoretical comparisons for (Al2O3 – Alfa Aesar) .......................................... 69

10. Values for theoretical comparisons for (CeO2 – Alfa Aesar) .......................................... 72

11. Absolute thermal conductivity and viscosity values versus temperature.

Results are obtained from both UBHAM and KTH ......................................................... 74

12. Relative values of thermal conductivity and viscosity. Results are obtained

from KTH and UBHAM .................................................................................................... 75

13. Test section parameters ............................................................................................... 115

14. Nanofluids' parameters ................................................................................................ 115

15. Error values for different measured parameters ......................................................... 127

16. Description of nanofluids used in this study ................................................................ 136

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Nomenclature

D Diameter [m]

L Length [m]

Δ Difference [-]

Mass flow rate [kg/hr]

ρ Density [kg/m3]

cp Specific heat [kJ/kgK]

µ Viscosity [kg/ms]

Gz Graetz [-]

f Friction factor [-]

V Volume concentration [%]

W Weight concentration [%]

u Test section velocity [m/s]

h Heat transfer coefficient [W/m2K]

k Thermal conductivity [W/mK]

Nu Nusselt number [-]

Pr Prandtl number [-]

Re Reynolds number [-]

P Pressure [bar]

T Temperature [K]

Q Power [W]

Q Heat flux power [W/ m2]

Q Volume flow rate [mL/min]

X Distance [m]

x* Non-dimensional length [-]

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Abbreviations

DC Direct current

CNT Carbon nanotubes

HTC Heat transfer coefficient

UBHAM University of Birmingham

KTH Kungliga Tekniska Högskolan

LEV Levasil

EV Evonik

ITN ITNanovation

AA Alfa Aesar

NV Normal values

v% Volume concentration

w% Weight concentration

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Subscripts

avg Average

in Inlet

out Outlet

nf Nanofluid

np Nanoparticle

f, bf Base fluid

exp Experimental

therm Thermal

elec Electric

pressdrop Pressure drop

ts Outer surface

‘_ts Inner surface

tub Tube

agg Agreggated

o Outer

i Inner

mes Measurement

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1. INTRODUCTION

Last decades, technology has undergone a considerable evolution in all different

sectors of industry. In this way, the need to achieve better results through optimizing benefits,

minimize losses and, above all, improve methods performance and also new properties, has

led to a situation such that almost all research groups have discovered the benefit of

nanotechnology on their respective fields of study.

Thereby, heat transfer is not an exception, since is a very important issue that has to

be taken into account for most present industrial processes such as power generation or

chemical, physical and biological processes. On the other hand it is also essential for the field

of refrigeration chambers, electronic cooling systems, data centers and power electronics. But

heat transfer is not only needed at industrial scale, but also for environmental conditioning of

homes, as well as private and public buildings. Thus, this makes it a matter which affects the

whole society.

However, traditional coolants like water, oils and ethylene glycol, are keeping stagnant

because of their limitations regarding to increasing heat transfer capability. These liquids have

constant values for their thermo-physical properties, so, the only way to improve their heat

transfer features has to be done through the device, that is to say, through augmenting the

heat exchange area or the flow rates of coolants. Nevertheless, this solution implies a higher

heat exchange potential, but it doesn’t enhance the efficiency of the procedure, that is the

relevant question.

Therefore, all exposed before brings into existence of a demand to meet the needs

showed before. Then, this is where nanotechnology appears as an option to consider, in order

to analyzing the possibilities it offers to fix heat exchange transfer demands at industrial scale.

In this case, there is a growing thought that considers this demand can be fulfilled

through the usage of nanofluids. For this reason, at the moment, there are lots of research

groups investigating this path, and some promising results are being observed ([26], [31], [35])

although the physical background for nanofluids are still under research and development.

Nanofluids are homogeneous mixtures of solids and liquids when these solid particles

are smaller than 100 nm [2]. These added solid particles are supposed to improve thermo-

physical properties and heat transfer behavior of its base fluid. Moreover, as was said above,

traditional coolants are an option to be improved from thermo-physical view point in order to

cover the needs of refrigeration in electronic systems; because of that, nanofluids are

expected to fill this gap.

NanoHex project is a project that KTH-Energy Technology is one of its partner and this

project focus on important research about nanofluids [1], as is the world’s largest collaborative

project for development and research of nanofluid coolants. It is expected to develop and

optimize safe processes for the production of high performance nanofluids coolants for use in

industrial heat management. It will be done by developing an analytical model that can

20

accurately predict thermal performance (thermo-physical properties and behavior in industrial

applications) of such nanofluids refrigerants.

This thesis is about experimental and modeling thermal properties like thermal

conductivity and viscosity, in addition to the evaluation of different nanofluids behavior tested

in a test section, which simulates a microelectronic pipe. The aim of this thesis was to measure

thermal conductivity and viscosity of nanofluids in a small microtube in order to evaluate their

heat transfer performance based on different criteria.

1.1. Nanofluid concept

The first time the term nanofluid was defined was in 1995, when Choi coined it [2],

while working in a research project at Argonne National Laboratory [3]. According to

bibliography [2], he defined it as “an innovative new class of heat transfer fluids that can

be engineered by suspending nanoparticles in conventional heat transfer fluids” and able

to enhance significantly the thermal conductivity and convective heat transfer

performance of its base fluids; in this way, their values are order-of-magnitude higher [3],

than those of traditional base fluids (ethylene glycol, water, oils). Deepening in the

literature, particle size of nanoparticles dispersed in based fluids usually has diameters or

lengths (not always nanoparticles are spheres) within a range from 1 up to 100 nm [2].

So, it can be understood that nanofluid consists of the following parts:

nanoparticle and base fluid. However, as stabilization of the dilution is a relevant aspect

to get trustable results, sometimes additives such as dispersants are added to avoid

sedimentation of particles, in case the sample is clearly heterogeneous; therefore, as is

desired, a single-phase fluid will be obtained. Moreover, different facets of these samples

can be analyzed in order to discover the reasons lead to have great unexpected results for

common thermophysical properties. The main important parameters affect nanofluids

behaviors are: particle size, concentration and shape, nanoparticle material, base fluid

nature, sonication time of sample, method manufacturer employed or pH-value of

dilution.

According to Choi [2], enhancement of thermal conductivity is because of the

enormous thermal conductivity of solid particles, which usually are hundred or even

thousand times larger than traditional base fluids, as can be seen in Table 1:

21

Table 1. Conductivity values for different solids and liquids (metallic and non-metallic) [4]

.

Solid / Liquids Material Thermal Conductivity (W/mK)

Metallic solids

Silver 429

Copper 401

Aluminum 237

Non-metallic solids

Diamond 3300

Carbon nanotubes 3000

Silicon 1458

Alumina (Al2O3) 40

Metallic liquids Sodium @644K 72,3

Non-metallic liquids

Water 0,613

Ethylene glycol 0,253

Engine oil 0,145

Although thermal conductivity improvement is important, after knowing that,

nanofluid should be tested for forced-convection cooling applications in both laminar and

turbulent regime. In that case, when evaluation of nanofluid behavior in a cooling system

is needed, the determining parameter is heat transfer coefficient.

Thereby, heat transfer coefficient reaches higher values than are expected due to

two possibilities [6]. The first one is the chaotic movement of nanoparticles, which gets

better the energy exchange process in nanofluids. The other reason was mentioned above

these lines, where was explained through Choi experiments thermal conductivity of solid

particles were the reason of these unexpected enhancements, so, the same occurs for

heat exchange coefficient.

In this manner, there are some experiments proving the enhancement of that

coefficient in flowing liquids while these are working in forced-convection cooling

applications; furthermore, as was found through the literature survey [8], some great

increase have been detected for different nanofluids tested in conditions mentioned

before. So, can be said that nanofluids play an important role in heat exchange field, and

its potential impact about finding a solution for the problem have been established in the

previous introduction could be really big.

1.2. Characteristic parameters

At the previous chapter nanofluid has been defined, but nothing regarding its

main properties has been discussed. In this way, there are four characteristic parameters

22

[3], thermal conductivity (maybe the most important one), specific heat, dynamic viscosity

and density. Subsequently, these mentioned properties are going to be explained by a

brief definition, just to have an idea about what they mean:

- Thermal conductivity (k): is the property that gives an idea about the ability of a

substance to conduct heat. It is determined by the rate of heat normally through

an area in the substance divided by the area and by minus the component of the

temperature gradient in the direction of flow, so, its units are W/mK. Thermal

conductivity is a very important characteristic since it is expected, when high

thermal conductivity nanoparticles are added to a fluid, to reach higher value for

thermal conductivity of dispersion.

- Specific heat (cp): is defined as the ratio of the amount of energy that has to be

transferred to or from one unit of mass or amount of substance to change the

system temperature by one degree. It is measured usually with J/kgK. Thereby, it

will be better if dilutions are going to be used have high specific heats because it

will help to achieve high heat coefficient transfer in processes.

- Dynamic viscosity (µ): first of all is better to define viscosity as a general concept.

This is a measure of the resistance of a fluid which is being deformed by either

shear or tensile stress; furthermore, viscosity describes a fluid’s internal resistance

to flow and may be thought of as a measure of fluid friction; moreover, in common

terms, viscosity is the thinness or thickness of the fluid. It is equal to the tangential

stress on a liquid undergoing streamline flow divided by its velocity gradient. Once

absolute viscosity has been defined, it is turn to talk about the difference between

dynamic and kinematic viscosities. The first one is the quantitative expression of a

fluid’s resistance to flow (shear), while kinematic is a ratio of the viscous force to

the inertial force. In this study only dynamic viscosity will be used, because by its

measurement is possible to guess the Newtonian or non-Newtonian behavior of

the sample. For microelectronics applications is better for nanofluids to show low

viscosity values, since it is important that the fluid flows properly through the

microchannels.

- Density (ρ): is defined as its mass per unit volume, so its units are kg/m3. A

relevant aspect is that density varies with temperature and pressure; therefore, it

is an issue to take in account when temperature effect is studied. Also this

property is important when preparing dispersions, given that for materials with

different densities is difficult to get a homogeneous mixture.

23

Once known the most remarkable thermo-physical properties that affect

nanofluids behavior, should be said the point is to find out one which combines the best

things of each property, in order to reach a great heat exchange coefficient, but, of

course, that is not an easy work.

On the other hand, these parameters have to be mixed with the following goals [5]:

- High heat conduction: is the main reason which are investigating the nanofluids,

and good results are expected to observe in this field.

- Stability: is very important inasmuch as when a sample is not stable or if it looks

like heterogeneous, thermo-physical properties are not the same through the

whole dispersion. For this reason sonication processes are used to avoid

destabilization.

- Reduction in pumping power: this is also a relevant question, because refrigeration

systems spent a lot of energy in pumping the fluids through the facilities. In this

way, is expected for nanofluids to reduce pumping power needed in this kind of

devices.

- Reduce erosion: erosion is important because causes wear in the pipes and,

although is a slow progression and is a long-term problem, should be reduced with

the aim of caring facilities.

1.3. Production methods

The stable nature of nanofluids is essential in order to achieve homogeneous

suspensions to optimize their thermophysical properties, and that is done by the

achievement of successful synthesis processes [9]. But there is not only one specific

procedure to prepare them, as be described later.

Before talking about nanofluids production methods, is recommendable mention

different ways nanoparticles are produced and substances used to prepare nanofluids [3].

Metals like Ag, Au, Cu, Fe; or ceramic oxides such as Al2O3, CuO, CeO2; semiconductors like

TiO2; and single-, double- or multi-walled carbon nanotubes are the most used particles.

But each time there are more and more new materials employed for the purpose of

discover interesting properties while testing different innovative nanofluids.

According to the literature there are two general methods:

- Physical methods: mechanical grinding and inert-gas condensation.

24

- Chemical methods: chemical precipitation, chemical vapor deposition, micro-

emulsions, spray pyrolysis and thermal spraying.

Furthermore, nanoparticles in powder form, are easier to disperse in base fluids

and, in this way, get a homogeneous dilution will be not difficult. Another question is the

shape of nanoparticles, which usually are spherical, cubic, ellipsoidal, nanotubes and

sometimes can be integrated into arrays. Despite of this variety, the most common shape

are spheres.

Once nanoparticles preparation methods have been seen, it is time to go further

and talk about nanofluids manufacture procedures, which are mainly two: one and two

steps processes. However, there are more methods, but this aspect will be treated later.

1.3.1. Two steps process

As the name of the method shows, it has two stages, the first one is when

nanoparticles are prepared, and the second one consists of the nanoparticles dispersion

into a base fluid.

Depending on the kind of nanoparticles are going to be used [9], first step is often

done by chemical vapor deposition or inert-gas condensation. An advantage of the later

process is that has already been scaled up to commercial nano-powder production [10], so

it is cheaper to produce nanofluids by this method; though that is not the only reason,

since particle concentration and size distribution can be controlled as well.

For the second step, namely, the dispersion of nanoparticles into the selected

base fluid, simple techniques [11] such as addition of surfactants to the fluids, changing

nanofluids’ pH value and both mechanical and ultrasonic agitation are needed in order to

obtain stable samples, since minimization of particle aggregation and dispersion

improvement will be achieved.

1.3.2. One step process

The difference between this method and the previous one is that, while in two-

step process first nanoparticles are produced and after that these particles are dispersed

into the base fluid, in the case of one-step process both stages are done at the same time.

25

A good point of this method is that the processes of drying, storage,

transportation, and dispersion of nanoparticles are avoided, so, the agglomeration of

nanoparticles is minimized and the stability of fluids is increased [12]. On the other hand,

this method is also used because prevents oxidation of metallic particles when high-

conductivity metals are used [3], [10].

But, for this purpose, there is not only one way to do it, there are various tested

methods that can be employed depending on the materials properties and limitations [3].

For instance, direct evaporation (under vacuum conditions) has been used to

produce nanofluids with metal nanoparticles [3], [9]. Whereas it presents the advantage of

aggregation effect is reduced, this technique is only valid for low vapor pressure fluids.

Another physical method [13] is the submerged arc nanoparticle synthesis system

(SANSS), particularly for TiO2 in deionized water. Like before, vacuum conditions are

needed to condense the liquid while vaporization of the solid material by the submerged

arc is being done.

Although physical one-step process shows good results according to the

literature, they are expensive talking about industrial or commercial scale [3], besides

limits the production because of vacuum conditions, which make slow the process.

For this reason chemical one-step methods have been also analyzed; it is possible

because of the ability of chemistry to manipulate atoms and molecules in the liquid phase [10]. It should be mentioned one has been employed to prepare nanofluids with Cu

nanoparticles [14] in ethylene glycol as base fluid and using polyvinylpyrrolidone to obtain

a stable nanofluid and avoid aggregation effect. Even though this method could be faster

than one-step physical methods [3], is still slower than two-step processes.

One of the matters regarding chemical one-step process is that the residual

reactants are left in the nanofluids due to incomplete reaction or stabilization. It is

difficult to elucidate the nanoparticle effect without eliminating this impurity effect [11].

So, it should be pointed that, talking about industrial and commercial scale, two-

step method is better than one-step process, because of all reasons have been mentioned

along these paragraphs.

1.3.3. Other processes

The described processes are suitable for several kinds of nanofluids, namely, for

different types of both nanoparticles and host fluids. However, in case of novel processes,

there are more limitations due to these methods are designed for specific nanoparticles

and fluids, more or less the same than occurs with chemical one-step method.

26

In this manner, processes such as [3] templating, micro-droplet drying, electrolysis

metal deposition, layer-by-layer assembly and other colloid chemistry techniques are fit

to nanoparticles with specific porosities, densities, geometries, charge, and surface

chemistries.

According to bibliography, other processes have been experimented: one way to

synthesize copper nanofluids through a microfluidic microreactor in a continuous flow [11];

obtaining of monodisperse noble metal (such as Ag or Au) colloids using a phase-transfer

method, and is also used to prepare kerosene based Fe3O4 nanofluids [11]; a chemical

solution method adjudges to nanofluids both higher conductivity enhancement and

better stability than those produced by the other methods [10].

As have been observed in some papers [3], the existing discrepancies between

research groups when thermal conductivity values are reported could be explained

because of different synthesis processes, since the structural characteristics of

nanoparticles like particle size distribution, mean particle size and shape depend on the

process has been used.

1.4. Applications

Nanofluids technology is an interdisciplinary field with substances in chemistry,

physics, biology and engineering. By provoking alterations in the nanoscale structure of a

nanoparticle is possible to change the functionality of a nanofluid. In this way, these kind

of fluids offer many applications for several scientific fields such as biomedicine, industrial

cooling, heating buildings and reducing pollution, transportation, nuclear systems cooling,

space and defense, electronic cooling, energy storage, friction reduction, magnetic

sealing, optical applications, among other examples [3], [11], [19].

For this reason, although to date much work about nanofluids have been done in

national laboratories and academia, each time more and more companies and institutions

are starting to be interested in these advances. However a commercial nanofluid for

cooling application still does not exist in the market.

Subsequently, some of mentioned applications will be commented, but focusing,

above all, in heat transfer improvements, since is the topic more related to the current

work.

27

1.4.1. Electronic cooling applications

Given that nanofluids are coolants that can be used in heat transfer process; they

can play a really important role in electronic cooling field, since generally, there are two

approaches to improve the heat removal for electronic equipment [11]: find an optimum

geometry of cooling devices and increase the heat transfer capacity. Going farther,

bearing in mind that new electronic stuff are appearing each time smaller and, at the

same time, require more heat exchange capability. Nanofluids could be a good answer to

solve upcoming problems in this field due to different thermo-physical behavior than

conventional coolants. This aspect is accentuated even further when discussing

microprocessors and integrated circuits, since have been radically increased during last

decades, and is expected to increase over time. Because of that, traditional ways to

remove surplus heat generated at equipments like air-cooling techniques are becoming

obsolete, so it is necessary to find new paths to face this matter. Thereby, this thesis deals

on to provide some conclusions than could be useful and offer a small contribution to

improve investigations in this direction.

By checking literature [15], a cooling system was designed through combining

microchannel heat sink with nanofluids containing multi walled carbon nanotubes

(MWCNTs). Higher cooling performance was obtained when compared to the device using

pure water and also using nanofluids with spherical nanoparticles. Some advantages were

observed, like a reduction in both thermal resistance and temperature gradient between

the microchannel wall and the coolant.

Additionally, Nguyen et al. [16] designed a closed liquid-circuit in order to analyze

the heat transfer capacity of the cooling equipment. What they did was use an Al2O3

nanofluid with distilled water as a based fluid instead of the previous coolant (distilled

water). After experiments were done, a considerable enhancement has been observed in

heat transfer coefficient of the cooling system. Different concentrations and flow rates

(also Reynolds number changes) were evaluated, but the sample prepared with a 4.5 %

volume concentration reached an enhancement of 23% with respect to that of the base

fluid (for Re=10000).

On the other hand, some investigations regarding thermal necessities of

computers have been carried out, since are more exigent with the increment of thermal

dissipation in CPUs. In this direction, employing nanofluids in heat pipes was a way to

solve the problem, obtaining as a result higher thermal performances, having the

potential as a substitute for conventional water in heat pipe. For the same volume, there

is a significant reduction in thermal resistance of heat pipe with gold nanofluid when

compared with water [17].

28

1.4.2. Other applications

One of the main applications of nanofluids relapses on industrial cooling, in view

of the fact that they are expected to enhance the heat transfer coefficient some orders

higher than conventional fluids with no penalty in pressure drop. This makes nanofluids a

powerful coolant for the next generation.

In this manner, there is an example regarding this issue: a project which through

the usage of nanofluids as coolants achieved reduction of emissions and significant energy

savings. Thereby, was calculated that from the replacement of cooling and heating water

with nanofluids has the potential to conserve 1 trillion Btu/year of energy in U.S.

industries. Furthermore, talking about electric power industry, using nanofluids in

closedloop cooling cycles could save about 10–30 trillion Btu per year, which is a

noteworthy amount of energy. On the other side, treating emissions this amount could

reach in the order of 5,6 million metric tons of carbon dioxide; 8600 metric tons of

nitrogen oxides; and 21000 metric tons of sulfur dioxide [19].

They also reported that in the case of Michelin North America tire plants [19], as

the productivity of numerous industrial processes is restricted because of cooling systems,

is intended to reach an enhancement of 10% on its process productivity by using water-

based nanofluids, if can be developed and commercially produced in economic way.

Another interesting field to study is building heating systems, above all

considering Sweden is a cold region which really needs effective heating systems. In this

way, some experiments have been done [18] in order to find out if it will be possible to

implant nanofluids. Given that in cold regions, it is ordinary the usage of ethylene or

propylene glycol mixed with water, they have used as a base fluid a mixture of ethylene

glycol and water. Obtained results showed that using nanofluids in heat exchangers could

reduce volumetric and mass flow rates, so this leads to a reduction in employed pumping

power. Finally, they concluded that smaller heating systems were required (rebounding

on the initial investment) and, consequently, the amount of environmental pollutants

were released.

To end with industrial applications, it should be mentioned some experiments

done in nuclear area, like one which was carried out at Massachusetts Institute of

Technology [20], [21], in order to evaluate the feasibility of nanofluids in nuclear applications

through the improvement of the performance of cooling nuclear system, which is heat

removal limited. The tests showed that employing nanofluids instead of water, the fuel

rods become covered with nanoparticles avoiding the formation of a layer of vapor

around the rod; therefore, mentioned layer improves the wettability of the surface. Given

that enhancement on wettability Moreover, dilute dispersions of nanoparticles in water

increases critical heat flux (CHF, thermal limit where a phase change occurs during

heating) in boiling experiments.

29

On the other hand, nanofluids are important in biomedical field, since are

becoming protagonist in different areas, above all during passing years. One of these

mentioned areas is nanodrug delivery [19]: while conventional way is based on the “high-

and-low” phenomenon, microdevices facilitate precise drug delivery through the

employment of nanodrug delivery systems, where controlled drug release takes place

over an extended period of time; in so doing, the desired drug concentration will be

sustained within the therapeutic window as required.

Going beyond delivery, another remarkable application is nanocryosurgery [22],

whose definition it could be a kind of surgery which uses freezing power to destroy

undesired tissues, and has important clinical advantages, hence is becoming an

alternative to traditional treatments.

In the same direction, there is another similar field than previous one, which is

cryopreservation. There is a study [23] that provides a new technique to carry out ultra-fast

cooling processes using quartz micro-capillary; this method overcomes conventional

procedures, since avoids cell injury through keeping away from dehydration or toxicity

conditions.

Although exist more areas in biomedical applications where nanofluids’ usage can

be very interesting, now it is turn to analyze other application areas. For example

transportation, where nanofluids have great potentials to improve automotive and heavy-

duty engine cooling rates [11], so it can be removed more heat from higher horsepower

engines with the same size of cooling system.

Moreover, at Argonne National Laboratory have been evaluated some functions

of nanofluids for transportation [24]. In this manner they report that nanofluids in radiators

can reduce the frontal area of the radiator up to 10%, while for fuel saving reaches 5%.

Additionally, they contribute to diminish friction and wear, reducing parasitic losses,

operation of components such as pumps and compressors, and subsequently leading to

more than 6% fuel savings. For all these reasons, with using nanofluids on engine cooling

systems, the engine radiator, for instance, cooled by a nanofluid will be smaller and

lighter. So, finally they conclude that through varying the position and reducing the size of

the radiator, a decrement in weight and wind resistance could enable greater fuel

efficiency and lower exhaust emissions.

To the moment some general areas have been treated in this section, but also

there are more fields where nanofluids can play a transcendental role in coming years [3],

[11], [19], such as detergents, more biomedical applications, space and defense, mass

transfer processes, energy storage, mechanical applications and so forth.

30

1.5. Literature survey

In current chapter are going to analyze several investigations carried out by

different research groups during a couple of last decade. Thereby, it will be possible to

evaluate nanofluids evolution over time, as well as the goodness of using nanoparticles so

as to enhance main thermophysical properties, such as thermal conductivity and viscosity,

and heat transfer coefficient as well.

Below these lines, there is a graph showing recent publications on this field in last

decade [25], where is clear to see that nanofluids are an issue which is becoming very

important in engineering world, since are rising high expectations due to large possibilities

they offer.

Figure 1. Number of publications studying nanofluids during last years.

In this way, some publications from 2003 until 2010 will be commented

subsequently.

According to a publication [26] (2003), nanofluids incorporate a temperature

dependence thermal conductivity. On the other hand, ther is another paper [65] which

studies the increments in critical heat flux in pool boiling and in the heat transfer

coefficient at low particle concentrations. However, not all authors agree with these

affirmations [44], [45], [46] , as will be explained during this chapter.

In other interesting reports a notable enhancement in heat transfer performance,

up to 60% [7] (2002), has been achieved using 2 vol% copper nanoparticles with water as a

based fluid, although this increment against the base fluid was observed for the same

Reynolds number, so the comparison is not fair at all. On the other hand, another

31

experiment carried out with copper nanoparticles in water [6] (2003) showed great

increments on Nusselt number, above all for the case of 2 vol% sample, which conferred a

39% enhancement versus its base fluid (Reynolds number varied between the range

10000-25000).

Wen and Ding [27] (2004), studied a nanofluid consisting of deionized water, SDBS

dispersant (sodium dodecylbenzene sulfonate) and aluminum oxide nanoparticles (0.6 -

1.6 vol%). Observed local heat transfer coefficient was within 41%- 47% enhancement

comparing to its base fluid while working with laminar flow (Re=500-1200).

Continuing with CuO nanoparticles evaluation, there is a publication which

compares their performance against Al2O3 ones, using always water as base liquid [28]

(2006); both nanofluids were tested in laminar condition (Reynolds from 650 to 2050).

The set up employed consisted of a 6 mm annular tube which worked in laminar

conditions. It was checked better behavior in Al2O3 than in CuO, talking about heat

transfer performance (both convective heat transfer coefficient and Peclet number).

Finally, it was concluded that heat transfer enhancement by nanofluid depended on

several factors such as increment of thermal conductivity, nanoparticles chaotic

movements, fluctuations and interactions.

Ding et al. [29] (2006), measured heat transfer with multi-walled carbon nanotubes

in aqueous solution at low concentrations (less than 1 vol% and 0,5 w%) using Arabic gum

as dispersant. An enormous enhancement in heat transfer of 350% in Re = 800 was found.

Williams et al. [33] (2008) tested water-based nanofluids with ZrO2 and Al2O3

nanofluids in turbulent conditions (Re=9000-63000). They observed that pressure loss and

heat transfer behavior could be described with traditional equations if the effective

nanofluid properties were used in calculating the dimensionless numbers, while working

within a temperature range of 21-76°C and particle concentrations of 0.9 – 3.6 vol%

(alumina) and 0.2 – 0.9 vol% (zirconia).

Kulkarni et al. [34] (2008) evaluated particle size and volume concentration effects.

They employed SiO2 nanoparticles of three different sizes: 20, 50 and 100 nm, dissolved in

a mixture of ethylene glycol and water (60:40). The test section was a 3,14 mm diameter

copper pipe working on turbulent conditions and heated by a DC power supply. The

conclusions of the tests were that as higher is the size particle, higher is the heat transfer

coefficient (at a fixed Reynolds number). In this direction, 16% maximum increase at 10%

concentration was obtained for 20 nm and Re=10000. Experiments were tested in

turbulent flow condition, since Reynolds changed from 3000 to 12000.

Kim et al. [35] (2008) studied the effect of nanofluids on convective heat transfer

bymeans of using alumina and amorphous carbonic in water in both turbulent and

laminar flow. Through employing a 4,57 mm stainless tube was observed for alumina 3

vol.% an enhancement of 15% and 20% for laminar and turbulent condition (Re from 800

up to 6600), while results for amorphous carbonic, at 3,5 vol.%, showed an increase of 8%

in laminar condition, though nothing significant in turbulent condition.

32

K.B. Anoop, T. Sundararajan and S.K. Das [30] (2009), treated an interesting effect

not mentioned yet in this section, which is particle size influence. Reynolds number varied

between 500 and 2000, so laminar flow was only tested. They employed alumina particles

nanoparticles in water. The nanofluids passed through a 4.75mm diameter copper pipe

flowing in laminar conditions. This circular tube was heated by a DC power supply. Results

showed higher increase of heat transfer for smaller particles, since for the smallest

particles they tried was observed a maximum increase of 25% for heat transfer an 6% for

thermal conductivity (Re=1550), while for the highest ones only reached 11% (Reynolds

1550).

Keeping going on Al2O3 nanoparticles in water, in this case higher than were

analyzed before (170 nm diameter) [31] (2009), tests carried out in laminar flow (Re varied

from 5 to 300) showed 32% improvement for heat transfer in a rectangular micro-tube

heated by a DC power supply for 1,8 vol% and a Reynolds value of 80.

Duangthongsuk and Wongwises [36] (2009) experimented with TiO2 nanofluid with

water as a base fluid and a volume concentration of 0,2% in a horizontal double-tube

counter flow heat exchanger working in turbulent conditions (Re=4000-18000). The

results showed 6-11% higher heat transfer coefficient with nanofluid than the obtained

value for water.

Another interesting experiment, in this case involving alumina nanoparticles of 30

nm in water [37] (2009) reached an increase of 8% in heat transfer (0,3 vol%, Re=700) using

a stainless steel tube of 1.812mm diameter, working with alternating current (AC).

X. Wu, H. Wu and P. Cheng [38] (2009) experimented with alumina 56 nm

nanoparticles dispersed in water (0,15 and 0,26 vol %) and performed in laminar flow (Re

varied from 190 up to 1020). In this trial, a trapezoidal micro-tube made of silicon was

used, heated by a constant DC power supply. The highest increment of the heat transfer

was 15.8% for 0,26 vol.%.

Returning to Al2O3 nanofluids using water as a base fluid, there is an experiment

performing in laminar condition through the usage of a rectangular microchannel [32]

(2010) heated by a DC power supply, observed data revealed a spectacular increase in

heat transfer coefficient, up to 70% (local value) and 30% (average value) at 1 vol.% and

Reynolds 1544. On the other hand, the thermal resistance dropped 25%.

H.A. Mohammed, et al. [39] (2011) studied nanofluids such as Ag, SiO2, Al2O3 and

TiO2 in water, in a laminar flow condition. The purpose of this analysis consists of

evaluating the effect of changing the Reynolds number from 100 to 800 and also the

volume fraction using 2%, 5% and 10%. One microchannel heat exchanger composed of

25 channels for hot fluid and others 25 for cold fluid was used. The analysis of the data

demonstrated that silver had the lowest pressure drop and that alumina the highest heat

transfer coefficient.

33

2. MEASUREMENT INSTRUMENTATION AND RESULTS

2.1. Thermal conductivity instrument

For the measurement of this thermo-physical property, in this project a TPS

2500S machine from Hot Disk AB has been employed. Operation of this instrument is

based on a Transient Plane Source (TPS) technique, which involves the use of a plane

sensor and a mathematical model describing the heat conductivity; these two things,

combined with electronics, enables the method to be used to measure thermal transport

properties. Mentioned sensor is made of a very thin double metal spiral, sandwiched

between two layers of Kapton, in close contact with the material to be investigated. The

thin Kapton provides electrical insulation and mechanical stability to the sensor.

Moreover, during the measurement a current passes through the metal and creates an

increase in temperature; the heat generated dissipates through the sample on either side

of the sensor at a rate depending on the thermal transport characteristics of the material.

By recording temperature vs. time response in the sensor, the characteristics of the

material can be calculated.

Figure 2. Thermal conductivity instrument.

Once the basis of the technique explained, now it is turn to describe how to use it.

First of all, is really important cleaning and drying the sample holder before each

measurement, in order to remove all settled particles belonging to previous samples.

After that, nanofluid should be ready (that is to say, homogeneous, with all particles well

dispersed through sonication process) to be injected inside the metallic box and put it into

the water bath at the desired temperature. Past a time for stabilization (20-30 minutes

more or less after we see no changes on the bath temperature), measurement can be

34

carried out through the Hot Disk software, which needs some specific parameters

depending on the set temperature. It should be said that there are two important

parameters, applied power and time, for obtaining valid results [56]. When the

measurement is finished, it is required to work with software so that obtain valid results

based on a good dispersion criteria.

Figure 3. Sample holder of termal conductivity instrument inside water bath.

2.2. Viscosity instrument

For the measurement of this thermo-physical property, in this project has been

employed a Rotating Coaxial Cylinders viscometer, concretely Brookfield DV-II+Pro

instrument. Like most modern viscometers, is computer-controlled and performs

automatic calculations based on the particular geometry used. This type of viscometer can

be used for Newtonian and non-Newtonian liquids, from low up to high viscosity values

(depending on the spindle, from 1 to 600 cP) though this instrument is more accurate for

low viscosity fluids (above all between 1 and 5 cP) by using UL adaptor. Moreover, this

geometry allows having the same shear rate everywhere, namely, throughout the sheared

liquid. By setting a range of rotation velocity (RPM) different shear rate values will be

tested, in order to find out rheological behaviour (Newtonian or non-Newtonian) of the

liquid and determine its viscosity average. Additionally to these parameters, torque value

has to been controlled as well.

35

Figure 4. Viscosity instrument.

Once the concept of the technique explained, now it is time to define how to use

it. As was recommended for thermal conductivity instrument, first thing to do is cleaning

and drying the sample holder before each measurement, for the same reason than

before. When dispersion is stable, should be taken off from its container between 16-17

mL; with the spindle inside the cylindrical container, nanofluid can be poured in sample

holder. After that, the cylinder has to be fixed on the viscometer carefully and water bath,

Rheocalc software and DV-II+Pro viscometer can be turned on (last one should be auto

zeroed before starting measurements). Fifteen minutes later, it will be time to test the

sample with the intention to find the upper and low limits talking about RPM and taking in

account torque values of each other. Found them, a program should be set depending of

the previous calculated limit values.

Figure 5. Sample holder of viscosity instrument.

36

2.3. Results

2.3.1. Weight concentration effect

As was said in previous chapters, thermal conductivity and viscosity are two

characteristic thermophysical properties of nanofluids, so, measuring them is an

important task in this thesis.

First of all, is good to know the components of nanofluids that are going to be

used. They have a common factor, which is all of them are water based fluid. Moreover

there are some differences between each other, for instance the type of particles have

been dispersed in distilled water, such as Al2O3, TiO2, CeO2 and SiO2. Another difference is

weight concentration of dilutions have been prepared, in order to study the influence of

its effect on thermal conductivity and viscosity values. Weight concentration is really

important also because there are some particles whose cost is elevated, so it will be

better if it is possible to achieve good results with low weight percentages.

On the other hand, primary particle size of nanoparticles changes among all

tested nanofluids (from 13 nm the smallest particle diameter until 70 nm), although it will

be shown later that primary particle size it doesn’t keep constant, as a consequence of

aggregation effect, so, these diameters will be increased. Furthermore, exists one more

difference, which consists of the production method of nanofluid dispersions, since in

preceding episodes has been explained there are two basic processes: one and two-step

methods (all nanofluids except the one which contains silica nanoparticles from Levasil

are prepared employing a two-step process).

Talking about the provenance of these nanofluids, high concentrated samples are

received at KTH from a partner of the project, which are Birmingham University (UBHAM)

and ITN Nanovation. In this way, several dilutions are prepared by addition of distilled

water to the original dispersion, with the purpose of obtain a range of samples, from 3

w% up to the concentration of the original sample (it could reach 50 w% for the most

concentrated sample).

Moreover, it is very important know if observed of both properties which are

measured in this chapter are reasonable, namely, it is recommendable to check results

obtained at KTH by comparing to other experimental data, as well as also to theoretical

expressions; thereby, it will be possible to analyze data in a properly way and discern the

value of the data.

For this reason, both theoretical and experimental (from UBHAM, and also from

other researchers) data have been included to validate and compare KTH tests. From a

theoretical point of view, two models are used to compare thermal conductivity data:

Maxwell equation for the prediction of relative thermal conductivity, because is the most

seen equation in publications dealing about thermal conductivity of nanofluids when

37

nanoparticles are spheres dispersed in a continuous medium [3]; but also Prasher model

for absolute thermal conductivity, which includes aggregation of nanoparticles effect, as

was recommended in some literature [3]. It generally predicts values for thermal

conductivity lower than Maxwell equation, although, as be seen later, Prasher is closer to

Maxwell when low concentrations are analyzed (from 3 up to 9 w% samples).

Where:

knf= thermal conductivity of nanofluid

kf= thermal conductivity of base fluid

kp= thermal conductivity of nanoparticles

Φ= volume concentration

Where:

knf= thermal conductivity of nanofluid

kf= thermal conductivity of base fluid

ka= thermal conductivity of nanoparticles

Φp= volumetric concentration of nanoparticles

ra= aggregated particles radius

rp=nanoparticles radius

df= fractal dimension, which is a measure of the space-filling capacity of a pattern that

tells how a fractal scales differently than the space it is embedded in; a fractal

dimension is greater than the dimension of the space containing it and does not have

to be an integer. According to literature [3], [52], [61], [62] its value varies between 1,5-2,5

for nanofluids.

38

Emphasizing the viscosity evaluation, more than two correlations have been

studied, according to the literature. Expressions such as Einstein [3] (spherical

nanoparticles), Nielsen [60], Maiga [3] (nanofluids using Al2O3 particles and distilled water as

a based fluid) and Krieger-Dougherty [51], [60], [61], [63] which, like Prasher in thermal

conductivity, includes nanoparticles aggregation influence, are going to be analyzed in this

project. Subsequently, equations regarding to viscosity modeling:

Where:

µnf= nanofluid viscosity

µf= base fluid viscosity


Where:




Φm= maximum particle packing fraction, which is 0,64 for this equation [60]

Where:




39

Where:



Φm= maximum particle packing fraction, which is 0,62 for spheres [51], [61], [63]

Φagg= volume fraction of aggregates

η= intrinsic viscosity, which is 2,5 for monodisperse suspensions of hard spheres [51],

[61], [63]

Where, for Krieger-Dougherty equation [8]:


Ra= aggregated particles radius

dv=nanoparticles diameter

Df= fractal dimension= 1,8 [48]

In this way, as have been found in literature survey [4], [7] that aggregation could

affect nanofluids properties, a DLS (Dynamic Light Scattering, also known as photon

correlation spectroscopy or quasi-elastic light scattering) technique has been applied by

University of Birmingham to samples, in order to know the real diameter of nanoparticles

and its difference against the size they were supposed to present. Graphs analyzing these

size distribution profiles will be plotted while the evaluation of each nanofluid.

Besides size distribution study, is recommended to apply an ultrasonic vibration

(sonification) process to the dilutions and aggregation effect will be decreased. The

method employed to carry out these experiments was a sonification bath (during 5-10

minutes depending on the stability of each sample, using always the same power), which

helps to break agglomerated particles, but not as well as tip sonification does, given that

using the first mentioned method ultrasonic waves travel through the water bath whereas

40

using tip sonification process ultrasonic waves come directly from the tip and immediately

contact the liquid. Anyway, after each sample has been sonificated inside the bath it was

tested in both thermal conductivity and viscosity measurement instruments.

As this section deals about on the effect of weight concentration on conductivity

and viscosity, both properties are represented such that thermo-physical property takes Y

axis and weight percentage X axis. In order to deepening on the evaluation, absolute and

relative values will be analyzed depending on the data, since there are values presented

with either absolute or relative magnitudes.

Once explained the bases of this chapter, it is turn to show obtained results (all

tests have been done at T=20 ºC), first of all through numerical tables and after that with

several kinds of graphs:

41

Table 2. Thermal conductivity and viscosity values versus concentrations. Results are obtained from KTH and UBHAM. Difference percentage has been calculated regarding to UBHAM values.

KTH UBHAM Difference (%)

Sample Weight concentration

(%) krelative µrelative krelative µrelative krelative µrelative

Al

2O

3 - E

vo

nik

40 1,327 23,671 1,257 19,494 5,567 21,427

30 1,222 5,387 1,173 5,096 4,176 5,717

20 1,150 2,572 1,108 2,425 3,860 6,083

15 1,098 1,917 1,072 1,752 2,379 9,423

9 1,058 1,438 1,044 1,408 1,420 2,167

6 1,037 1,282 1,031 1,194 0,549 7,394

3 1,017 1,164 1,020 1,110 -0,308 4,862

ITN

- A

l 2O

3 - 1

3

40 1,895 4,344 1,4898 2,8165 27,175 54,230

30 1,512 1,800 1,3258 1,5879 14,047 13,358

20 1,267 1,460 1,1798 1,2936 7,349 12,831

15 1,186 1,306 1,0948 1,1821 8,306 10,518

9 1,122 1,189 1,0591 1,1044 5,906 7,653

6 1,080 1,168 1,0319 1,0701 4,699 9,190

3 1,040 1,104 1,0252 1,0273 1,397 7,504

Ti O

2 - E

vo

nik

40 1,374 4,884 1,284 5,010 7,056 -2,517

30 1,245 2,574 1,193 2,510 4,339 2,568

20 1,150 1,739 1,116 1,619 3,106 7,386

15 1,106 1,484 1,093 1,422 1,242 4,306

9 1,057 1,276 1,060 1,191 -0,191 7,106

6 1,036 1,182 1,029 1,163 0,653 1,675

3 1,018 1,102 1,017 1,060 0,186 3,927

ITN

- T

iO 2

-10

20 1,087 5,579 1,153 2,936 -5,723 90,027

15 1,073 2,707 1,096 1,955 -2,069 38,472

9 1,035 1,967 1,057 1,415 -2,128 39,089

6 1,013 1,604 1,034 1,316 -1,997 21,911

3 1,008 1,224 1,025 1,160 -1,633 5,555

Si O

2 -

Evo

nik

45 1,235 7,332 1,165 7,537 6,019 -2,720

40 1,202 4,377 1,143 4,118 5,162 6,296

30 1,134 2,410 1,097 2,277 3,315 5,825

20 1,089 1,686 1,069 1,543 1,864 9,207

15 1,067 1,438

9 1,038 1,226 1,029 1,182 0,871 3,789

6 1,017 1,210 1,019 1,101 -0,186 9,880

3 1,012 1,098 1,013 1,056 -0,113 4,024

42

Table 3. Thermal conductivity and viscosity values versus concentrations. Difference percentage has not been calculated because weight concentration of samples belonging to KTH and UBHAM are not the same.

KTH UBHAM

Sample Weight concentration (%) krelative µrelative Weight concentration (%) krelative µrelative

Al

2O

3 - A

lfa_

Aes

ar 40 1,329

30 1,234 7,050

20 1,100 2,023

15 1,081 1,656 14,17 1,059 1,500

9 1,050 1,370 10,92 1,039 1,450

6 1,038 1,241 7,48 1,029 1,200

3 1,027 1,200 3,85 1,017 1,100

TiO

2 - A

lfa_A

esa

r

40

30

20 1,102 1,369

15 1,082 1,272

9 1,053 1,228 17,53 1,088 1,2

6 1,037 1,165 12,3 1,065 1,11

3 1,021 1,098 6,49 1,029 1,05

2.3.1.1. Al2O3 Evonik

First nanofluid to be shown is Al2O3 – Evonik, and subsequently a particle size

distribution is presented, since before was accorded to study this problem with the

purpose to know the real size of the particles:

Figure 6. Size particle distribution (Al2O3 – Evonik).

0

5

10

15

10 100 1000

Inte

nsi

ty (

%)

Size (nm)

Al2O3 - Evonik

43

The primary particle size of this nanoparticle was 13 nm, but through Figure 6 is

clearly not 13 nm, the size is really higher than it should be. For this reason, an average

has been made in order to calculate the aggregation ratio that will be used for Krieger-

Dougherty model regarding to relative viscosity. Therefore, this average reaches 190 nm,

namely, aggregation effect is present in this nanofluid, since the aggregates size is more

than ten times the primary particle diameter.

Figure 7. Relative thermal conductivity vs weight concentration (Al2O3 - Evonik). Are shown both KTH and UBHAM experimental data and Maxwell prediction, with an acceptance range of ± 5%.

It´s easy to see at Figure 7 that results for relative thermal conductivity at

different weight percentages are similar by comparing between KTH data and UBHAM

values. Furthermore, by checking Table 1, concretely column of difference (%), is clear

that KTH results are within ± 5% rank regarding to UBHAM data, except for highest value

of concentration, which is 5,567 %, although it´s still an acceptable value. By contrast,

experimental data are not well suited to Maxwell equation for the whole range of

concentrations: at low percentages, concretely from 3% up to 15%, KTH data are within

the acceptable rank (± 5% from Maxwell equation), but, as w (%) is increased, namely, for

20%, 30 % and 40 %, the relative thermal conductivity value is outside the mentioned

rank. So, in this case, water based nanofluid with aluminum oxide particles, Maxwell

prediction fits to both experimental data only for low weight percentages values (until

15%).

Deepening in thermal conductivity, as was mentioned before, there is a prediction

(Prasher) that considers aggregation effect, with the purpose of explaining non-expected

values for this thermo-physical property. So, below these lines KTH data is represented

versus Prasher expression:

0,9000

1,0000

1,1000

1,2000

1,3000

1,4000

1,5000

1,6000

1,7000

0 0,2 0,4 0,6 Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Weight Conc.

Al2O3 - Evonik

KTH

UBHAM

Maxwell Equation

Maxwell (+/-) 5%

44

Figure 8. Effective thermal conductivity vs weight concentration (Al2O3 - Evonik). Is shown KTH data and Prasher prediction, with an acceptance range of ± 10%.

At Figure 8 can be appreciated that used correlation is underestimating absolute

thermal conductivity and, although experimental values are within ± 10% Prasher, the

trend for KTH results is almost linear, by contrast, Prasher prediction shows non-linear

behavior for this property. So, it should be said that, despite Prasher includes aggregation

influence, this expression is not accurate enough, at least for this case.

Figure 9. KTH data against other research groups. Relative thermal conductivity is plotted versus volume percentage.

So as to guess the reason of the low values which this sample presents, at Figure 9

KTH data is compared to other research groups. The trend for KTH data is similar to other

groups’ results; however, the values are lower. As was mentioned in previous chapters, it

could be because of the different diameters of nanoparticles and also synthesis process

have been employed for each nanofluid, since it affects the nanostructure of materials

0,500

0,550

0,600

0,650

0,700

0,750

0,800

0,850

0 0,2 0,4 0,6 The

rmal

Co

nd

uct

ivit

y (W

/mK

)

Weight Conc.

Al2O3 - Evonik

KTH

Prasher (±10 %)

Prasher

1

1,05

1,1

1,15

1,2

1,25

1,3

0 5 10 15

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Volume (%)

Al2O3 - Evonik

Sarit Kumar

Das et al.

Al_EV_KTH

Xing Zhang and Hua Gu

45

and can have repercussions in thermal conductivity [3]. Furthermore, this comparison

coincides with Figure 7, since obtained results are lower than were expected to be

through the collating versus Maxwell prediction and other experimental data.

Once thermal conductivity has been analyzed, is time to see what happens with

viscosity of Al2O3 dilutions. Talking about experimental values, by looking at Figure 10 and

Table 2, existing differences between UBHAM and KTH are higher than thermal

conductivity percentages, but it can be explained given that UBHAM instrument for

measuring viscosity is more accurate than KTH uses. Furthermore, viscosity value for 40 %

sample is higher than it should be because viscosity instrument at KTH with UL adaptor is

pretty good for low viscosity fluids; but not for high viscosity values (different spindle is

needed with large sample volume).

Moreover, there is also a theoretical examination, by using Einstein, Nielsen,

Maiga and Krieger models, recommended from literature papers referred before.

Table 4. Values for theoretical comparisons (Al2O3 - Evonik).

Sample Relative Viscosity

Weight Conc.

Volume Conc.

Einstein Nielsen Maiga φ aggregation Krieger

0,4 0,169 1,423 2,032 5,751 0,536 22,107

0,3 0,116 1,289 1,633 3,491 0,367 4,003

0,2 0,071 1,177 1,355 2,136 0,225 2,009

0,15 0,051 1,128 1,246 1,695 0,162 1,599

0,09 0,029 1,073 1,135 1,320 0,093 1,286

0,06 0,019 1,048 1,086 1,184 0,061 1,173

0,03 0,009 1,023 1,041 1,079 0,030 1,079

Figure 10. Relative viscosity vs weight concentration (Al2O3 - Evonik). Einstein, Nielsen, Maiga, and Krieger-Dougherty models are used in order to compare against KTH and UBHAM experimental data.

0,000

5,000

10,000

15,000

20,000

25,000

0 0,1 0,2 0,3 0,4 0,5

Re

lati

ve v

isco

sity

Weight Conc.

Al2O3 - Evonik

KTH

UBHAM

Einstein Model Nielsen

Maiga (Al2O3) Krieger (Modified)

46

After checking Figure 10 and Table 4, it is clear that Einstein and Nielsen

predictions only fit with low weight percentage values. That occurs because Einstein is a

linear equation and Nielsen is shy exponential correlation, tested both for low

concentration values. Better than these predictions is Maiga expression, as can be

observed at the graph, since is coupled almost until 30 w% dispersion but is clearly

underestimating relative viscosity for 40 w% sample. On the other hand, it is easy to see

goodness of Krieger prediction, which is the best one. Then, can be observed that for low

volume concentrations, the value for aggregation concentration is very low, but, the more

concentration is increased, the more aggregates concentration is increased, as can be

watched through Table 4.

Figure 11. KTH data against other research groups. Absolute viscosity is represented versus volume percentage.

As was done before for relative thermal conductivity, a comparison between KTH

experiments and data from other researchers is shown by Figure 11. It is possible to check

that data belonging to KTH fit quite well to the rest of the data, above all Nguyen-

Desgranges 47 nm Al2O3 nanofluid. However, data at high concentration such as 40 w%

was not found, so is not possible to know the reason of that high value obtained at KTH

for this sample.

0

1

2

3

4

5

6

0 5 10 15

Vis

cosi

ty (

cP)

Volume (%)

Al2O3 - Evonik

NGUYEN-DESGRANGES_47nm

WANG et al.

Al_EV_KTH

TAWMAN-TURGUT

N-D_47nm_2

47

Figure 12. Absolute viscosity vs shear rate (Al2O3 - Evonik).

For finishing with this nanofluid, absolute viscosity is plotted against shear rate, in

order to guess the behavior of each sample. If viscosity keeps itself constant while shear

rate is increasing, this sample will have Newtonian behavior; but, if not, the sample will

present non-Newtonian behavior. So, it is clear to see all samples have Newtonian

behavior, excluding 40 w%.

2.3.1.2. ITN-Al2O3-13

Subsequently, is the turn of next alumina sample: ITN-Al2O3-13; being particle size

used for preparing the dilution the difference regarding to the previous one. Thereby,

after analyzing every characteristic of this sample, it will be possible to decide which one

of them is better for its usage as a coolant liquid. So, as was preceded before, the first

graph belonging to ITN-Al2O3-13 lies in the study of size particle distribution.

0

5

10

15

20

25

30

0 50 100 150 200

Vis

cosi

ty (

CP

)

Shear Rate (1/s)

Al2O3 - Evonik Al2O3-KTH-3WT%

Al2O3-KTH-6WT%

Al2O3-KTH-9 WT%

Al2O3-KTH-15 WT%

Al2O3-KTH-20 WT%

Al2O3-KTH-30 WT%

Al2O3-KTH-40 WT%

48

Figure 13. Size particle distribution (ITN - Al2O3 – 13).


clearly not 70 nm, the size is higher than it should be. An average has been made to

estimate the aggregation ratio that will be used for Krieger-Dougherty model regarding to

relative viscosity. Therefore, this average reaches 223 nm, that is, aggregation effect is

present in this nanofluid, given that the aggregates size is more than three times the

primary particle diameter, although the aggregation ratio is lower than observed for

Al2O3-Evonik nanofluid.

Figure 14. Relative thermal conductivity vs weight concentration (ITN - Al2O3 - 13).

Looking at Figure 14 and Table 2, unlike the previous case, experimental data

from KTH are not close to UBHAM´s, and, as w% is increased, this difference becomes

higher. Only for samples from 3 w% until 9% similar results have been obtained, and for

15-40 w% dilutions, thermal conductivity change over a rank of 8,3-27,1 difference %

regarding to UBHAM data.

0

5

10

15

20

25

10 100 1000

Inte

nsi

ty (

%)

Size (nm)

ITN - Al2O3 - 13

0,90

1,10

1,30

1,50

1,70

1,90

2,10

0 0,2 0,4 0,6 Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Weight Conc.

ITN - Al2O3 - 13

KTH

UBHAM

Maxwell Equation

Maxwell (+/-) 5%

49

Analyzing the results from a theoretical viewpoint, UBHAM data show almost the

same values than Maxwell prediction, unlike KTH experiments, which are within Maxwell

acceptance rank for low concentrations, but from 20 w% are outside the mentioned rank.

Deepening in the preparation of the dilutions, it could be possible to find the

reason of these results, which are more elevated than were expected to be. Every

concentrated sample received from UBHAM should be sonificated during some minutes

(time that can change depending on kind of nanoparticles have been used), but, this

original sample used to prepare more diluted nanofluids had not been sonificated in a

properly way at the first time, so, the dilutions that were prepared showed very strange

values, namely, without a clear trend; sometimes thermal conductivity grown up as

weight concentration was increased, and sometimes thermal conductivity decreased.

It means that, as well as the concentrated nanofluid was bad sonificated, its

concentration could be non-homogeneous, and that´s why those abnormal results.

Consequently, with the intention of correcting this mistake, new dilutions were prepared.

This second time, the concentrated sample have been sonificated correctly, but, because

of extracting some liquid with irregular composition when first dilutions were made, the

concentration of this main sample could have been increased. Therefore, this is the

reason that leads to these high values obtained at KTH laboratory, since weight

concentration is higher than it should be.

Going farther in thermal conductivity now is time to analyze how works Prasher

equation for this nanofluid, with the aim of have an idea about the aggregation effect of

nanoparticles. Subsequently, this model is evaluated:

Figure 15. Effective thermal conductivity vs weight concentration (ITN - Al2O3 - 13). Is shown KTH data and Prasher prediction, with an acceptance range of ± 10%.

At Figure 15 can be seen that correlation is underestimating, again, absolute

thermal conductivity and, furthermore, only low concentration samples are within ± 10%

Prasher. By contrast, the observed trend for KTH results follows more or less the same

type of trend than Prasher one, contrary to what has happened in the previous case

0,500

0,600

0,700

0,800

0,900

1,000

1,100

1,200

0 0,2 0,4 0,6

The

rmal

Co

nd

uct

ivit

y (W

/mK

)

Weight Conc.

ITN - Al2O3 - 13

KTH

Prasher (±10 %)

Prasher

50

(Al2O3-Evonik), when trend was different regarding to Prasher prediction. However, this

prediction one more time is not accurate enough.


In the same direction than before sample, at Figure 16 is shown KTH data for

aluminum oxide nanofluid against other tested results. But, if for Evonik nanofluid was

found data for a large range of concentrations in this case only have been found data up

to 6% volume concentration, value which corresponds to that of 20 % weight

concentration. Contrary to what was seen regarding to Maxwell and Prasher predictions,

here is possible to watch that KTH results are quite similar to other values presented. It

could imply that this nanofluid has very good conditions talking about thermal

conductivity, since all results overcome what was expected for them.

After thermal conductivity study, next step consists on evaluation of relative

viscosity against weight percentage. By observing Figure 17, results belonging to KTH

could seem quite similar to UBHAM ones, but, checking Table 2 is possible to see that the

difference % is only acceptable from 3 until 9 w%, because the other samples present

percentages above 10 % difference; despite of instrument accuracy are values too far

from UBHAM data. In addition, relative viscosity for 40 w% sample is near to 55 % higher

than UBHAM result.

As was done before, to achieve a great examination of relative viscosity results,

the same theoretical predictions are used for this nanofluid:

1

1,05

1,1

1,15

1,2

1,25

1,3

1,35

0 2 4 6 8

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Volume (%)

ITN - Al2O3 - 13 Wen-Ding_27-56nm

Koo-Kleinstreuer [68]

Yu-Choi [69]

Al_13_KTH

Stephen U. S. Choi

Eastman-Choi

. Xie, J. Wang, T. Xi, Y. Liu, F. Ai, Q. Wu

51

Table 5. Values for theoretical comparisons for (ITN - Al2O3 - 13).


Weight Conc.

Volume Conc.


0,4 0,144 1,359 1,832 4,583 0,289 2,647

0,3 0,097 1,243 1,513 2,874 0,196 1,802

0,2 0,059 1,148 1,289 1,862 0,119 1,392

0,15 0,042 1,106 1,201 1,532 0,086 1,259

0,09 0,024 1,061 1,111 1,250 0,049 1,136

0,06 0,016 1,039 1,071 1,146 0,032 1,085

0,03 0,008 1,019 1,034 1,064 0,016 1,040

Figure 17. Relative viscosity vs weight concentration (ITN - Al2O3 - 13). Einstein, Nielsen, Maiga, and Krieger-Dougherty models are used in order to compare against KTH and UBHAM experimental data.

After checking Figure 17 and Table 5, it is clear that Einstein and Nielsen

predictions only fit with low weight percentage values, though Nielsen correlation couples

quite well to UBHAM data until 30 w% sample. By contrast, Maiga equation shows a

strange trend, given that only presents alike values for very low and very high

concentrations. Better than these predictions is Krieger-Dougherty expression, like

occurred with Al2O3-Evonik nanofluid. This time Krieger encases for most samples, with

the exception of highest concentration dispersion. Despite of this question, Krieger is

once more the best equation to predict values for relative viscosity.

-0,500

0,500

1,500

2,500

3,500

4,500

0 0,1 0,2 0,3 0,4 0,5

Re

lati

ve v

isco

sity

Weight Conc.

ITN - Al2O3 - 13 KTH

UBHAM


52


As was done before for relative thermal conductivity, a comparison between KTH

experiments and data from other researchers is shown by Figure 18. It is possible to check

that data belonging to KTH fit quite well to the rest of the data, above all Nguyen-

Desgranges 36 nm Al2O3 nanofluid. By contrast, it is easy to see that Hamilton-Crosser

model is underestimating viscosity.

Figure 19. Absolute viscosity vs shear rate (ITN - Al2O3 - 13).

Last study for this nanofluid consists on determinate Newtonian or non-

Newtonian behavour for each dilution. Proceeding like the previous case, it´s easy to

describe the behaviors of these samples. Therefore, all samples present Newtonian

behavior, excluding 40 w%, that shows changes in its viscosity value, from near to 6 down

to 4 cP.

0

1

2

3

4

5

0 10 20

Vis

cosi

ty (

cP)

Volume (%)

ITN - Al2O3 - 13

WANG et al.

Al_13_KTH

Nguyen-Desgranges_36nm

Hamilton-Crosser

0

1

2

3

4

5

6

0 50 100 150 200

Vis

cosi

ty (

CP

)

Shear Rate (1/s)

ITN - Al2O3 - 13 ITN-Al-13_KTH-3WT%

ITN-Al-13_KTH-6WT%

ITN-Al-13_KTH-9WT%

ITN-Al-13_KTH-15WT%

ITN-Al-13_KTH-20WT%

ITN-Al-13_KTH-30WT%

ITN-Al-13_KTH-40WT%

53

2.3.1.3. TiO2 Evonik

Until the moment, alumina nanofluids has been studied, but now is turn to

evaluate results belonging to TiO2 nanoparticles dispersed in distilled water, concretely,

TiO2-Evonik. Thereby, as preceding cases, first of all, size particle distribution is going to be

examined:

Figure 20. Size particle distribution (ITN - Al2O3 – 13).


obviously not 21 nm. For this reason, an average has been made for analyzing the

aggregation ratio that will be used for Krieger-Dougherty model regarding to relative

viscosity. Thereby, this average reaches 127 nm, that is to say, aggregation effect is

present in this nanofluid, given that the aggregates size is around six times the primary

particle diameter.

Figure 21. Relative thermal conductivity vs weight concentration (TiO2 - Evonik).

0

2

4

6

8

10

12

14

10 100 1000

Inte

nsi

ty (

%)

Size (nm)

TiO2 - Evonik

0,9000

1,0000

1,1000

1,2000

1,3000

1,4000

1,5000

1,6000

0 0,2 0,4 0,6

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Weight Conc.

TiO2 - Evonik

KTH

UBHAM

Maxwell Equation

Maxwell (+/-) 5%

54



values. Furthermore, by checking Table 2, concretely column of difference (%), KTH results

are within ± 5% range regarding to UBHAM data, except for highest value of

concentration, which is 7,056 %, though it´s still an acceptable value because that point

follows the tendency of previous ones, representing all together a good trend and,

moreover, this point is within Maxwell rank. Additionally, these values fit very well to

Maxwell equation, but, as was seen before, experimental relative thermal conductivity

data for low percentages are closer to the theoretical prediction than high percentages,

like 30 and 40 %. However, all data is within the ± 5% acceptance rank, so, obtained

results for this TiO2 nanofluid are pretty good talking about reliability against Maxwell

equation.

Deepening in thermal conductivity now is time to analyze the goodness of Prasher

equation for this nanofluid, like above cases:

Figure 22. Effective thermal conductivity vs weight concentration (TiO2 - Evonik). Is shown KTH data and Prasher prediction, with an acceptance range of ± 10%.

At Figure 22 can be appreciated that prediction is underestimating absolute

thermal conductivity and, although experimental values are within ± 10% Prasher, the

trend for KTH results is almost linear, as well as was seen for the first sample, namely,

Al2O3-Evonik. In the same direction, Prasher expression shows non-linear behavior for this

property. So, it should be said that, despite Prasher includes aggregation influence, this

expression again is not accurate sufficient.

0,500

0,550

0,600

0,650

0,700

0,750

0,800

0,850

0 0,2 0,4 0,6

The

rmal

Co

nd

uct

ivit

y (W

/mK

)

Weight Conc.

TiO2 - Evonik

KTH

Prasher (±10 %)

Prasher

55


Comparing different experimental data, it could be stated that results belonging

to KTH are really similar against other research groups. Even though values are a bit lower

than added data, all trends are analogous to each other. Moreover, wasp correlation fits

very well to KTH values.

Once thermal conductivity has been analyzed, is turn to study the relative

viscosity of titania dilutions. Treating experimental values, by watching Figure 24 and

Table 2, UBHAM and KTH values are really similar like mentioned chart shows, but

checking the table there are some points above 5 % difference, but are acceptable

because they are below 10 % difference. On the other hand, it should be commented the

case of 30 and 40 w%, because for the first one the increment in thermal conductivity it’s

higher than the increment in viscosity, but the case of 40 w% is rather better, since a 7 %

increment is observed for thermal conductivity and the viscosity value is lower than

UBHAM one.

At Figure 24 are also included theoretical predictions (in this case Maiga is not

used because is only valid for aluminum oxide nanofluids):

0,98

1,03

1,08

1,13

1,18

1,23

1,28

1,33

1,38

1,43

0 2 4 6 8 10 12

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Volume (%)

TiO2 - Evonik

Wang

Masuda

Ti_EV_KTH

Yu-Choi

Wasp [67]

Bruggeman

56

Table 6. Values for theoretical comparisons for (TiO2 - Evonik).


Weight Conc. Volume Conc. Einstein Nielsen φ aggregation Krieger

0,4 0,149 1,373 1,873 0,402 5,070

0,3 0,101 1,253 1,538 0,273 2,462

0,2 0,062 1,154 1,303 0,166 1,623

0,15 0,044 1,111 1,210 0,120 1,394

0,09 0,025 1,063 1,116 0,068 1,199

0,06 0,016 1,041 1,074 0,045 1,122

0,03 0,008 1,020 1,036 0,022 1,057

Figure 24. Relative viscosity vs weight concentration (TiO2 - Evonik).

After checking Figure 24 and Table 6, it is clear that Einstein prediction only fits

with low weight percentage values, as well as occurred with the previous nanofluids. So

this correlation is not valid to compare against KTH experiments. It occurs more or less

the same for Nielsen correlation that, unlike the latter case, only is valid for very low

concentrations. But Krieger model is really better than those models mentioned, since

couples almost perfect with both KTH and UBHAM data.

0,000

1,000

2,000

3,000

4,000

5,000

6,000

0 0,1 0,2 0,3 0,4 0,5

Re

lati

ve v

isco

sity

Weight Conc.

TiO2 - Evonik

KTH

UBHAM


Krieger (Modified)

57


As was being done before during this chapter, Figure 25 compares KTH results to

some experimental data. It is possible to check that data belonging to KTH it is reasonably

similar to the rest. A good point is that for some samples viscosity is even lower.

Figure 26. Absolute viscosity vs shear rate (TiO2 - Evonik).

Last chart for this nanofluid is viscosity against shear rate. As the way to know if a

fluid is Newtonian or not has been explained previously, it is easy to see all samples have

Newtonian behavior, thing that is very good thinking about its usage for electronic cooling

systems.

0

0,5

1

1,5

2

2,5

3

3,5

0 2 4 6 8 10 12

Vis

cosi

ty (

cP)

Volume (%)

TiO2 - Evonik

Ti_EV_KTH

Masuda

Wang

0

1

2

3

4

5

6

0 50 100 150

Vis

cosi

ty (

CP

)

Shear Rate (1/s)

TiO2 - Evonik TiO2-KTH-3WT%

TiO2-KTH-6WT%

TiO2-KTH-9WT%

TiO2-KTH-15WT%

TiO2-KTH-20WT%

TiO2-KTH-30WT%

TiO2-KTH-40WT%

58

2.3.1.4. ITN-TiO2-10

The second titania nanofluid tested at KTH is ITN-TiO2-10, and just as with alumina

samples, the differences between nanofluids is the particle size dispersed in the base

fluid. Below these lines its size particle distribution chart is shown:

Figure 27. Size particle distribution (ITN – TiO2 - 10).

The primary particle size of this nanoparticle was between 20 and 30 nm, but

through Figure 27, for sure is not 20-30 nm, the size is quite higher than it should be.

Then, by calculating a particle size average was found a real diameter of 173 nm, that is,

aggregation effect is present in this nanofluid, since the aggregates size is between six and

seven times the primary particle diameter.

Figure 28. Relative thermal conductivity vs weight concentration (ITN - TiO2 - 10).

0

5

10

15

10 100 1000

Inte

nsi

ty (

%)

Size (nm)

ITN - TiO2 - 10

0,9000

0,9500

1,0000

1,0500

1,1000

1,1500

1,2000

1,2500

0 0,1 0,2 0,3

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Weight Conc.

ITN - TiO2 - 10

KTH

UBHAM

Maxwell Equation

Maxwell (+/-) 5%

59

Checking Figure 28 and Table 2, is possible to see that, unlike what has occurred

to the previous samples, obtained values at KTH are lower than UBHAM ones, and also

there are differences both universities for all values, above all for the most concentrated

dilution. For this reason, these results were commented with the partner in this project to

find which could be the motive. After doing that, it was conclude the problem deals on

the different way to sonificate the samples between both research groups, as UBHAM

used a tip sonificator and KTH used a sonification bath, which is worse. Moreover, the

batch of nanofluid for this specific type was not the same in UBHAM and KTH. This is the

reason that explains KTH values are lower than UBHAM’s.

Analyzing the results from a theoretical point of view, UBHAM data show almost

the same values than Maxwell prediction, unlike KTH experiments, which are within

Maxwell acceptance range for low concentrations, but from 20 w% are outside the

mentioned rank.

Delving into absolute thermal conductivity, below these lines KTH data are

represented versus Prasher expression:

Figure 29. Effective thermal conductivity vs weight concentration (ITN - TiO2 - 10). Is shown KTH data and Prasher prediction, with an acceptance range of ± 10%.

At Figure 29 can be observed that this is the first time used correlation fits well

obtained results from KTH. This issue could be used to confirm the goodness of tip

sonification comparing to bath sonification, since for all previous samples Prasher was

underestimating and now couples nice to data.

0,500

0,550

0,600

0,650

0,700

0,750

0 0,1 0,2 0,3

The

rmal

Co

nd

uct

ivit

y (W

/mK

)

Weight Conc.

ITN - TiO2 - 10

KTH

Prasher (±10 %)

Prasher

60


As is being done for every studied nanofluid, at Figure 30 are plotted KTH data

compared to other research groups. Clearly, values for thermal conductivity are lower

than other experimental data. As was mentioned previously, it could be because of the

sonication process employed by KTH, which is less effective than UBHAM used, for

example.

In order to evaluate relative viscosity, the same theoretical predictions than

before are used:

Table 7. Values for theoretical comparisons for (ITN – TiO2 - 10).



0,2 0,057 1,142 1,276 0,416 5,610

0,15 0,041 1,102 1,192 0,299 2,771

0,09 0,023 1,058 1,106 0,170 1,646

0,06 0,015 1,038 1,068 0,111 1,357

0,03 0,007 1,018 1,033 0,054 1,152

1

1,02

1,04

1,06

1,08

1,1

1,12

0 2 4 6 Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Volume (%)

ITN - TiO2 - 10

Tavman-Turgut

Zhang

Ti_10_KTH

61

Figure 31. Relative viscosity vs weight concentration (ITN - TiO2 - 10).

After checking Figure 31 and Table 7, it is obvious that Einstein prediction only fits

with low weight percentage values, as well as occurred with prior nanofluids, and exactly

the same could be said regarding Nielsen model. But Krieger model is really better than

Einstein and Nielsen, although this is the first time Krieger doesn’t predict really close to

data, since can be appreciated that for 6 and 9 w% samples is underestimating viscosity

value. Anyway, it is still a good equation to guess the rheological behavior of this

nanofluid.


Figure 32 compares KTH results to some experimental data. It is possible to check

that data belonging to KTH it is reasonably similar to the rest. It should be pointed

Murshed experiments presents strange behavior for the highest dilutions, since is

expected for viscosity to increase as concentration of nanoparticles is increased also.

0,000

1,000

2,000

3,000

4,000

5,000

6,000

0 0,05 0,1 0,15 0,2 0,25

Re

lati

ve v

isco

sity

Weight Conc.

ITN - TiO2 - 10

KTH

UBHAM

Einstein Model

Nielsen

0

0,5

1

1,5

2

2,5

3

3,5

0 2 4 6

Vis

cosi

ty (

cP)

Volume (%)

ITN - TiO2 - 10

Tawman-Turgut

Ti_10_KTH

Murshed

62

Figure 33. Absolute viscosity vs shear rate (ITN - TiO2 - 10).

In Figure 33 is shown the rheological behavior for each dilution of TiO2 nanofluid.

Just it should be said, as most studied cases, every sample presents Newtonian behavior,

except the highest concentration, which has non-Newtonian behavior.

2.3.1.5. SiO2 Levasil

As was done for previous cases, first of all, results treating size particle

distribution are evaluated:

Figure 34. Size particle distribution (SiO2 - LEV).

The primary particle size of this nanoparticle was 30 nm, but watching at Figure

34, it is obviously its size is more elevated than it might be. Hence, an average has been

made to calculate the aggregation ratio that will be used for Krieger-Dougherty model

regarding to relative viscosity. This average reaches 122 nm, namely, aggregation effect is

0

1

2

3

4

5

6

7

8

0 50 100 150 200

Vis

cosi

ty (

CP

)

Shear Rate (1/s)

ITN - TiO2 - 10 ITN-Ti-10_KTH-3WT%

ITN-Ti-10_KTH-6WT%

ITN-Ti-10_KTH-9WT%

ITN-Ti-10_KTH-15WT%

ITN-Ti-10_KTH-20WT%

0

5

10

15

20

10 100 1000

Inte

nsi

ty (

%)

Size (nm)

SiO2 - LEV

63

present in this nanofluid, because the aggregates size is more than four times the primary

particle diameter.

Figure 35. Relative thermal conductivity vs weight concentration (SiO2 - LEV).



values just for low concentrate dilutions, from 3 up to 20 %. However, by watching Table

2, these differences between both universities are not so high, because only 5 %

difference is exceeded for 40 w% sample, and not too much, since its value is 6 %. On the

other hand, following the theoretical Maxwell lines at the chart, UBHAM values are within

acceptance rank from 3 w% until 20 w% dilution, 30 w% value is on the lower edge,

whereas 40 and 45 w% are outside the rank. But in KTH case, although the trend is similar

to UBHAM one, relative thermal conductivity values are almost on the Maxwell prediction

line, from 3 w% up to 20w%, while 30, 40 and 45 % are little by little getting farer from the

theoretical equation. Despite this, all KTH results follow quite good Maxwell prediction, as

well as happened with TiO2-Evonik nanofluid.

Going farther on thermal conductivity, subsequently KTH data is represented

versus Prasher equation:

0,9000

1,0000

1,1000

1,2000

1,3000

1,4000

0 0,2 0,4 0,6

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Weight Conc.

SiO2 - LEV

KTH

UBHAM

Maxwell Equation

64

Figure 36. Effective thermal conductivity vs weight concentration (SiO2 - LEV). Is shown KTH data and Prasher prediction, with an acceptance range of ± 10%.

By watching the graph above these lines, a similar behavior than the first analyzed

samples can be observed between KTH and Prasher, given that experiments are within

the ±10% acceptance range, but showing different trend regarding to the theoretical

prediction.


Like previous cases, at Figure 37 is represented KTH data compared to other

research groups. Notice that values for thermal conductivity are very similar to other

experimental data.

Talking about the viscosity of the nanofluid, experimental values obtained at KTH

and UBHAM can be observed at Figure 38. Unlike thermal conductivity, the results are

very similar between both universities, or, at least, is what the chart shows. But, in fact,

by checking Table 8 is clear that actually they aren’t close at all, because their difference

0,500

0,550

0,600

0,650

0,700

0,750

0,800

0 0,2 0,4 0,6 Th

erm

al C

on

du

ctiv

ity

(W/m

K)

Weight Conc.

SiO2 - LEV

KTH

Prasher (±10 %)

Prasher

1

1,05

1,1

1,15

1,2

1,25

0 10 20 30

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Volume (%)

SiO2 - LEV

Kakac-Yazicioglu

Kang

KTH

Devenus

Eapen et al.

M-G Model

65

% changes from negative values up to near to 10 %, being always below this limit. That’s

why is better to discuss about both things, graphs and tables, in order to be more

confident with conclusions. Otherwise, it should be noted something that has occurred

before with TiO2-Evonik, consisting on obtaining higher values for thermal conductivity

against UBHAM ones and lower for viscosity, such as 45 w% case, which shows an

increment of 6,012 for relative thermal conductivity and a decrement of -2,720 for

relative viscosity.

Figure 38 and Table 8 include the same theoretical models than before:

Table 8. Values for theoretical comparisons for (SiO2 - Evonik).



0,45 0,271 1,677 3,048 0,446 7,146

0,4 0,232 1,581 2,618 0,382 4,420

0,3 0,163 1,407 1,981 0,268 2,405

0,2 0,102 1,255 1,542 0,168 1,630

0,15 0,074 1,185 1,373 0,122 1,405

0,09 0,043 1,107 1,203 0,071 1,206

0,06 0,028 1,070 1,129 0,046 1,128

0,03 0,014 1,035 1,062 0,023 1,060

Figure 38. Relative viscosity vs weight concentration (SiO2 - Levasil).

Once Figure 38 have been checked, it is obvious that Einstein prediction only fits

with low weight percentage values, as well as occurred with the previous nanofluids. By

contrast, Nielsen model couples quite well to data up to 30 w%, as happened with ITN-

Al2O3-13 nanofluid. But Krieger model is rather better than Einstein and Nielsen, since

predict all values in a very good way as could be seen at the mentioned graph.

0,000

2,000

4,000

6,000

8,000

0 0,2 0,4 0,6

Re

lati

ve v

isco

sity

Weight Conc.

SiO2 - LEV

KTH

UBHAM

Einstein Model

Nielsen

66


Figure 39 is used to make comparisons between KTH results and some

experimental data. It is possible to check that data belonging to KTH it is reasonably

similar to the rest, so it is a good new.

Figure 40. Absolute viscosity vs shear rate (SiO2 - Levasil).

In Figure 40 absolute viscosity is plotted versus shear rate at different weight

percentages of nanofluid. In this case it’s easy to conclude that all dilutions have

Newtonian behavior, so, it means this sample is good to be used in electronic cooling

performance, but considering high concentration samples present elevate values for

absolute viscosity, it should be analyzed more deeply.

0

2

4

6

8

10

0 10 20 30 40 V

isco

sity

(cP

)

Volume (%)

SiO2 - LEV

Si_EV_KTH

W. Escher; T. Brunschwile; N. Shalkevic

Zihao Zhang

0

1

2

3

4

5

6

7

8

0 50 100 150 200

Vis

cosi

ty (

CP

)

Shear Rate (1/s)

SiO2 - LEV Si-EV-KTH-3WT%

Si-EV-KTH-6WT%

Si-EV-KTH-9WT%

Si-EV-KTH-15WT%

Si-EV-KTH-20WT%

Si-EV-KTH-30WT%

Si-EV-KTH-40WT%

Si-EV-KTH-45WT%

67

2.3.1.6. Al2O3 Alfa Aesar

First Alfa Aesar nanofluid to be analyzed uses Al2O3 nanoparticles, and its particle

size distribution is evaluated on Figure 41:

Figure 41. Size particle distribution (Al2O3 – Alfa Aesar).

Primary particle size of this nanoparticle was 40 nm, but checking at Figure 41, it is

clear to observe that is higher than was expected to be. So, an average is done to guess

aggregation ratio that will be used for Krieger-Dougherty model. This average goes up to

166 nm, what means aggregation effect is present in this nanofluid, because the

aggregates size is more than four times the initial particle diameter.

Figure 42. Relative thermal conductivity vs weight concentration (Al2O3 – Alfa Aesar).

0

5

10

15

20

10 100 1000

Inte

nsi

ty (

%)

Size (nm)

Al2O3 - Alfa Aesar

0,90

1,10

1,30

1,50

1,70

1,90

0 0,2 0,4 0,6

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Weight Conc.

Al2O3 - Alfa Aesar

KTH

UBHAM

Maxwell Equation

Maxwell (+/-) 5%

68

It´s simple to see at Figure 42 that results for relative thermal conductivity at


values, but the problem is that UBHAM has only prepared low percentages samples, so,

comparisons for the higher ones cannot been made. Furthermore, unlike the above cases,

difference (%) has not been evaluated because the weight percentages from KTH and

UBHAM are not the same. On the other hand, by watching Figure 42, similar trends are

observed for both cases, and also values seem to be closer against each other. By

contrast, points for high weight concentration are outside the acceptance rank for

Maxwell prediction, though only for the most concentrated samples, 40 and 50 w%.

Continuing thermal conductivity analysis, below these lines KTH data is

represented versus Prasher equation:

Figure 43. Effective thermal conductivity vs weight concentration (Al2O3 – Alfa Aesar). Is shown KTH data and Prasher prediction, with an acceptance range of ± 10%.

By watching the chart, this is the second time in this project that Prasher equation

predicts quite well thermal conductivity values, as well as happened with ITN-TiO2-10. In

this way, results couples to used expression, above all for low weight concentration

samples; moreover, despite high concentrated nanofluids are not on the line that Prasher

predicts, are not much far from it and also are within the acceptance range.

After thermal conductivity study, next step consists on evaluation of relative

viscosity against weight percentage. By observing Graph 44, results belonging to KTH

seem quite similar to UBHAM ones, but, as occurred for thermal conductivity, the weight

percentages prepared by each university are different so only is possible to compare the

trends observed from graph and not to compare numerical values, as was done with other

cases. In this way, it’s clear that both trends are almost the same, what mean results from

KTH are acceptable regarding to UBHAM ones.

Subsequently, to achieve a great examination of relative viscosity results, the

same theoretical predictions are used for this nanofluid, including also Maiga, given that

this is an alumina nanofluid:

0,500 0,550 0,600 0,650 0,700 0,750 0,800 0,850 0,900

0 0,2 0,4 0,6

The

rmal

Co

nd

uct

ivit

y (W

/mK

)

Weight Conc.

Al2O3 - Alfa Aesar

KTH

Prasher (±10 %)

Prasher

69

Table 9. Values for theoretical comparisons for (Al2O3 – Alfa Aesar).


Weight Conc.

Volume Conc.


0,4 0,144 1,359 1,832 4,583 0,445 7,101

0,2 0,059 1,148 1,289 1,862 0,183 1,722

0,15 0,042 1,106 1,201 1,532 0,132 1,448

0,09 0,024 1,061 1,111 1,250 0,075 1,222

0,06 0,016 1,039 1,071 1,146 0,049 1,136

0,03 0,008 1,019 1,034 1,064 0,024 1,063

Figure 44. Relative viscosity vs weight concentration (Al2O3 – Alfa Aesar).

After checking Figure 44 and Table 9, it is easy to check that Einstein and Nielsen

predictions only encase with low weight percentage values. By contrast, Maiga equation

shows an acceptable trend, although not for the most concentrated sample. Finally, like

almost every case, better than these predictions is Krieger-Dougherty expression. This

time Krieger fits for all samples, so, as we are advancing on nanofluids analysis is being

observed is a good correlation in order to predict values for relative viscosity values of

nanofluids. On the other hand, it should be mentioned the problem occurred while

measuring 50 w% dilution, since it showed very high value for viscosity and unstable

behavior on viscosity measurement instrument, hence, was not possible to achieve an

exact value for it, reason why is not plotted at Figure 44.

0,000

2,000

4,000

6,000

8,000

0 0,1 0,2 0,3 0,4 0,5

Re

lati

ve v

isco

sity

Weight Conc.

Al2O3 - Alfa Aesar

KTH

UBHAM


70

Figure 45. Absolute viscosity vs shear rate (Al2O3 – Alfa Aesar).

At Figure 45 absolute viscosity against shear rate at different weight percentages

of nanofluid is shown. In this case it’s easy to conclude that all dilutions have Newtonian

behavior, so, it means this sample is good to be used in electronic cooling systems.

2.3.1.7. CeO2 Alfa Aesar

Once the evaluation of alumina nanofluid belonging to Alfa Aesar has been done,

it is ceria nanofluid turn. In this direction, particle size distribution is the first graph to be

examined:

Figure 46. Size particle distribution (CeO2 – Alfa Aesar).

0

1

2

3

4

5

6

7

8

0 50 100 150 200

Vis

cosi

ty (

CP

)

Shear Rate (1/s)

Al2O3 - Alfa Aesar

Alfa_Aesar_Al2O3_40% Alfa_Aesar_Al2O3_20% Alfa_Aesar_Al2O3_15% Alfa_Aesar_Al2O3_9% Alfa_Aesar_Al2O3_6%

0

2

4

6

8

10

12

14

16

10 100 1000

Inte

nsi

ty (

%)

Size (nm)

CeO2 - Alfa Aesar

71

The primary particle size of this nanoparticle was 30 nm, but checking at Figure

46, it is evident that is more elevated than it might be. For this reason, an average has

been made in order to calculate the aggregation ratio that will be used for Krieger-

Dougherty model. Therefore, this average reaches 180 nm, that is, aggregation effect is

present in this nanofluid, since the aggregates size is more than six times the primary

particle diameter.

Its relative thermal conductivity value against weight concentration is plotted by

the following graph:

Figure 47. Relative thermal conductivity vs weight concentration (CeO2 – Alfa Aesar).

At Figure 47 very good results are observed for both universities: KTH and

UBHAM. Although weight concentrations prepared by each university are not equal,

evaluating their trends is clear that the points between both sources are really similar

regarding to each other. Moreover, from a theoretical viewpoint, all values are within the

± 5 % Maxwell equation range, what means that results are close to the values are

expected to appear. Furthermore, comparing to the previous case, Al2O3 Alfa Aesar,

relative thermal conductivity values are very closer as is possible to check on Table 3.

Figure 48. Effective thermal conductivity vs weight concentration (CeO2 – Alfa Aesar). Is shown KTH data and Prasher prediction, with an acceptance range of ± 10%.

0,90

0,95

1,00

1,05

1,10

1,15

0 0,1 0,2 0,3

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Weight Conc.

CeO2 - Alfa Aesar

KTH

UBHAM

Maxwell Equation

Maxwell (+/-) 5%

0,500

0,550

0,600

0,650

0,700

0 0,1 0,2 0,3

The

rmal

Co

nd

uct

ivit

y (W

/mK

)

Weight Conc.

CeO2 - Alfa Aesar

KTH

Prasher (±10 %)

Prasher

72

By observing Figure 48, although experimental points are within ± 10 % range

from Prasher equation, it is easy to see that the behavior of the sample is linear.

Moreover, as concentration gets increased, data is farer from the line of predicted values.

When relative viscosity against weight percentage is evaluated, at Graph 49 is

possible to check that UBHAM values show lower viscosity than KTH ones, but not too

much, and this difference could be explained because of, as was seen before, KTH thermal

conductivity was higher than UBHAM data. On the other hand, if the previous nanofluid is

compared to the current one, better results are observed, since at Table 3 is shown that

both nanofluids have almost the same relative thermal conductivity, but, relative viscosity

of CeO2 is really lower than Al2O3, so, ceria Alfa Aesar is better talking about both

properties.

One more time, like all previous cases have been studied, is good to get an idea

about the agglomeration grade nanofluid could present:

Table 10. Values for theoretical comparisons for (CeO2 – Alfa Aesar).



0,2 0,033 1,083 1,155 0,148 1,527

0,15 0,024 1,059 1,108 0,106 1,336

0,09 0,013 1,034 1,060 0,060 1,170

0,06 0,009 1,022 1,039 0,039 1,105

0,03 0,004 1,011 1,019 0,019 1,049

Figure 49. Relative viscosity vs weight concentration (CeO2 – Alfa Aesar).

0,000

0,500

1,000

1,500

2,000

0 0,05 0,1 0,15 0,2 0,25

Re

lati

ve v

isco

sity

Weight Conc.

CeO2 - Alfa Aesar

KTH

UBHAM

Einstein Model

73

Watching at Figure 49 and Table 10, it is easy to check that Einstein and Nielsen

predictions only couple with low weight percentage values for KTH experiments, while

Nielsen is acceptable for UBHAM tests. However, Krieger is not much good for UBHAM

dilutions, whereas is acceptable for KTH data, although is not the best talking about other

nanoifluids have been studied in this section.

Figure 50. Absolute viscosity vs shear rate (CeO2 – Alfa Aesar).

At Figure 50 absolute viscosity is shown versust shear rate at different weight

percentages of nanofluid. It should be mentioned this nanofluids presents low viscosity

values compared to all above cases have been studied. And finally just say that viscosity

values are very similar between each sample.

2.3.2. Temperature effect

After analyzing weight concentration effect on both thermal conductivity and

viscosity, in this headland will be studied the effect provoked by temperature increment

on those two thermophysical properties that have been mentioned. In this way,

nanofluids have been tested at 20, 30, 40 and 50 ºC (for thermal conductivity; for viscosity

measurements at 50 ºC were not done); unlike previous section, as is wanted to analyze

temperature effect, weight concentration keeps constant, concretely at 9 w%.

Moreover, was agreed with UBHAM to divide tasks of viscosity and thermal

conductivity measurements. Thereby, at KTH have been tested nanofluids at 9 w% for

obtaining thermal conductivity values, while measurements for viscosity have been

carried out at UBHAM.

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 50 100 150

Vis

cosi

ty (

CP

)

Shear Rate (1/s)

CeO2 - Alfa Aesar

Alfa_Aesar_Ceria_20% Alfa_Aesar_Ceria_15% Alfa_Aesar_Ceria_9% Alfa_Aesar_Ceria_6% Alfa_Aesar_Ceria_3%

74

Subsequently, results obtained by both universities are presented through Table

11 and 12, whereas the whole graph series will be shown later.

Table 11. Absolute thermal conductivity and viscosity values versus temperature. Results are obtained from both UBHAM and KTH.

Sample T k (W/mK) µ (cP) Sample T k (W/mK) µ (cP)

Al2O3 - Evonik - 9 w%

20 0,633 1,344

SiO2 - Evonik - 9 w%

20 0,619 1,123

30 0,650 1,108 30 0,641 0,922

40 0,671 0,923 40 0,661 0,771

50 0,688 50 0,677

ITN - Al2O3 - 13 - 9 w%

20 0,678 1,070

Al2O3 - Alfa Aesar - 9 w%

20 0,614 1,312

30 0,697 0,878 30 0,635 1,085

40 0,721 0,740 40 0,650 0,909

50 0,757 50 0,671

TiO2 - Evonik - 9 w%

20 0,634 1,193

CeO2 - Alfa Aesar - 9 w%

20 0,616 1,113

30 0,653 0,977 30 0,641 0,886

40 0,672 0,824 40 0,658 0,738

50 0,683 50 0,674

ITN - TiO2 - 10 - 9 w%

20 0,626 1,424

30 0,651 1,154

40 0,669 0,985

50 0,685

75

Table 12. Relative values of thermal conductivity and viscosity. Results are obtained from KTH and UBHAM.

Sample T (ºC) krelative µrelative


20 1,057 1,39

30 1,056 1,41

40 1,064 1,38

50 1,069

ITN - Al2O3 - 13 - 9 w%

20 1,133 1,11

30 1,132 1,11

40 1,143 1,11

50 1,177


20 1,060 1,23

30 1,062 1,24

40 1,065 1,23

50 1,062

ITN - TiO2 - 10 - 9 w%

20 1,046 1,47

30 1,057 1,45

40 1,061 1,48

50 1,065

SiO2 - Evonik - 9 w%

20 1,035 1,16

30 1,041 1,17

40 1,048 1,16

50 1,052


20 1,026 1,358

30 1,031 1,371

40 1,031 1,345

50 1,042


20 1,029 1,147

30 1,041 1,120

40 1,044 1,113

50 1,048

Observing Table 11 it follows that effective thermal conductivity values decrease

while temperature increases, by contrast, in the case of viscosity the obtained trend is just

the opposite, since it decreases when temperature goes up.

By checking Table 12 is it possible to observe that, in the case of relative thermal

conductivity, there is a timid upward trend while temperature increases for all cases,

unless for TiO2-Evonik-9%. Furthermore, it can be appreciated that talking about

increments versus their respective base fluid (always distilled water) in this thermo-

physical parameter, most cases are below 6%, so it is a small enhancement; however, ITN-

Al2O3-13-9w% sample shows increases from 13 up to 17%, which are more significant.

On the other hand, treating relative viscosity values, it seems there is a strange

behavior as temperature is increased, since sometimes viscosity increases, occasionally

76

decreases and in one case, ITN-Al2O3-13-9w%, it keeps constant; hence, for this latter case

is a good new, given that thermal conductivity it has been enhanced while viscosity have

been kept constant.

After reasoning about tested values and seeing strange results, it is

recommendable to check some literature in order to know what is expected to happen

while working with nanofluids at different temperatures. In this direction, thermal

conductivity will be first in being analyzed and then viscosity discuss will proceed.

In summary one can say absolute thermal conductivity of nanofluids increases

with temperature dependence on temperature was observed for relative thermal

conductivity.

Most publications agree the first scenario, like Das et al. [26], who conclude that

hypothesis using both Al and Cu oxide nanofluids in water within a range of temperatures

of 21-51 ºC. Deepening on alumina water-based dispersions, Li and Peterson [40], observed

a remarkable enhancement comparing the value reached at 36 ºC with the one tested at

27,5 ºC, seeing as it was three times higher than for lower temperature; furthermore, an

enhancement of 30% was observed for . Another experimented to be commented is one

carried out by Ding et al. [29], who by using CNT (carbon nanotubes)-water nanofluids,

noticed a linear increment with temperature until 30°C, but, after this temperature, no

influence was observed.

Once first situation for temperature-thermal conductivity has been analyzed, it is

time to evaluate the second one, namely, when thermo-physical parameter decreases

while temperature increases. In this way, Masuda et al. [41], found this atypical behavior

using Al2O3, SiO2, and TiO2 nanoparticles at different temperatures, contrarily to most

publications. Besides this experiment, there is another one [42], in which Bi2Te3 nanorods

in perfluorohexane are examined showing a decrement in the effective thermal

conductivity as the temperature increased from 5 to 50 ºC.

Finally, is turn to cite the third situation, when no relation is observed between

thermal conductivity and temperature. Thus, Turgut et al. [43], studied TiO2 nanoparticles

dispersed in deionized water within a temperature range from 13 until 55 ºC and found

no dependence between two mentioned parameters; according to some literature [44], it

could be due to the importance of the usage of surfactants in nanofluids, because no

surfactant was used in this study. Another experiment [45] which reaches the same

conclusion analyzed Au nanoparticles in water and Al2O3 in petroleum oil between 25-75

ºC, using forced Rayleigh scattering method.

After thermal conductivity evaluation, the same analysis is going to be done for

the other thermo-physical parameter studied in this chapter, that is to say, viscosity.

Unlike was proceeded before, first case will be the decrease of viscosity while

temperature increases. For instance, Nguyen et al. [46], analyzed CuO and Al2O3 water

based nanofluids within a temperature range of ambient temperature-75 ºC and they

concluded temperature had a positive effect on viscosity, given that as temperature was

77

increased, viscosity decreased. Another experiment in this direction was carried out using

CuO and Al2O3 nanoparticles both of them dispersed in ethylene glycol [47] in different

concentrations and temperatures; tests led to the mentioned hypothesis. Going farther

on the kind of relation between viscosity and temperature, according to a publication [48],

some authors observed exponential evolution for viscosity as temperature increases [49],

[50].

In order to finish with literature survey regarding viscosity behavior, last situation

to be contemplated is going to be analyzed, which deals on viscosity independence of

temperature. In this way, Prasher et al. [51], by using Al2O3 nanoparticles no effect of

temperature was obtained during the tests of the samples at different temperatures,

contrarily to most investigations. Furthermore, the same publication was pointed out

before [48], report that there are some investigators [52], [53] who also reached this

hypothesis.

After this analysis of several publications, it could be said that the most expected

results for thermal conductivity support the theory in which thermal conductivity should

increase with temperature, it means, temperature increment has a positive effect on this

thermo-physical parameter. Although sometimes is observed the opposite conclusion or

no effect of temperature, but with less assiduity. On the other hand, talking about

viscosity is mostly expected to decrease while temperature increases; however, there are

investigations that show different tendencies.

2.3.2.1. Al2O3-Evonik 9 w%

First nanofluid to be shown is Al2O3-Evonik-9w%:

Figure 51. Absolute thermal conductivity vs temperature (Al2O3 – Evonik – 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 5%.

0,500

0,600

0,700

0,800

0,900

0 20 40 60

k (W

/mK

)

Temperature (ºC)


KTH

Joan

(±5%) Joan

78

Watching at Figure 51 an upward trend is observed for this case. It seems this

tendency is linear, so, for this reason, a linear equation has been tested for this nanofluid

(presenting a very good fit with data) and also for the rest of samples, given that it will be

nice if a general prediction will be found. Deepening in this correlation, the equation has

the following form:

(1)

Looking at this expression, thermal conductivity only shows the influence of

temperature; hence, the values that this equation will reach are going to be the same for

all analyzed dilutions.

But analysis of absolute value is not enough, because of that, subsequently,

relative values are going to be examined, which evaluate the ratio of enhancement

regarding to the based fluid has been used, just to see if this first enhancement is present

also when comparing to based fluid increment.

Figure 52. Relative thermal conductivity vs temperature (Al2O3 – Evonik – 9 w%). Are shown experimental data and Maxwell prediction, with an acceptance range of ± 5%.

By the observation of Figure 52 it is easy to check there is a timid enhancement in

thermal conductivity along temperature increments. This is confirmed taking a look to

Table 12, where is possible to see that this thermo-physical parameter is getting

improved, but, actually, not too much and might be because of the possible convection in

higher temperatures. Moreover, Maxwell equation is used and is clear that points are

quite close to this prediction, since they are within the acceptance rank of ± 5 %. As

Maxwell doesn’t include influence of temperature, it could be said that, though exists a

temperature effect, this is not sufficiently high to consider models including temperature.

0,9000

0,9500

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1,0500

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1,1500

1,2000

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ivit

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Temperature (ºC)


KTH

Maxwell Equation

Maxwell (+/-) 5%

79

Figure 53. Absolute viscsosity vs temperature (Al2O3 – Evonik – 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 12%.

In Figure 53 a clear downtrend is observed. It looks like an exponential tendency;

therefore, an exponential expression has been tried for this nanofluid (although it is

underestimating values, but not too much, it seems acceptable, seeing as it is within the

acceptance rank), and also for the rest of samples, because, as the same way than

thermal conductivity expression, it will be perfect if a general prediction will be found for

all studied cases. Deepening in this correlation, the equation has the following form:

, (2)

Looking at this expression, viscosity only includes the effect of temperature; so,

the values that this equation will reach are going to be the same for all studied samples.

Figure 54. Relative viscosity vs temperature (Al2O3 – Evonik – 9 w%).

0,000

0,500

1,000

1,500

2,000

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Temperature (ºC)


KTH

Joan

0,000

0,500

1,000

1,500

0 10 20 30 40 50

Re

lati

ve V

isco

sity

Temperature (ºC)


80

Apparently, looking at Figure 54, there is no difference between alumina

nanofluid while changing temperature; however, checking numerical values at Table 12,

those are different. Despite this, a strange behavior is observed, since 30 ºC viscosity is

higher than 20 ºC one, but also than 40 ºC test, what means that temperature doesn’t

affect relative viscosity of this nanofluid. However, given that the difference between

tests is very small, it could happened due to the accuracy of the instrument.

Figure 55. Absolute viscosity vs shear rate (Al2O3 – Evonik – 9 w%).

For finishing with this nanofluid, absolute viscosity is plotted against shear rate, in

order to guess the behavior of each sample. It is clear to see all samples have Newtonian

behavior, what is a good characteristic of Al2O3–Evonik–9w%.

2.3.2.2. ITN-Al2O3-13- 9 w%

Once alumina nanofluid from Evonik has been evaluated, the following one is

alumina belonging to ITN. Watching at Figure 56 it could be observed a similar trend than

the previous sample for thermal conductivity, since a clear augmenting trend is shown for

this case. As occurred before, this tendency is linear, therefore, the same equation than

prior, that is to say, equation 1, is used in order to model the behavior of this thermo-

physical parameter. Unlike what has happened for previous sample, the prediction

doesn’t couple at all with data, which means that this nanofluid presents higher values

than expected.

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 50 100 150

Vis

cosi

ty (

cP)

Shear Rate (1/s)


AL-EV-9_T=20

AL-EV-9_T=30

AL-EV-9_T=40

81

Figure 56. Absolute thermal conductivity vs temperature (ITN - Al2O3 – 13 – 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 5%.

Figure 57. Relative thermal conductivity vs temperature (ITN - Al2O3 – 13 – 9 w%). Are shown experimental data and Maxwell prediction, with an acceptance range of ± 5%.

By checking Figure 57 it is easy to see that relative values keep almost constant

until 40 ºC, but an unexpected enhancement is obtained in the case of 50 ºC. So, it can be

deduced that thermal conductivity of based fluid increases the same quantity than

nanofluid for 20, 30 and 40 ºC, but, for 50 ºC, nanofluid’s increment is higher than based

fluid one. Moreover, all points are out of ± 5% Maxwell acceptance range, what means

that maybe in this case there is a temperature effect on relative thermal conductivity,

contrarily to first alumina sample.

0,500

0,600

0,700

0,800

0,900

0 20 40 60

k (W

/mK

)

Temperature (ºC)

ITN - Al2O3 - 13 - 9 w%

KTH

Joan

0,9000

0,9500

1,0000

1,0500

1,1000

1,1500

1,2000

0 20 40 60

Re

lati

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co

nd

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ivit

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Temperature (ºC)

ITN - Al2O3 - 13 - 9 w%

KTH

Maxwell Equation

Maxwell (+/-) 5%

82

Figure 58. Absolute viscosity vs temperature (ITN - Al2O3 – 13 – 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 12%.

Like previous nanofluid, viscosity decreases exponentially while temperature

increases. It is possible to check at Figure 58 that, although equation 2 is underestimating

results, data is within the acceptance rank, or, it would be better to say that is on the

lower edge of acceptance range. Moreover, the way that tested results evolve follows the

same form that the prediction, though below the expected values.

Figure 59. Relative viscosity vs temperature (ITN - Al2O3 – 13 – 9 w%).

Looking at Figure 59 and Table 12 is clear that relative viscosity values don’t

change along temperature increments, it is always 1,11 cP. That is a good point because

while, for this nanofluid, relative thermal conductivity increases, viscosity keeps constant,

so it could be a potential nanofluid for using at electronic applications.

0,000

0,500

1,000

1,500

2,000

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Temperature (ºC)

ITN - Al2O3 - 13 - 9 w%

KTH

Joan

0,000

0,200

0,400

0,600

0,800

1,000

1,200

1,400

0 10 20 30 40 50

Re

lati

ve V

isco

sity

Temperature (ºC)

ITN - Al2O3 - 13 - 9 w%

83

Figure 60. Absolute viscosity vs shear rate (ITN - Al2O3 – 13 – 9 w%).

Last graph for this sample analyses its rheological behavior. In this way, it occurs

the same than previous nanofluid, that is, all tests at different temperatures present

Newtonian behavior.

2.3.2.3. TiO2-Evonik 9 w%

After ITN-Al2O3-13-9w% nanofluid analysis, the next one is TiO2-Evonik-9w%. As

has been done with preceding cases, first property to be examined is absolute thermal

conductivity. At Figure 61 can be appreciated an alike behavior than the first sample has

been studied, namely, Al2O3-Evonik-9w%, given that data couples really well to own-made

prediction (equation 1).

Figure 61. Absolute thermal conductivity vs temperature (TiO2 – Evonik – 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 5%.

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 50 100 150

Vis

cosi

ty (

cP)

Shear Rate (1/s)

ITN - Al2O3 - 13 - 9 w%

AL-13-9_T=20

AL-13-9_T=30

AL-13-9_T=40

0,500

0,600

0,700

0,800

0,900

0 20 40 60

k (W

/mK

)

Temperature (ºC)


KTH

Joan

(±5%) Joan

84

Figure 62. Relative thermal conductivity vs temperature (TiO2 – Evonik – 9 w%). Are shown experimental data and Maxwell prediction, with an acceptance range of ± 5%.

By the observation of Figure 62, it is easy to check there is a very small

enhancement in thermal conductivity along temperature increments. This is confirmed

taking a look at Table 12, where is possible to see that this thermo-physical parameter is

getting improved, but, actually, not too much; moreover, it takes the same value for both

30 and 50 ºC. It means there is an upward trend until 40 ºC, but, after this temperature,

relative thermal conductivity decreases again. On the other hand, Maxwell equation is

used and it shows that points are really close to Maxwell equation, what is more, are

almost on the line drawn by Maxwell prediction. So, since Maxwell doesn’t include

influence of temperature, it could be said that influence of temperature is not high

enough to consider models including it.

Figure 63. Absolute viscosity vs temperature (TiO2 – Evonik – 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 12%.

Like two previous samples, viscosity results decrease exponentially while

temperature increases. Checking Figure 63, obtained values from UBHAM are within the

0,9000

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1,0000

1,0500

1,1000

1,1500

0 20 40 60 Re

lati

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rmal

co

nd

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ivit

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Temperature (ºC)


KTH

Maxwell Equation

Maxwell (+/-) 5%

0,000

0,500

1,000

1,500

2,000

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Temperature (ºC)


KTH

Joan

85

acceptance range regarding to equation 2; furthermore, this is the first time values couple

quite well to the own-made prediction, that is to say, better than before cases.

Figure 64. Relative viscosity vs temperature (TiO2 – Evonik – 9 w%).


change too much while temperature increases, since their values are 1,23; 1,24 and 1,23

cP for each temperature. These results follow more or less the same tendency than

relative thermal conductivity, since first went up and then it was decreased. But, seeing at

this strange behavior, it could be concluded that there is no temperature influence for this

nanofluid regarding to relative viscosity. It is because viscosity of both nanofluid and host

fluid change at the same way.

Figure 65. Absolute viscosity vs shear rate (TiO2 – Evonik – 9 w%).

0,000

0,500

1,000

1,500

0 10 20 30 40 50

Re

lati

ve V

isco

sity

T emperature (ºC)


0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 50 100 150

Vis

cosi

ty (

cP)

Shear Rate (1/s)


TI-EV-9_T=20

TI-EV-9_T=30

TI-EV-9_T=40

86

For finishing with TiO2-Evonik-9 w%, absolute viscosity is represented versus shear

rate, so that to know the behavior of each sample. It is clear to see all samples have

Newtonian behavior, what is a good characteristic of this nanofluid.

2.3.2.4. ITN-TiO2-10- 9 w%

Once the first titanium oxide nanofluid has been evaluated, the following one is a

nanofluid belonging to ITN, using again TiO2 nanoparticles. Observing Figure 66 it could be

seen a similar trend than the previous sample for thermal conductivity, given that a linear

upward trend is shown for this case. As happened with all prior cases, equation 1 is

employed for modeling the behavior of this parameter. Like first and last sample, the

equation predicts very good experimental points, seeing as data is almost on the line of

predicted values.

Figure 66. Absolute thermal conductivity vs temperature (ITN - TiO2 – 10 – 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 5%.

0,500

0,550

0,600

0,650

0,700

0,750

0,800

0,850

0,900

0 20 40 60

k (W

/mK

)

Temperature (ºC)

ITN - TiO2 - 10 - 9 w%

KTH

Joan

(±5%) Joan

87

Figure 67. Relative thermal conductivity vs temperature (ITN - TiO2 – 10 – 9 w%). Are shown experimental data and Maxwell prediction, with an acceptance range of ± 5%.

Checking Figure 67, a timid increment is present while temperature increases;

however, it is not significant seeing as all data is fairly close to Maxwell prediction. In this

direction, it means that, as Maxwell doesn’t take account of temperature effect, it could

be concluded that influence of temperature is not high enough to consider models

including it.

Figure 68. Absolute viscosity vs temperature (ITN - TiO2 – 10 – 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 12%.

As well as occurred in previous cases, viscosity decreases exponentially with

temperature increments. Watching at Figure 68, although equation 2 is underestimating

results, data is almost on the higher border of the acceptance rank. However, though

results are a bit far from equation 2, the way that tested results evolve follows the same

form that the prediction.

0,9000

0,9500

1,0000

1,0500

1,1000

1,1500

0 20 40 60 Re

lati

ve t

he

rmal

co

nd

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ivit

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Temperature (ºC)

ITN - TiO2 - 10 - 9 w%

KTH

Maxwell Equation

Maxwell (+/-) 5%

0,000

0,500

1,000

1,500

2,000

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Temperature (ºC)

ITN - TiO2 - 10 - 9 w%

KTH

Joan

88

Figure 69. Relative viscosity vs temperature (ITN - TiO2 – 10 – 9 w%).

At first sight, looking at Figure 69, there is no difference between titanium oxide

nanofluid while changing temperature; however, checking numerical values at Table 12,

those are different. Thereby, a weird behavior is observed, since 20 ºC viscosity is higher

than 30 ºC one, as it was expected; but, on the other hand, 40 ºC test shows highest

viscosity, even more than 20 ºC value. It means that temperature doesn’t affect relative

viscosity of this nanofluid.

Figure 70. Absolute viscosity vs shear rate (ITN - TiO2 – 10 – 9 w%).

Last graph for this sample analyses its rheological behavior. In this way, it occurs

the same than previous nanofluid, that is, all tests at different temperatures present

Newtonian behavior.

0,000

0,500

1,000

1,500

0 10 20 30 40 50

Re

lati

ve V

isco

sity

Temperature (ºC)

ITN - TiO2 - 10 - 9 w%

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 50 100 150

Vis

cosi

ty (

cP)

Shear Rate (1/s)

ITN - TiO2 - 10 - 9 w%

TI-10-9_T=20

TI-10-9_T=30

TI-10-9_T=40

89

2.3.2.5. SiO2 Levasil

After evaluating titanium oxide nanofluids, the following one contains SiO2

nanoparticles diluted in distilled water, from Levasil. Like previous samples, first thermo-

physical parameter analyzed is absolute thermal conductivity. At Figure 71 can be

observed that there is a linear positive evolution with temperature; besides that, model

prediction through equation 1 fits in a properly way to data, given that results are on the

line of predicted values for experimental points.

Figure 71. Absolute thermal conductivity vs temperature (SiO2 – Levasil – 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 5%.

Figure 72. Relative thermal conductivity vs temperature (SiO2 – Levasil – 9 w%). Are shown experimental data and Maxwell prediction, with an acceptance range of ± 5%.

Talking about relative value of thermal conductivity, for this sample the same

trend than prior case is presented, since a shy linear increment is shown at Figure72. In

0,500

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0,600

0,650

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0,750

0,800

0,850

0,900

0 20 40 60

k (W

/mK

)

Temperature (ºC)

SiO2 - Levasil - 9 w%

KTH

Joan

(±5%) Joan

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0,9500

1,0000

1,0500

1,1000

1,1500

0 20 40 60 Re

lati

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Temperature (ºC)


KTH

Maxwell Equation

Maxwell (+/-) 5%

90

the same direction, this increment it is not noteworthy seeing as all data is moderately

close to Maxwell prediction. Therefore, as Maxwell doesn’t take account of temperature

effect, it could be said that influence of temperature is not sufficiently high to take in

account models which comprise temperature.

Figure 73. Absolute viscosity vs temperature (SiO2 – Levasil – 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 12%.

As has been observed for all studied nanofluids till the moment, viscosity

decreases exponentially while temperature increases. Taking a look at Figure 73, although

equation 2 is underestimating results, data is within ± 12% acceptance rank.

Figure 74. Relative viscosity vs temperature (SiO2 – Levasil – 9 w%).


change too much while temperature increases, since their values are 1,16; 1,17 and again

0,000

0,500

1,000

1,500

2,000

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Temperature (ºC)


KTH

Joan

(±12%) Joan

0,000

0,200

0,400

0,600

0,800

1,000

1,200

1,400

0 10 20 30 40 50

Re

lati

ve V

isco

sity

Temperature (ºC)


91

1,16 cP for each temperature. Here happens exactly the same than for TiO2 – Evonik – 9

w% nanofluid, seeing as first relative viscosity goes up and then decreases. So, seeing at

this strange behavior, it could be concluded that there is no temperature influence for this

nanofluid regarding to relative viscosity. It is because viscosity of both nanofluid and host

fluid evolve at the same way.

Figure 75. Absolute viscosity vs shear rate (SiO2 – Levasil – 9 w%).

For finishing with SiO2 – Levasil – 9 w%, absolute viscosity is represented versus

shear rate, so that to know the behavior of each sample. It is clear to see all samples have

Newtonian behavior, what is a good characteristic of this silica nanofluid.

2.3.2.6. Al2O3-Alfa Aesar- 9 w%

Now it is turn to evaluate nanofluids belonging to Alfa Aesar; the first one is Al2O3-

Alfa Aesar-9w%. Through Figure 76 can be appreciated a linear increasing evolution with

temperature; in this case, model prediction from equation 1 overestimates a little

experimental results. Nonetheless, these are within acceptance range, and, as

temperature increases, data is closer to the theoretical expression. So, it can be

concluded that own-made equation is also good for the current nanofluid.

0

0,5

1

0 50 100 150

Vis

cosi

ty (

cP)

Shear Rate (1/s)


SI-EV-9_T=20

Si-EV-9_T=30

SI-EV-9_T=40

92

Figure 76. Absolute thermal conductivity vs temperature (Al2O3 – Alfa Aesar - 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 5%.

Figure 77. Relative thermal conductivity vs temperature (Al2O3 – Alfa Aesar - 9 w%). Are shown experimental data and Maxwell prediction, with an acceptance range of ± 5%.

By the observation of Figure 77 it is easy to check there is a shy improvement in

thermal conductivity along temperature increments. This is confirmed taking a look to

Table 2, where is possible to see that this thermo-physical parameter is going up, but,

actually, not too much. Moreover, Maxwell equation is used and is clear that points are

within the acceptance rank of ± 5 %. As Maxwell doesn’t include influence of

temperature, it could be said that, though exists a temperature effect, this is not

sufficiently high to consider models including temperature.

0,500

0,550

0,600

0,650

0,700

0,750

0,800

0,850

0,900

0 20 40 60

k (W

/mK

)

Temperature (ºC)


KTH

Joan

(±5%) Joan

0,9000

0,9500

1,0000

1,0500

1,1000

1,1500

0 20 40 60

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Temperature (ºC)


KTH

Maxwell Equation

Maxwell (+/-) 5%

93

Figure 78. Absolute viscosity vs temperature (Al2O3 – Alfa Aesar - 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 12%.

In Figure 78 a clear downtrend is observed. It looks like an exponential tendency;

therefore, the same exponential expression (equation 2) than prior nanofluids has been

employed. This case is very similar to the first nanofluid analyzed in this chapter, that is,

Al2O3-Evonik-9w%, since the own-made prediction underestimates viscosity values but is

inside the acceptance range.

Figure 79. Relative viscosity vs temperature (Al2O3 – Alfa Aesar - 9 w%).

From checking Figure 79 and Table 12 it can be appreciated a coincidence with

other nanofluid, concretely, the last one being analyzed: SiO2-Levasil-9w%. This is said

because, as the same way than before, the graph shows similar values for the sample at

different temperatures, but seeing at the mentioned table is possible to observe that

values are not the same, given that result for 30 ºC is higher than both 20 and 40 ºC.

Therefore, after this weird behavior it could be reached the hypothesis that presents no

relation between relative viscosity and temperature.

0,000

0,500

1,000

1,500

2,000

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Temperature (ºC)


KTH

Joan

0,000

0,500

1,000

1,500

0 10 20 30 40 50

Re

lati

ve V

isco

sity

Temperature (ºC)


94

Figure 80. Absolute viscosity vs shear rate (Al2O3 – Alfa Aesar - 9 w%).

The latest chart of this nanofluid evaluates its rheological behavior. In this

direction, it happens the same than before samples, namely, all tests at different

temperatures present Newtonian behavior.

2.3.2.7. CeO2-Alfa Aesar- 9 w%

Second sample belonging to Alfa Aesar contains CeO2 nanoparticles in distilled

water. A linear upward trend is observed while temperature goes up, like all nanofluids

have been tested. Beyond that common fact, its behavior is really analogous to SiO2-

Levasil-9w%, since thermal conductivity values are almost on the line of prediction,

though this one overestimates (only a little) some points, such as the experimental value

corresponding to 20ºC.

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 50 100 150

Vis

cosi

ty (

cP)

Shear Rate (1/s)


Al2O3-AA-9_T=20

Al2O3-AA-9_T=30

Al2O3-AA-9_T=40

95

Figure 81. Absolute thermal conductivity vs temperature (CeO2 – Alfa Aesar - 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 5%.

Figure 82. Relative thermal conductivity vs temperature (CeO2 – Alfa Aesar - 9 w%). Are shown experimental data and Maxwell prediction, with an acceptance range of ± 5%.

Talking about relative value of thermal conductivity, for this sample the same

trend than preceding cases is presented, since a shy linear increment is shown at Figure

82. Nevertheless, it seems that there is an increment only between 20 and 30ºC, because

values for other temperatures are quite similar, at least checking the mentioned graph.

Despite of this, through taking a look at Table 2 is seen that relative thermal conductivity

always increases with temperature, but the existing increment between two lower

temperatures is higher than the others. After that, evaluating experimental results against

Maxwell equation, it should be said that data fit moderately well to this prediction, given

that is within the ± 5% acceptance range; for this reason, as Maxwell doesn’t take account

of temperature effect, it could be concluded that temperature effect is not adequately

high to consider models which including temperature.

0,500

0,550

0,600

0,650

0,700

0,750

0,800

0,850

0,900

0 20 40 60

k (W

/mK

)

Temperature (ºC)


KTH

Joan

(±5%) Joan

0,9000

0,9500

1,0000

1,0500

1,1000

0 20 40 60

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Temperature (ºC)


KTH

Maxwell Equation

Maxwell (+/-) 5%

96

Figure 83. Absolute viscosity vs temperature (CeO2 – Alfa Aesar - 9 w%). Also an own-made prediction is plotted, with an acceptance range of ± 12%.

Now, analyzing viscosity results, it has been realized that CeO2-Alfa Aesar-9w%

nanofluid has some coincidences with SiO2-Levasil-9w%; besides having comparable

behavior regarding to voth absolute and relative thermal conductivity, their absolute

values for viscosity tests fit in analogous way to the prediction calculated through

equation 2. That is said because in both nanofluids, experimental results are quite close to

the lower border of the acceptance rank. As has been observed for all studied nanofluids

till the moment, viscosity decreases exponentially while temperature increases. Taking a

look at Figure 83, although equation 2 is underestimating results, data is within ± 12%

acceptance rank. Moreover, though values are a bit far from equation 2, the way that

tested results evolve follows the same form that the prediction.

Figure 84. Relative viscosity vs temperature (CeO2 – Alfa Aesar - 9 w%).

Looking at Figure 84 it seems values regarding to relative viscosity are the same,

or almost the same. However, if Table 2 is checked it will be discovered that is the first

time that relative viscosity shows a decreasing trend while temperature increases.

0,000

0,500

1,000

1,500

2,000

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Temperature (ºC)


KTH

Joan

0,000

0,500

1,000

1,500

0 10 20 30 40 50

Re

lati

ve V

isco

sity

Temperature (ºC)


97

Figure 85. Absolute viscosity vs shear rate (CeO2 – Alfa Aesar - 9 w%).

For finishing with CeO2 – Alfa Aesar – 9 w%, absolute viscosity is represented

versus shear rate, so that to know the behavior of each sample. It is clear to see all

samples have Newtonian behavior, what is a good characteristic of this silica nanofluid.

2.3.3. Comparisons

After analyzing temperature and weight concentration effects on thermal

conductivity and viscosity of all tested nanofluids it could be recommendable to make

some comparisons in order to discover which nanofluid shows the best properties to be

used in electronic cooling systems.

Thereby, first of all some evaluations between samples using the same

nanoparticles are going to be presented. Other nanofluids used in previous chapters, such

as silica and ceria nanolfuids are not included in this comparisons chapter since only one

nanofluid of each kind has been tested. In this direction, subsequently, alumina nanofluids

are examined:

0

0,5

1

0 50 100 150

Vis

cosi

ty (

cP)

Shear Rate (1/s)


CeO2-AA-9_T=20

CeO2-AA-9-T=30

CeO2-AA-9_T=40

98

Figure 86. Relative thermal conductivity vs weight concentration. Are shown experimental data from KTH and UBHAM for Al2O3 nanofluids belonging to Evonik, ITN and Alfa Aesar.

By observing Figure 86, it can be appreciated that UBHAM and KTH experimental

results are similar for Evonik and, above all, Alfa Aesar samples, but there is a

considerable difference in the case of ITN sample.

On the other hand, comparing samples, it follows that nanofluids from Evonik and

Alfa Aesar present values for relative thermal conductivity close to each other, especially

at low concentrations. By contrast, ITN-Al2O3-13 shows better results for this

thermophysical parameter in both KTH and UBHAM results.

Figure 87. Relative thermal conductivity vs temperature. Are shown experimental data from KTH for Al2O3 nanofluids belonging to Evonik, ITN and Alfa Aesar.

Besides weight concentration effect, also temperature effect has been studied,

for this reason Figure 87 are plotted obtained results for mentioned case. It is clear that

best nanofluid is one which comes from ITN. These tests just carried out at KTH.

0,90

1,10

1,30

1,50

1,70

1,90

0 0,2 0,4 0,6

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Weight Conc.

Al2O3

Al-EV-KTH

Al-EV-UBHAM

ITN-Al-13-KTH

ITN-Al-13-UBHAM

Al2O3-AA-KTH

Al2O3-AA-UBHAM

1,00

1,05

1,10

1,15

1,20

10 30 50 70

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Temperature (ºC)

Al2O3 - 9w%

Al-EV-KTH

ITN-Al-13-KTH

Al2O3-AA-KTH

99

Figure 88. Relative viscosity vs weight concentration. Are shown experimental data from KTH and UBHAM for Al2O3 nanofluids belonging to Evonik, ITN and Alfa Aesar.

Talking about viscosity results, through Figure 88 it can be seen that all nanofluids

have comparable values until 15 w%; from this weight concentration viscosities start to

increase in a different way depending on their source and synthesis. Furthermore, it

should be mentioned that the case of Al2O3-Evonik-40w% seems to be anomalous.

Figure 89. Relative viscosity vs temperature. Are shown experimental data from UBHAM for Al2O3 nanofluids belonging to Evonik, ITN and Alfa Aesar.

Also for viscosity temperature effect study has been carried out at University of

Birmingham to support this study, so, at Figure 89 are presented data belonging to this

analysis. It is clear that best nanofluid is one which comes from ITN, since shows lower

viscosity and, as was checked before, higher thermal conductivity.

0,00

5,00

10,00

15,00

20,00

25,00

0 0,2 0,4 0,6

Re

lati

ve V

isco

sity

Weight Conc.

Al2O3

Al-EV-KTH

Al-EV-UBHAM

ITN-Al-13-KTH

ITN-Al-13-UBHAM

Al2O3-AA-KTH

Al2O3-AA-UBHAM

1,000

1,050

1,100

1,150

1,200

1,250

1,300

1,350

1,400

1,450

1,500

0 20 40 60

Re

lati

ve t

he

rmal

vis

cosi

ty

Temperature (ºC)

Al2O3 - 9w%

Al-EV-UBHAM

ITN-Al-13-UBHAM

Al2O3-AA-UBHAM

100

Once Al2O3 nanofluids have been evaluated, it is time to analyze titanium oxide

samples. As was done above, first of all, graph for relative thermal conductivity is shown:

Figure 90. Relative viscosity vs weight concentration. Are shown experimental data from KTH and UBHAM for TiO2 nanofluids belonging to Evonik and ITN.

By checking Figure 90, it can be observed that UBHAM and KTH experimental

results are nearby for both ITN and Evonik dispersions. In addition to this, it is clear that

there is no significant difference between these nanofluids’ thermal conductivity.

Figure 91. Relative thermal conductivity vs temperature. Are shown experimental data from KTH for TiO2 nanofluids belonging to Evonik and ITN.

0,90

1,00

1,10

1,20

1,30

1,40

1,50

0 0,2 0,4 0,6

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Weight Conc.

TiO2

Ti-EV-KTH

Ti-EV-UBHAM

ITN-Ti-10-KTH

ITN-Ti-10-UBHAM

1,00

1,02

1,04

1,06

1,08

1,10

10 30 50 70

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Temperature (ºC)

TiO2 - 9w%

Ti-EV-KTH

ITN-Ti-10-KTH

101

Contrarily to previous case, that is, alumina nanofluids at different temperatures,

now both titanium oxide samples are quite close to each other, though some strange

tendencies are seen. In this direction, this graph is not sufficient to decide which one is

better.

Figure 92. Relative viscosity vs weight concentration. Are shown experimental data from KTH and UBHAM for TiO2 nanofluids belonging to Evonik and ITN.

Analyzing viscosity experimental values, taking a look at Figure 92 it can be

appreciated that results for Evonik sample are really close between KTH and UBHAM.

However the difference between the measurements at KTH and UBHAM is much higher

for ITN nanofluid. The reason is at UBHAM they re-stabiles these samples by some

process.

Figure 93. Relative viscosity vs temperature. Are shown experimental data from UBHAM for TiO2 nanofluids belonging to Evonik and ITN.

0,90

1,90

2,90

3,90

4,90

5,90

0 0,2 0,4 0,6

Re

lati

ve V

isco

sity

Weight Conc.

TiO2

Ti-EV-KTH

Ti-EV-UBHAM

ITN-Ti-10-KTH

ITN-Ti-10-UBHAM

1,00

1,10

1,20

1,30

1,40

1,50

1,60

10 20 30 40 50

Re

lati

ve t

he

rmal

co

nd

uct

ivit

y

Temperature (ºC)

TiO2 - 9w%

Ti-EV-KTH

ITN-Ti-10-KTH

102

Like before, this type of graph is useful in order to choose which nanofluid fits,

since it can be deduced that sample belonging to Evonik presents lower viscosity fit better

to the required needs.

Once the comparisons between nanofluids using the same nanoparticles have

been done, an analysis including all tested nanofluids is going to be carried out. For this

aim, graphs including all experimental data from tested samples against different general

predictions have been used with some deviation ranges. In this way, while weight

concentration effect was evaluated, two predictions were used: Maxwell for thermal

conductivity and Krieger for viscosity; moreover, while temperature influence analysis two

correlations were employed: those calculated through equations 1 and 2.

103

Figure 94. Experimental data vs Maxwell equation. Are also plotted ± 5% and ± 10% deviation ranges from prediction. Points correspond to weight concentration analysis, so are represented nanofluids at different w%.

Looking at Figure 94, where experimental data is shown against Maxwell

prediction for effective thermal conductivity, it can be pointed out some conclusions. First

of all, it should be said that Maxwell expression works very well for low weight

concentration values ( in most cases up to 15-20 w%), given that all tests are within its ±

5% deviation range. However, it is clear that, as concentration is increased, thermal

conductivity keeps away from this correlation. In this direction, it must be distinguished

cases of alumina nanofluids, because for highest concentrations (20-40 w%) of both Al2O3-

Evonik and Al2O3-Alfa Aesar Maxwell prediction overestimates too much thermal

conductivity, seeing as these points are below ± 10% deviation range. Moreover, for ITN-

Al2O3-13 the cited equation underestimates their values because it presents unexpected

values.

0,58

0,68

0,78

0,88

0,98

1,08

0,58 0,68 0,78 0,88 0,98 1,08

k e

xper

ime

nta

l (W

/mK

)

k Maxwell (W/mK)

TI-EV-40

SI-LEV-45

Al-EV-40

TI-10-20

Al-13-40

Al2O3-Alfa_Aesar-50 CeO2-Alfa_Aesar-20 Kmaxwell (X)

Maxwell (±5%)

Maxwell (±10%)

104

Figure 95. Experimental data vs Krieger equation. Are also plotted ± 5%, ± 10% and ± 15% deviation ranges from prediction. Points correspond to weight concentration analysis, so are represented nanofluids at different w%.

Continuing analyzing models used for weight concentration study, checking Figure

95, it is easy to see that Krieger equation predicts fairly well with a deviation range of ±

15%. As the same way than Maxwell, Krieger generally predicts better viscosities working

with low concentrations (not always, but mos times from 3 w% up to 15 w%) than higher

ones (although sometimes, as can be appreciated at Figure 10, Krieger fits very well to

highest concentrated data). This is not the case of Al2O3-Alfa Aesar, for instance, which

most of their points are on the +15% edge; like other two alumina nanofluids, as they

show higher values than Krieger for high concentrations.

0,90

1,90

2,90

3,90

4,90

5,90

6,90

7,90

0,90 2,90 4,90 6,90

µ e

xper

ime

nta

l (c

P)

µ Krieger (cP)

TI-EV-40

SI-LEV-45

Al-EV-40

TI-10-20

Al-13-40

Al2O3-Alfa_Aesar-50

CeO2-Alfa_Aesar-20

µ Krieger (X)

Krieger (±10%)

Krieger (±15%)

105

Figure 96. Experimental data vs Joan equation. Are also plotted ± 2,5% and ± 5% deviation ranges from prediction. Points correspond to temperature analysis, so are represented nanofluids at different temperatures.

After weight concentration analysis, then followed temperature study about

thermo-physical properties. In that case, an own-made equation (1), has been used in

order to model the behavior of absolute thermal conductivity parameter of nanofluids

while testing them at different temperatures. So that to evaluate the validity of this

prediction the experimental points are plotted through the Figure 96, where are

represented experimental data against the mentioned expression and ± 2,5 % and ± 5%

deviation ranges. It is easy to check that this prediction models quite well most tested

nanofluids, with the exception of ITN-Al2O3-13-9w%, which is underestimated. A good

point is that almost every experimental values are within the ± 2,5% acceptance range.

0,600

0,620

0,640

0,660

0,680

0,700

0,720

0,740

0,760

0,60 0,62 0,64 0,66 0,68 0,70 0,72

Ke

xper

ime

nta

l

KJoan

TI-EV-9

SI-LEV-9

Al-EV-9

TI-10-9

Al-13-9

Al2O3-Alfa_Aesar-9

CeO2-Alfa_Aesar-9

k Joan

Joan (±5%)

Joan (±2,5%)

106

Figure 97. Experimental data vs Joan equation. Are also plotted ± 5%, ± 10% and ± 15% deviation ranges from prediction. Points correspond to temperature analysis, so are represented nanofluids at different temperatures.

At the end of this chapter, at Figure 97 is shown the behavior of nanofluids tested

at different temperatures compared to the own-made equation (2) used to predict

effective viscosity values; to get an idea about the validity of the mentioned expression

also are plotted some deviation ranges: ± 5%, ± 10% and ± 15%. It can be appreciated that

this estimation is not exact at all, since there are no points on the equation line, but is

useful if it is need to get estimation, seeing as most points are within ± 10% interval.

0,700

0,800

0,900

1,000

1,100

1,200

1,300

1,400

0,80 0,90 1,00 1,10 1,20 1,30

µ e

xper

ime

nta

l (cP

)

µ Joan (cP)

TI-EV-9

SI-LEV-9

Al-EV-9

TI-10-9

Al-13-9

Al2O3-Alfa_Aesar-9

CeO2-Alfa_Aesar-9

µ joan (X)

Joan (±15%)

Joan (±10%)

107

2.3.4. Sensitivity analysis for TPS method

Once all samples test are explained, now it is turn to analyze the sensitivity of the

measurements on thermal conductivity. It has been applied to one selected sample with

lower differences versus either Maxwell or UBHAM: SiO2 nanofluid from Levasil. In fact in

this part we wanted to check how sensitive the calculation background for TPS method is

affected by changing volumetric specific heat, normal specific heat and density. Then the

calculation in each case was repeated by changing those parameters, and in all case based

on the following figures the thermal conductivity calculated by TPS instrument was the

with (+/-) 5% of the values calculated by correct volumetric specific heat values.

Figure 98. Thermal conductivity analysis with specific heat (in volumetric units) variations.

Figure 99. Thermal conductivity analysis with specific heat variations.

0,5

0,55

0,6

0,65

0,7

0,75

0,8

0 0,1 0,2 0,3 0,4 0,5

k (W

/mK

)

Weight Conc.

Cv (+) 10%

Cv (-) 10%

Normal Values

NV (+/-) 5%

0,5

0,55

0,6

0,65

0,7

0,75

0,8

0 0,1 0,2 0,3 0,4 0,5

k (W

/mK

)

Weight Conc.

Cp (+) 10%

Cp (-) 10%

Normal Values

NV (+/-) 5%

108

Figure 100. Thermal conductivity analysis with specific heat variations.

At this charts is possible to see that with a cv variation consisting of plus minus

10% from normal values, it becomes a plus minus 5% range from normal values, and this

result is not good, it could be better, maybe around 1%. It occurs more or less the same

when cp variations are evaluated. Moreover, for ρ observed results show similar results

than the other comparisons.

0,5

0,55

0,6

0,65

0,7

0,75

0,8

0 0,1 0,2 0,3 0,4 0,5

Effe

ctiv

e t

he

rmal

co

nd

uct

ivit

y

Weight Conc.

ρ (+) 10%

ρ (-) 10%

Normal Values

NV (+/-) 5%

109

3. TEST SECTION

After analyzing and discussing thermo-physical properties of dispersions, is of

particular interest carry out some test in order to observe how they work in terms of heat

transfer while flowing through a pipe. As the main aim of this project consists of the study of

nanofluids behavior for microelectronics applications, an open flow loop using a micro-tube

has been built so that some samples would be tested.

Nanofluids chosen to work with the mentioned test section include one of the

dilutions used in thermal conductivity and viscosity experiments (ITN-Al2O3-13), given that this

sample has shown great results regarding to thermal conductivity. Moreover, other samples

were also employed to be analyzed.

3.1. Design

For the purpose indicated before, an open flow loop has been designed to

conduct several dilutions along a micro-tube in laminar flow conditions and,

subsequently, measure their heat transfer coefficients. To have an idea about this

assembly, a basic drawing is presented at Figure 101 and a picture is shown at Figure 102.

Differential pressure

transducer

DC Power

SupplyStorage

tank

Logger

Computer

Injection

syringes

Thermocouples

Clamp 1 Clamp 2TEST SECTION

Safety

system

Scale

Figure 101. Schematic representation of the experimental set-up.

110

Figure 102. Experimental set-up.

As can be seen through above pictures, some auxiliary components are required

to carry out the experiments in a proper way. First of all, as the principal goal is the

measurement of the heat transfer coefficient, a Direct Current power supply is needed to

warm up the pipe (heat is applied using two clamps, one at the beginning of the tube and

one more at the end); in this manner, after the passage of nanofluid it will be possible to

see how temperatures evolve along the micro-tube. In order to follow temperatures’

evolution, also different thermocouples (Figure 103) are distributed along the pipe.

Figure 103. Thermocouples used to measure temperatures along the test section.

On the other hand, pressure drop is an important parameter, since is related to

the needs of pumping (the more pressure is present the more strength is required to

make flowing nanofluid); for this reason a pressure transducer is used to measure the

111

pressure between inlet and outlet points. Another important unit to be cited is a logger

(measurement unit); since it is the instrument that allows converting observed signals into

data through a computer.

A double syringe injecting pump (Figure 104) is used to make flow advance

through the test section, and, given that is an open loop, at the end of the pipe there is a

plastic tube which conducts nanofluid to a storage tank. With the intention to measure

the real flow rate, that storage tank is placed on a scale; by the usage of software which

measures elapsed time and is connected to the scale, experimental flow rate will be

obtained.

Figure 104. Injecting pump consisting of two syringes.

By observing Figure 105 is possible to check that the micro-tube was well

insulated to reduce as much as possible the heat transfer loss. Furthermore, a Plexiglass

cover (Figure 2) is employed to cover the whole set-up to minimize temperature changes

in the environment.

Finally, it should be said that a temperature safety system was installed to control

the maximum temperature reached at the test section, because an excess increase of

temperature could provoke burning of the set-up, and it takes long time to prepare a new

one with the same features.

112

Figure 105. Insulated test section.

3.2. Operation

As was explained before, nanofluids are injected into the pipe using a Legato 200

KDScientific pump, which has a flow rate accuracy of ±0,35 %; furthermore, it can conduct

a flow rate from 5 pL/min to 215,803 mL/min. Moreover, the syringes have a 38 mm inner

diameter and the outer size is 40 mm; its length is 155 mm. Their volume capacity is 140

mL and the accuracy 5mL.

Once the nanofluid is pumped, it enters in the stainless steel test section. It

consists of an annular tube with a diameter of 0,50 mm, a thickness of 0,3 mm and a

length of 29,8 cm. The micro-tube is insulated thermally in order to reduce the heat loss

from the test section to the ambient. It is made of two Polyethylene foam layers

(Armaflex) with the following dimensions: width of 5 cm, a length of 28 cm and a

thickness of 1 cm. In addition to this, a support is positioned under the test section to

keep it straight. It has a rectangular shape with a length and a width of 28 cm and 5 cm

respectively.

113

T3

T5T7 T9T6 T8 T10 T11

T13

T12T4

30

2.15

3

1 1.5 2 3.72 3.72 3.72 3.72 3.72

T1 T2 T15

T16

Figure 106. Distribution of thermocouples on test section.

The set-up has an overall of 15 thermocouples; however, only 7 of these

thermocouples are used to record electrically warming part of the test section (using

Omega OB-101-1/2 glue, which is thermally conductive and electrical insulator).

Thermocouples are distributed at axial positions like it follows: the first one is attached at

the first cross connection between plastic tube which conducts liquid from syringe to pipe

and the beginning of the test section (T1); after that, first thermocouple (T3) on the test

section is between the entry and the first clamp (T4), concretely 0,5 cm before the clamp;

subsequently, next seven thermocouples are located on the heated stretch of the micro-

tube: T5 is situated 1 cm after clamp, the length between T5 and T6 is 1,5 cm and T7 is

attached 2 cm after T6; the other 4 thermocouples on the wall are distributed every 3,72

cm (T8, T9, T10 and T11); T12 is located at the second clamp and is also used for the

temperature safety system; like T3, thermocouple T13 is at a distance of 0,5 cm but, in

this case, after clamp, not before; last thermocouples are attached outside of test section,

since T2 measures temperature inside cross connection, while T14 and T15 measure

temperature of liquid which is coming out from the valve and is going to the storage tank.

The test section is attached to two double cross connections at both ends to

connect differential pressure transducer, and inlet and outlet tubing and thermocouples.

The dimensions of these plastic tubes are an outside diameter of 5 mm and a thickness of

2 mm.

The DC power supply provides a constant heat flux along the test section, so, the

test section is uniformly heated. The model of the heating unit is GW instek PSP-405. The

test section was heated taking in account previous studies [54], which recommended to

work with a current value of 5A and 3,89 V for voltage.

The differential pressure is measured by the PTX5062 pressure transducer from

UNIK 5000. This pressure transducer is attached to the micro-tube at both ends of it. The

pressure range goes from 0 to 2 bar differential and the accuracy of this device is up to

±0,08 bar.

114

Figure 107. Experimental set-up in 3D. Source: http://www.kth.se/itm/inst/energiteknik/forskning/ett/projekt/nanohex/measurements/htc/setup-1-1.291042.

The temperature and pressure measurements are recorded by the data

acquisition system (DAQ) and then, they are controlled by a computer program which

provides different diagrams of them. The model of this logger is Agilent 34970A.

An accurate scale, KERN FKB 16K0.05 balance with ±0,01 g accuracy , has been

used to measure the mass flow by the increase in mass. This balance has been connected

to the computer with this purpose.

3.3. Calculation procedure

In this chapter several steps are followed in order to obtain the parameters that

show the behavior of a nanofluid when working at the test section. First of all, some

thermo-physical properties are needed for the calculations, such as: thermal conductivity,

viscosity, specific heat and density. With these values is possible to deepen in heat

transfer performance and obtain the values of parameters regarding to transportation

behavior, as heat flux, convective heat transfer coefficient or Nusselt number.


115

Table 13. Test section parameters.

Outer diameter (D0) 0,8 mm

Inner diameter (Di) 0,5 mm

Length (L) 0,298 m

Thermal conductivity of the tube (Ktub) 13,3 W/mK

Table 14. Nanofluids' parameters.

Nanoparticle W (%) Cp,p

(kJ/kgK)

ρp

(kg/m3) Kp

(W/mK)

Ag < 1 0,765 3970 430

Al2O3 9 0,765 3970 27

SiC 9 0,715 3160 114

CeO2 10 0,6164 7216 6

When experiment is finished, new parameters can be achieved, mainly those that

correspond to heat transfer transportation. Their average values are calculated with

experimental data recorded from the stabilized region of the experiment, that is to say,

most of them are extracted from last 2-3 minutes of test, given that at the end of the

experiment was when experimental points were more stable. In order to understand

better the calculation steps, a flow chart is presented below.

116

Measured / Calculated Q, Tin, Tout, Twalls, ρ, cp, k, μ, V, I, ΔP, m

Calculate thermal and electrical power and heat loss

TcmQnfpmestherm **

IVQ elec *

100*_elec

electherm

Q

QQlossHeat

Calculate haverage over length of tube

Calculate friction factor and pressure drop

21**

*

2u

DL

P

fi

2

***32

D

uVLP

Calculate local flow temperature, h and Nu

p

iitherminf

cm

XDqTT

*

***"

_

fts

therm

TT

qh

_

'

_

"

exp

Maxwellnf

i

k

DhNu

,

exp *

LD

Qq

i

therm

therm**

"

1

1))1ln(1(*

***4

'

Lk

QTT

tub

thermtsts

Figure 108. Schematic calculation procedure.

117

3.3.1. Thermo-physical properties of nanofluids

In order to analyze the heat transfer performance on the test section some

properties of nanofluids are needed. In this way, the average fluid bulk temperature and

the difference temperature are required for later:

When these parameters (Tin and Tout are inlet and outlet temperatures

respectively) are calculated, another ones can be obtained according to previous studies [54], [55], such as density (ρf), viscosity (μf), thermal conductivity (kf) and specific heat (cp,f),

given that are also necessary for carrying out calculations. These correlation are used

when the base fluid is water, employing data belonging to Nist database; using their

values, next correlations have been obtained:

118

As the same way temperature average was essential to calculate properties of

fluid, volume concentration is indispensable so that to achieve values of nanofluids’

properties (V, W, ρp and ρf are respectively volume and weight concentration and

nanoparticle and base fluid densities):

With volume concentration is possible to do like before, namely, acquire specific

heat, viscosity, thermal conductivity and density values, though in this case regarding to

nanofluid:

Where k and μ from measurement ratio are:

119

3.3.2. Global value’s calculation

After calculating properties of nanofluids, it is possible to take out other

parameters which are also needed to achieve values for both heat transfer coefficient and

Nusselt number, such as expected thermal conductivity from Maxwell equation, the

velocity of the fluid while flowing through the test section and the viscosity calculated

from pressure drop (Maxwell correlation):

Where m is mass flow rate and other parameters have been explained previously.

With ΔP is pressure drop and other parameters have been explained before.

Afterwards, two non-dimensional numbers are indispensable to continue with the

stduy, they are Reynolds an Prandtl numbers:

120

Moreover, is convenient thermal power and thermal heat flux:

For finishing with this part, whose main aim consists of the achievement of the

convective heat transfer coefficient, is directly related with the temperatures in different

parts of the micro-tube. Consequently, both surface temperatures of the test section,

inner and outer, and also the fluid temperatures need to be calculated [54], [55]. However,

the outer surface temperature is already known by the thermocouples.

Figure 109. Ubication of used temperatures from micro-pipe.

As T_ts is measured through thermocouples attached on the wall, it is possible to

calculate both T’_ts and T_f like it follows by using Fourier’s heat conduction equation [55]

with the assumptions that the heat flux to the ambient equals zero and the tube acts as

an inner heat source:

121

Where:

Talking about temperature of fluid:

Finally, once these two temperatures are known it is easy to calculate both

convective heat transfer coefficient and Nusselt number:

However, it is recommended [54] to quantify the heat loss in terms of Q (W). For

this reason, more parameters are needed:

122

3.3.3. Local value’s calculation

This part of calculation procedure deals on local properties of the nanofluids, that

is to say, it leads to their properties in different specific points along the test section

(where thermocouples are attached). Consequently, as fluid temperature is not always

the same since it changes while flowing through the micro-tube, different values of h

coefficient will be achieved.

As is recommendable [55] to evaluate experimental values against any theoretical

expression, local values are compared to Shah’s equation. The starting conditions to

develop it are Reynolds and Prandtl numbers, length and inner diameter of the test

section, mass flow rate, thermal conductivity and specific heat of the fluid.

First, Shah’s equations have a dependency on x*.This parameter could be defined

as follows:

But this correlation doesn’t fit the independency on Reynolds number, so, 3.30

can be replaced by:

On the other hand, Nusselt is calculated through the following expression, which

changes depending on x* value:

123

3.3.4. Average value’s calculation

Although local values are important to study the behavior of nanofluids while

flowing through the test section, it is also transcendental to calculate an average of main

parameters, with the intention to get a mean of these factors for making comparisons:

For local calculation was only used Shah correlation to compare experimental

data to a theoretical model, but, in this case, according to previous studies on this field [55], it is recommended to use also Stephan’s expression. The starting conditions to obtain

these correlations are the Reynolds and Prandtl numbers, the length and the inner

diameter of the test section, the flow rate and the thermal conductivity and specific heat

of the fluid.

On the one hand, Shah predicted a correlation for hydrodynamically developed

and thermally developing laminar flow with constant wall heat flux. For that, it is used the

Graetz number, which is defined as:

Nevertheless, it depends directly on Reynolds number and consequently on the

viscosity. For this reason, the next equation is finally used:

And Nusselt number can be obtained by:

124

However, Stephan proposed another correlation for hydrodynamically and

thermally developing laminar flow with constant wall heat flux for the following

conditions:

And the equation is:

3.3.5. Friction factor calculation

The stable nature of nanofluids is essential in order to achieve homogeneous

suspensions to optimize their thermophysical properties, and that is done by the

achievement of successful synthesis processes [9]. But there is not only one specific

procedure to prepare them, as will be described later.

This is the last term being examined in the current chapter. To calculate friction

factor are needed: nanofluid velocity while flowing through the micro-pipe, test section

length, pressure drop, inner diameter and nanofluid’s density:

This experimental factor is compared to Darcy and Shah’s correlations. Darcy only

needs one starting condition (Re); nevertheless, Shah requires two more: length and inner

diameter of micro-tube:

125

On the other hand, Shah’s expression depends on a new parameter:

It has been pointed out that, given that X from (3.40) changes along the test

section, it occurs the same for variable ζ. In this direction, the final friction factor will be

the average of all these local friction factors.

3.4. Error analysis

Frequently, the result of an experiment will not be measured directly. Rather, it

will be calculated from several measured physical quantities. Because of that,

subsequently will be shown a way to determinate the errors of different parameters when

they depends on other measured variables. This development is done according to some

bibliography [57], which joins to different works [58], [59] with the intention to evince some

basic rules for error analysis.

It says that given one parameter, Z, obtained through two measured variables, A

and B, expressed like it follows:

Its error, called ΔZ, can be calculated by:

126

Then, supposing there are two measurements, A and B, and the final result is Z =

F(A, B) for some function F. If A and B are perturbed by ΔA and ΔB respectively, Z will be

perturbed by:

Combining these by the Pythagorean Theorem yields:

Once the general formula has been obtained, the different relation between A

and B (sum, subtraction, multiplication, division and so on) [57] to get Z value will lead to

several formulas derived from the main one (3.44):

127

After posing these equations, it is possible to deepen in the error analysis of each

parameter. But before that, the error values from measurement instruments will be

shown at the below table:

Table 15. Error values for different measured parameters.

Variable Error Error Value

Mass Δm ± 0.01 g

Diameter ΔD ± 0.00001 m

Pressure drop ΔP ± 0.08 bar

Temperature ΔT ± 0.08 ºC

Thermal conductivity Δk ± (2%) W/mK

Viscosity Δμ ± (5 %) kg/ms

Then, it is time to calculate error expression for the parameters are going to be

analyzed versus convective heat transfer coefficient and Nusselt number (including also

them). First of all will be taken out the errors of mass and volumetric flows:

For obtaining mass flow expression is known that:

And, assuming the error for time is negligible because we used software to record

the data and this software used the PC clock for recording:

As time for each measurement is one second:

128

For volumetric flow is clear that:

As done with time, density calculation is assumed to be accurate enough to

disregard its error. In fact, for density of base fluids (either water or ethylene glycol based

nanofluids) well accepted reference values are used; moreover, for nanoparticles also

widely accepted heat transfer references are used. Therefore the error for density

assumed to be very small and almost negligible. The same situation is valid for specific

heat.

After that, it is turn of velocity error; so, from its definition:

It could be seen it depends on the area, thereby taking in account equation (3.47):

As the first term of the equality is a constant, it has no error:

129

Here it is easy to see that firstly is needed error of squared diameter, which is

possible to obtain using equation (3.49):

Replacing this expression in that one belonging to area error:

Now, errors about mass flow and area are known, so expression of velocity error

can be developed. It should be pointed out that, first of all, will be acquired the product

between area and density, in order to facilitate the later calculation of velocity:

From this development can be derived a new rule: when a parameter is function

of a constant multiplying one variable, the error function will be the constant mentioned

cross the error of parameter. To understand it easily, it means:

After this parenthesis, it has to continue with the velocity expression:

Working with this expression will be obtained the following one:

130

Once velocity error is found, it is possible to get the expression regarding to

applied power:

Developing it will arrive to below equation for power error:

Afterwards, it is turn to convective heat transfer coefficient, calculated as it

follows:

As this equation has a lot of terms, the development will be divided in several

small steps. This process will be started by calculating the error of temperature

differences:

So:

131

Got temperature difference error, Y term error will be evaluated:

For X term analysis first should be taken in account the following expression

(using equation 3.55):

Now is possible to analyze X error employing rule belonging to equation (3.47):

Found ΔX and ΔY errors, convective heat transfer coefficient error is easy to

obtain through its general expression and combining it with equations (3.48), (3.59) and

(3.60):

132

Operating with the above expression will be reached the following one, which is

the definitive equation for convective heat transfer coefficient (W/mK) and will be called

as equation (3.61):

Given that Nusselt non-dimensional number is function of h coefficient, it can be

acquired its error equation through equation (3.61) and Table 1:

As was done for h coefficient, calculations are divided in different steps:

Once achieved error expression for Nusselt, Reynolds’ one is going to be

calculated:

133

After showing Reynolds’ formula, working with all previous rules showed above

and dividing its calculation in several stages:

Another parameter to calculate in this chapter is non-dimensional length X*. But

its error expression is really easy to obtain because of its definition:

As was said above, its error equation is easy to reach, given that all variables are

constants, except mass flow, which presents an error mentioned before. In this manner:

134

Friction factor is one of the variables which are used to plot graphs against a non-

dimensional parameter, such as Reynolds number. For this reason, its error is also

obtained:

Like some previous variables, is better to obtain friction factor error dividing its

development in different steps:

So, through equation (3.55):

Now, it is easy to achieve the final expression for friction factor error by means of

replacing terms on equation (3.65):

135

Once local errors have been got, average ones can be calculated, such as de

average value for both convective heat transfer coefficient and Nusselt number. First of

all haverage expression is like follows:

So, the error of each point, it means, local error corresponding to point 1, 2…until

7 is obtained through:

Thus, so that to get haverage error formula, all points from first to seventh have to

be taken in account. Moreover, rule of equation (3.45) is needed:

Since Nuaverage is calculated by means of haverage it is really easy to obtain its

corresponding equation:

136

By replacing in equation (3.62), haverage instead of h, it is easy to see that:

3.5. Results and discussions

First of all, is good to know the components of nanofluids that are going to be

used. Samples are going to be analyzed are not the same than those that were tested on

thermo-physical analysis. In this case, there is only one dispersion analyzed before, which

is ITN-Al2O3-13 9 w%. The other dilutions employ different nanoparticles than previously,

since for the current analysis nanoparticles such as Ag, CeO2 and SiC are used. Samples are

generally water based fluid, except two of them, which use a 50% mixture of ethylene

glycol (EG) and distilled water. Moreover, concentration varies from below 1 w% up to 12

w%, as be seen later. Consequently, a summary table is shown in order to explain a little

each nanofluid.

Table 16. Description of nanofluids used in this study.

Name Base Fluid Nanoparticles Company Concentration

Nanogap_Ag Distilled Water Ag Nanogap < 1 w%

ITN-Al2O3-13 Distilled Water Al2O3 ITNanovation 9 w%

SiC_DW Distilled Water Sic UBHAM 9 w%

CeO2-Antaria Distilled Water CeO2 Antaria 10 w%

Nanogap_PVP DW-EG - Nanogap -

SiC_ANL DW-EG SiC ANL 12 w%

For analyzing heat transfer behavior on the test section, convective heat transfer

coefficient and Nusselt number are evaluated for each nanofluid, besides friction factor.

The average value of h coefficient is represented against mass and volumetric flow,

velocity, pressure drop, pumping power and Reynolds number; on the other hand,

average value of Nusselt number will be plotted versus Reynolds number (the same for

friction factor), while its local values are examined in function of non-dimensional length.

Moreover, error bars are included for these graphs. For each nanofluid, comparison is

performed in different ways: based on constant Reynolds number, mass flow rate, inlet

velocity, volume flow rate, pumping power and pressure drop. Although the comparison

137

based on constant Reynolds might not reflect the proper and fair interpretation, because

the increase in heat transfer in the same Reynolds number is due to higher flow rate in

the system must be pumped to compensate the difference between Reynolds numbers

due to higher viscosity of nanofluids. The other ways of comparisons though in different

situations are fair enough to evaluate nanofluids behavior.

First nanofluid to be evaluated is Nanogap-Ag:

Figure 110. Convective heat transfer coefficient vs volumetric flow rate. Nanogap-Ag.

Figure 111. Convective heat transfer coefficient vs mass flow rate. Nanogap-Ag.

4500

5000

5500

6000

6500

7000

7500

8000

0,00 10,00 20,00 30,00

h (

W/m

^2K

)

Q (ml/min)

DW-2011-10-19

Nanogap_Ag

Water (+/-) 10%

4500

5000

5500

6000

6500

7000

7500

0,000 0,500 1,000 1,500

h (

W/m

^2K

)

m (kg/hr)

DW-2011-10-19

Nanogap_Ag

138

Figure 112. Convective heat transfer coefficient vs velocity. Nanogap-Ag.

Figure 113. Convective heat transfer coefficient vs pressure drop. Nanogap-Ag.

Figure 114. Convective heat transfer coefficient vs pumping power. Nanogap-Ag.

4500

5000

5500

6000

6500

7000

0,00 0,50 1,00 1,50 2,00 2,50

h (

W/m

^2K

)

V (m/s)

DW-2011-10-19

Nanogap_Ag

4500

5000

5500

6000

6500

7000

7500

0,000 0,200 0,400 0,600 0,800

h (

W/m

^2K

)

ΔP (bar)

DW-2011-10-19

Nanogap_Ag

4500

5000

5500

6000

6500

7000

7500

0,0 10,0 20,0 30,0

h (

W/m

^2K

)

P (mW)

DW-2011-10-19

Nanogap_Ag

139

Figure 115. Convective heat transfer coefficient vs Reynolds number. Nanogap-Ag.

In this case, this sample shows that, for a given value of mass and volumetric flow

rate, and also velocity, pressure drop and pumping power, it confers lower h coefficient

than its base fluid, which is distilled water; this is a bad point, given that Ag nanoparticles

did not improve properties of base fluid for this system and concentration. However,

analyzing graph 115 is possible to check that experimental values are quite similar, from a

theoretical point of view, although again there is no enhancement comparing to distilled

water.

Figure 116. Nusselt number vs Reynolds number. Nanogap-Ag.

4500

5000

5500

6000

6500

7000

7500

0 500 1000 1500

h (

W/m

^2K

)

Re (-)

DW-2011-10-19

Nanogap_Ag

Water (+/-) 10%

3,50

4,00

4,50

5,00

5,50

6,00

0 500 1000 1500

Nu

(-)

Re (-)

DW-2011-10-19

Nanogap_Ag

140

Figure 117. Nusselt number vs Reynolds number (with theoretical Shah and Stephan predictions). Nanogap-Ag.

Figure 118. Local Nusselt number vs non-dimensional length (Shah prediction is included). Nanogap-Ag, 19 mL/min test.

Figure 119. Local Nusselt number vs non-dimensional length (Shah prediction is included). Nanogap-Ag, 21 mL/min test.

0

1

2

3

4

5

6

0 200 400 600 800 1000 1200 1400

Nu

(-)

Re (-)

Nu,avg,Shah

Nu,avg,stephan

DW-2011-10-19

Nanogap_Ag

3,50

4,50

5,50

6,50

7,50

8,50

0,000 0,020 0,040 0,060 0,080

Nu

(-)

X*(-)

DW-2011-10-19, Q=19 ml/min, Re=1025

Nanogap_Ag, Q=19 ml/min, Re=955

Nu,local,Shah

3,50

4,50

5,50

6,50

7,50

8,50

9,50

0,000 0,020 0,040 0,060 0,080

Nu

(-)

X*(-)

DW-2011-10-19, Q=21 ml/min, Re=1083

Nanogap_Ag, Q=21 ml/min, Re=1052

Nu,local,Shah

141

The same occurs for Nu versus Re chart, experimental results belonging to

samples, nanofluid and base fluid, are quite close to each other, but without any

increment. This can also be observed at Figure 117, besides that most points couple in a

properly way to Shah and Stephan correlations. After that, at graphs 118 and 119, local

Nusselt numbers are evaluated against non-dimensional length for 19 and 21 mL/min and

it is clear that for local values Shah equation works well in order to predict experimental

data.

Figure 120. Friction factor vs Reynolds number (Darcy-Weisbach equation is included in order to modeling data). Nanogap-Ag.

A good point for this dilution is that follows Darcy equation very well.

Next sample to be evaluated is the one which showed the best properties on

thermo-physical analysis. By checking Figures 121, 122, 123, 124 and 125 it is clear that

for a determined value of mass and volumetric flow rate, and also velocity, pressure drop

and pumping power, nanofluid presents better qualities than its base fluid, distilled water

once more. It can be confirmed at h versus Re graph (Figure 126), where an enhancement

higher than 10 % is achieved regarding to the base fluid, for all experiments have been

carried out.

0,00000

0,05000

0,10000

0,15000

0,20000

0 500 1000 1500

f (-

)

Re (-)

DW-2011-10-19

Nanogap_Ag

f,Darcy

142

Figure 121. Convective heat transfer coefficient vs volumetric flow rate. ITN-Al-13-9w%.

Figure 122. Convective heat transfer coefficient vs mass flow rate. ITN-Al-13-9w%.

Figure 123. Convective heat transfer coefficient vs velocity. ITN-Al-13-9w%.

4500

5500

6500

7500

8500

9500

0,00 10,00 20,00 30,00 40,00

h (

W/m

^2K

)

Q (ml/min)

DW-2011-11-28

ITN_Al_13_9%

Water (+/-) 10%

ITN_Al_13_9%_2nd

4500

5500

6500

7500

8500

9500

0,000 0,500 1,000 1,500 2,000

h (

W/m

^2K

)

m (kg/hr)

DW-2011-11-28

ITN_Al_13_9%

ITN_Al_13_9%_2nd

4500

5500

6500

7500

8500

9500

0,00 1,00 2,00 3,00

h (

W/m

^2K

)

V (m/s)

DW-2011-11-28

ITN_Al_13_9%

ITN_Al_13_9%_2nd

143

Figure 124.Convective heat transfer coefficient vs pressure drop. ITN-Al-13-9w%.

Figure 125. Convective heat transfer coefficient vs pumping power. ITN-Al-13-9w%.

Figure 126. Convective heat transfer coefficient vs Reynolds number. ITN-Al-13-9w%.

4500

5500

6500

7500

8500

9500

0,0000 0,5000 1,0000

h (

W/m

^2K

)

ΔP (bar)

DW-2011-11-28

ITN_Al_13_9%

ITN_Al_13_9%_2nd

4500

5500

6500

7500

8500

9500

0,0 20,0 40,0 60,0

h (

W/m

^2K

)

P (mW)

DW-2011-11-28

ITN_Al_13_9%

ITN_Al_13_9%_2nd

4500

5500

6500

7500

8500

9500

0 500 1000 1500 2000

h (

W/m

^2K

)

Re (-)

DW-2011-11-28

ITN_Al_13_9%

Water (+/-) 10%

ITN_Al_13_9%_2nd

144

On Nu versus Re chart a great increment is also obtained (Figure 127), for this

reason at the moment to compare to Shah and Stephan theoretical predictions nanofluid

experimental points overcome them (Figure 128). At Figures 129 and 130 local Nusselt

data exceeds the Shah prediction, as the same way that occurred for the average values.

Figure 127. Nusselt number vs Reynolds number. ITN-Al-13-9w%.

Figure 128. Nusselt number vs Reynolds number (with theoretical Shah and Stephan predictions). ITN-Al-13-9w%.

3,50

4,00

4,50

5,00

5,50

6,00

6,50

7,00

0 500 1000 1500 2000

Nu

(-)

Re (-)

DW-2011-11-28

ITN_Al_13_9%

ITN_Al_13_9%_2nd

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

0 500 1000 1500 2000

Nu

(-)

Re (-)

Nu,avg,Shah

Nu,avg,stephan

DW-2011-11-28

ITN_Al_13_9%

ITN_Al_13_9%_2nd

145

Figure 129. Local Nusselt number vs non-dimensional length (Shah prediction is included). ITN-Al-13-9w%, 9 mL/min test.

Figure 130. Local Nusselt number vs non-dimensional length (Shah prediction is included). ITN-Al-13-9w%, 11 mL/min test.

Figure 131. Friction factor vs Reynolds number (Darcy-Weisbach equation is included in order to modeling data). ITN-Al-13-9w%.

3,00

4,00

5,00

6,00

7,00

0,000 0,050 0,100 0,150

Nu

(-)

X*(-)

DW-2011-11-28, Q=9 ml/min, Re=486

ITN_Al_13_9%, Q=9 ml/min, Re=497

Nu,avg,Shah

ITN_Al_13_9%_2nd, Q=9 ml/min, Re=494

3,50

4,50

5,50

6,50

7,50

0,000 0,050 0,100 0,150

Nu

(-)

X*(-)

DW-2011-11-28, Q=11 ml/min, Re=584

ITN_Al_13_9%, Q=11 ml/min, Re=582

Nu,avg,Shah

ITN_Al_13_9%_2nd, Q=11 ml/min, Re=585

0,00000

0,02000

0,04000

0,06000

0,08000

0,10000

0,12000

0,14000

0,16000

0,18000

0,20000

0 500 1000 1500 2000

f (-

)

Re (-)

DW-2011-11-28

ITN_Al_13_9%

f,Darcy

ITN_Al_13_9%_2nd

146

A good point for this alumina dilution is that experimental data for friction factor

fits really well to Darcy prediction.

The following nanofluid contains silicon carbide nanoparticles diluted on distilled

water:

Figure 132. Convective heat transfer coefficient vs volumetric flow rate. SiC-DW-9%-UBHAM.

Figure 133. Convective heat transfer coefficient vs mass flow rate. SiC-DW-9%-UBHAM.

4500

5500

6500

7500

8500

0,00 10,00 20,00 30,00 40,00

h (

W/m

^2K

)

Q (ml/min)

DW-2011-12-14

SiC_DW_9%_UBHAM

Water (+/-) 10%

5000

5500

6000

6500

7000

7500

8000

0,000 0,500 1,000 1,500 2,000

h (

W/m

^2K

)

m (kg/hr)

DW-2011-12-14

SiC_DW_9%_UBHAM

147

Figure 134. Convective heat transfer coefficient vs velocity. SiC-DW-9%-UBHAM.

Figure 135. Convective heat transfer coefficient vs pressure drop. SiC-DW-9%-UBHAM.

Figure 136. Convective heat transfer coefficient vs pressure drop. SiC-DW-9%-UBHAM.

5000

5500

6000

6500

7000

7500

8000

0,00 1,00 2,00 3,00

h (

W/m

^2K

)

V (m/s)

DW-2011-12-14

SiC_DW_9%_UBHAM

5000

5500

6000

6500

7000

7500

8000

0,000 0,500 1,000 1,500

h (

W/m

^2K

)

ΔP (bar)

DW-2011-12-14

SiC_DW_9%_UBHAM

5000

5500

6000

6500

7000

7500

8000

0,0 20,0 40,0 60,0

h (

W/m

^2K

)

P (mW)

DW-2011-12-14

SiC_DW_9%_UBHAM

148

Figure 137. Convective heat transfer coefficient vs Reynolds number. SiC-DW-9%-UBHAM.

By checking Figures 132, 133, 134, 135 and 136 it is clear that for a determined

value of mass and volumetric flow rate, and also velocity, pressure drop and pumping

power, nanofluid presents better qualities than its base fluid, except for the case of

pressure drop, which results of both samples are really similar. It should be pointed out

that these increments are smaller than for the previous case. However, when analyzing h

versus Reynolds number graph the enhancement comparing to base fluid is higher than

ITN-Al-13-9w%. This is because of higher relative viscosity compared with the previous

case.

Figure 138. Nusselt number vs Reynolds number. SiC-DW-9%-UBHAM.

4500

5000

5500

6000

6500

7000

7500

8000

8500

0 500 1000 1500 2000

h (

W/m

^2K

)

Re (-)

DW-2011-12-14

SiC_DW_9%_UBHAM

Water (+/-) 10%

3,50

4,00

4,50

5,00

5,50

6,00

6,50

0 500 1000 1500 2000

Nu

(-)

Re (-)

DW-2011-12-14

SiC_DW_9%_UBHAM

149

Figure 139. Nusselt number vs Reynolds number (with theoretical Shah and Stephan predictions). SiC-DW-9%-UBHAM.

Figure 140. Local Nusselt number vs non-dimensional length (Shah prediction is included). SiC-DW-9%-UBHAM, 11 mL/min test.

Figure 141. Local Nusselt number vs non-dimensional length (Shah prediction is included). SiC-DW-9%-UBHAM, 13 mL/min test.

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

0 500 1000 1500

Nu

(-)

Re (-)

Nu,avg,Shah

Nu,avg,stephan

DW-2011-12-14

SiC_DW_9%_UBHAM

3,50

4,00

4,50

5,00

5,50

6,00

6,50

7,00

7,50

0,000 0,050 0,100

Nu

(-)

X*(-)

DW-2011-12-14, Q=11 ml/min, Re=592

SiC_DW_9%_UBHAM, Q=11 ml/min, Re=281

Nu,local,Shah

3,50

4,00

4,50

5,00

5,50

6,00

6,50

7,00

7,50

8,00

0,000 0,020 0,040 0,060 0,080 0,100 0,120

Nu

(-)

X*(-)

DW-2011-12-14, Q=13 ml/min, Re=663

SiC_DW_9%_UBHAM, Q=13 ml/min, Re=325

Nu,local,Shah

150

Analyzing average of Nusselt number is clear that enhancement observed when

comparing h coefficient to Re has remained. For this reason, points belonging to

experimental data are above the prediction lines of both Shah and Stephan. Nevertheless,

for local Nusselt evaluation, obtained results fit better to the theoretical equation, as can

be observed at Figures 139 and 140, because for low flow rates this theoretical prediction

works better for this nanofluid.

Figure 142. Friction factor vs Reynolds number (Darcy-Weisbach equation is included in order to modeling data). SiC-DW-9%-UBHAM.

This is the first time that a nanofluid doesn’t couple in a properly way to Darcy

equation, given that for the same Reynolds number, friction factor is lower than expected

for this prediction and also than obtained data for distilled water.

This cerium oxide nanofluid dispersed in distilled water is similar to the last

sample has been studied, since presents more than 10% enhancement on h coefficient

when comparing this parameter to Reynolds number. But, seeing at graphs regarding to

mass and volumetric flow rate, pressure drop and pumping power against h coefficient, it

is easy to appreciate that nanofluid’s data is closer than the prior dilution, above all when

high flow rates are evaluated.

0,00000

0,05000

0,10000

0,15000

0,20000

0 500 1000 1500 2000

f (-

)

Re (-)

DW-2011-12-14

SiC_DW_9%_UBHAM

f,Darcy

151

Figure 143. Convective heat transfer coefficient vs volumetric flow rate. CeO2-Antaria.

Figure 144. Convective heat transfer coefficient vs mass flow rate. CeO2-Antaria.

Figure 145. Convective heat transfer coefficient vs velocity. CeO2-Antaria.

4500

5500

6500

7500

8500

9500

0,00 10,00 20,00 30,00 40,00

h (

W/m

^2K

)

Q (ml/min)

DW-2011-11-30

CeO2-Antaria

Water (+/-) 10%

CeO2-Antaria_2nd

4500

5500

6500

7500

8500

0,000 0,500 1,000 1,500 2,000

h (

W/m

^2K

)

m (kg/hr)

DW-2011-11-30

CeO2-Antaria

CeO2-Antaria_2nd

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000

0,00 1,00 2,00 3,00

h (

W/m

^2K

)

V (m/s)

DW-2011-11-30

CeO2-Antaria

CeO2-Antaria_2nd

152

Figure 146. Convective heat transfer coefficient vs pressure drop. CeO2-Antaria.

Figure 147. Convective heat transfer coefficient vs pumping power. CeO2-Antaria.

Analyzing average of Nusselt number is clear that enhancement observed when

comparing h coefficient to Re has remained. For this reason, points belonging to

experimental data are above the prediction lines of both Shah and Stephan. Nevertheless,

for local Nusselt evaluation, obtained results fit better to the theoretical equation, as can

be observed at Figures 150 and 151, although data couple better for the case of 9 mL/min

than for 11 mL/min.

4500

5500

6500

7500

8500

0,0000 0,5000 1,0000 1,5000

h (

W/m

^2K

)

ΔP (bar)

DW-2011-11-30

CeO2-Antaria

CeO2-Antaria_2nd

4500

5500

6500

7500

8500

0,0 20,0 40,0 60,0

h (

W/m

^2K

)

P (mW)

DW-2011-11-30

CeO2-Antaria

CeO2-Antaria_2nd

153

Figure 148. Nusselt number vs Reynolds number. CeO2-Antaria.

Figure 149. Nusselt number vs Reynolds number (with theoretical Shah and Stephan predictions). CeO2-Antaria.

Figure 150. Local Nusselt number vs non-dimensional length (Shah prediction is included). CeO2-Antaria, 9 mL/min test.

3,50

4,00

4,50

5,00

5,50

6,00

6,50

7,00

0 500 1000 1500 2000

Nu

(-)

Re (-)

DW-2011-11-30

CeO2-Antaria

CeO2-Antaria_2nd

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

0 500 1000 1500 2000

Nu

(-)

Re (-)

Nu,avg,Shah

Nu,avg,stephan

DW-2011-11-28

ITN_Al_13_9%

ITN_Al_13_9%_2nd

3,00

3,50

4,00

4,50

5,00

5,50

6,00

6,50

7,00

7,50

0,000 0,050 0,100 0,150

Nu

(-)

X*(-)

DW-2011-11-30, Q=9 ml/min, Re=491

CeO2-Antaria, Q=9 ml/min, Re=322

Nu,local,Shah

CeO2-Antaria_2nd

154

Figure 151. Local Nusselt number vs non-dimensional length (Shah prediction is included). CeO2-Antaria, 11 mL/min test.

Contrarily to before nanofluid, now friction factor belonging to experimental data

from test section fit really well with Darcy equation, as can be seen at the next graph:

Figure 152. Friction factor vs Reynolds number (Darcy-Weisbach equation is included in order to modeling data). CeO2-Antaria.

Now is going to be studied the effect of adding a surfactant to the base fluid,

which, in this case, is a 50% mixture of distilled water and ethylene glycol:

3,50

4,00

4,50

5,00

5,50

6,00

6,50

7,00

7,50

8,00

0,000 0,050 0,100 0,150

Nu

(-)

X*(-)

DW-2011-11-30, Q=11 ml/min, Re=594

CeO2-Antaria, Q=11 ml/min, Re=385

Nu,local,Shah

CeO2-Antaria_2nd

0,00000

0,05000

0,10000

0,15000

0,20000

0 500 1000 1500 2000

f (-

)

Re (-)

DW-2011-11-30

CeO2-Antaria

f,Darcy

CeO2-Antaria_2nd

155

Figure 153. Convective heat transfer coefficient vs volumetric flow rate.

Figure 154. Convective heat transfer coefficient vs mass flow rate.

Figure 155. Convective heat transfer coefficient vs velocity.

3000

3500

4000

4500

5000

5500

0,00 10,00 20,00 30,00

h (

W/m

^2K

)

Q (ml/min)

DW_EG_50%

NanoGap_DW_EG_50%_PVP

DW_EG_50% (+/-) 10%

3000

3500

4000

4500

5000

0,000 0,500 1,000 1,500

h (

W/m

^2K

)

m (kg/hr)

DW_EG_50%


3000

3500

4000

4500

5000

0,00 0,50 1,00 1,50 2,00

h (

W/m

^2K

)

V (m/s)

DW_EG_50%


156

Figure 156. Convective heat transfer coefficient vs pressure drop.

Figure 157. Convective heat transfer coefficient vs pumping power.

Figure 158. Convective heat transfer coefficient vs Reynolds number.

3000

3500

4000

4500

5000

0,000 0,500 1,000 1,500 2,000

h (

W/m

^2K

)

ΔP (bar)

DW_EG_50%


3000

3500

4000

4500

5000

0,0 20,0 40,0 60,0

h (

W/m

^2K

)

P (mW)

DW_EG_50%


3000

3500

4000

4500

5000

5500

0 100 200 300 400

h (

W/m

^2K

)

Re (-)

DW_EG_50%


DW_EG_50% (+/-) 10%

157

It can be observed that in the cases of graphs from 153 until 157, the fact of

adding this surfactant is detrimental to heat transfer performance improvement;

however, as happened in some previous cases, when graph between h coefficient and

Reynolds number is analyzed, it is clear that data belonging to both samples is quite

similar, so there is no enhancement because of the surfactant.

Figure 159. Nusselt number vs Reynolds number.

Figure 160. Nusselt number vs Reynolds number (with theoretical Shah and Stephan predictions).

4,00

4,50

5,00

5,50

6,00

0 100 200 300 400

Nu

(-)

Re (-)

DW_EG_50%


0,00

1,00

2,00

3,00

4,00

5,00

6,00

0 100 200 300 400

Nu

(-)

Re (-)

Nu,avg,Shah

Nu,avg,stephan

DW_EG_50%


158

Figure 161. Local Nusselt number vs non-dimensional length (Shah prediction is included). Surfactant analysis, 13 mL/min test.

Figure 162. Local Nusselt number vs non-dimensional length (Shah prediction is included). Surfactant analysis, 15 mL/min test.

As the same way than h coefficient, at Figure 159, where Nusselt number

evolution is analyzed against Reynolds number, there is no increment derived from the

use of the surfactant, since data of both samples is quite similar to each other. Moreover,

studying the comparisons to theoretical prediction it could be said that data fit well to

them in both cases, local and average values.

3,50

4,00

4,50

5,00

5,50

6,00

6,50

7,00

7,50

8,00

8,50

0,000 0,020 0,040 0,060 0,080 0,100

Nu

(-)

X*(-)

DW_EG_50%, Q=13 ml/min, Re=223

NanoGap_DW_EG_50%_PVP, Q=13 ml/min, Re=212

Nu,local,Shah

3,50

4,50

5,50

6,50

7,50

8,50

0,000 0,020 0,040 0,060 0,080

Nu

(-)

X*(-)

DW_EG_50%, Q=15 ml/min, Re=252

NanoGap_DW_EG_50%_PVP, Q=15 ml/min, Re=234

Nu,local,Shah

159

Figure 163. Friction factor vs Reynolds number (Darcy-Weisbach equation is included in order to modeling data). Surfactant analysis.

This is second time that a nanofluid doesn’t couple in a proper way to Darcy

equation, given that for the same Reynolds number, friction factor is lower than expected

for this prediction and also than obtained data for distilled water.

Last nanofluid to be studied is using as a base fluid a 50% mixture of distilled

water and ethylene glycol and contains silicon carbide nanoparticles:


0,15000

0,20000

0,25000

0,30000

0,35000

0,40000

0 100 200 300 400

f (-

)

Re (-)

DW_EG_50%


f,Darcy

2000

2500

3000

3500

4000

4500

5000

0,00 5,00 10,00 15,00 20,00

h (

W/m

^2K

)

Q (ml/min)

DW-EG-KTH

SiC-ANL

BF (+/-) 10%

160


Figure 166. Convective heat transfer coefficient vs velocity.

Figure 167. Convective heat transfer coefficient vs pressure drop.

2000

2500

3000

3500

4000

4500

5000

0,000 0,500 1,000 1,500

h (

W/m

^2K

)

m (kg/hr)

DW-EG-KTH

SiC-ANL

2000

2500

3000

3500

4000

4500

5000

0,00 0,50 1,00 1,50

h (

W/m

^2K

)

V (m/s)

DW-EG-KTH

SiC-ANL

2000

2500

3000

3500

4000

4500

5000

0,00 0,50 1,00 1,50

h (

W/m

^2K

)

ΔP (bar)

DW-EG-KTH

SiC-ANL

161

Figure 168. Convective heat transfer coefficient vs pumping power.

Figure 169. Convective heat transfer coefficient vs Reynolds number.

This sample shows a similar behavior to ceria and alumina nanofluids, given that

for mass and volumetric flow rates, velocity, pressure drop and pumping power points

belonging to nanofluid show higher h coefficient than its base fluid Figures 164, 165, 166,

167 and 168). The same occurs for comparison between heat transfer coefficient and

Reynolds number (Figure 169) since nanofluid presents an increment above 10 % from

base fluid data.

2000

2500

3000

3500

4000

4500

5000

0,0 10,0 20,0 30,0

h (

W/m

^2K

)

P (mW)

DW-EG-KTH

SiC-ANL

2000

2500

3000

3500

4000

4500

5000

0 50 100 150 200

h (

W/m

^2K

)

Re (-)

DW-EG-KTH

SiC-ANL

BF (+/-) 10%

162

Figure 170. Nusselt number vs Reynolds number.

Figure 171. Nusselt number vs Reynolds number (with theoretical Shah and Stephan predictions).

Figure 172. Local Nusselt number vs non-dimensional length (Shah prediction is included). SiC-ANL, 9 mL/min test.

3,00

3,50

4,00

4,50

5,00

5,50

0 50 100 150 200

Nu

(-)

Re (-)

DW-EG-KTH

SiC-ANL

0,00

1,00

2,00

3,00

4,00

5,00

6,00

0 50 100 150 200

Nu

(-)

Re (-)

Nu,avg,Shah

Nu,avg,stephan

DW-EG-KTH

SiC-ANL

3,50

4,00

4,50

5,00

5,50

6,00

6,50

7,00

7,50

8,00

0,000 0,050 0,100

Nu

(-)

X*(-)

DW-EG-KTH , Q=9 ml/min, Re=127

SiC-ANL, Q=9 ml/min, Re=123

Nu,avg,Shah

163

Figure 173. Local Nusselt number vs non-dimensional length (Shah prediction is included). SiC-ANL, 9 mL/min test.

Analyzing average of Nusselt number is clear that nanofluid doesn’t improve te

behavior of its base fluid. For this reason, points belonging to experimental data are really

close to the prediction lines of both Shah and Stephan. In this direction, for local Nusselt

evaluation, obtained results fit quite well to the theoretical equation, as can be observed

at Figures 172 and 173, although data couple better for the case of 9 mL/min than for 11

mL/min.

Figure 174. Friction factor vs Reynolds number (Darcy-Weisbach equation is included in order to modeling data). Surfactant analysis.

As occurred in the previous sample analysis, nanofluid doesn’t couple in a proper

way to Darcy equation, given that for the same Reynolds number, friction factor is lower

than expected for this prediction and also than obtained data for distilled water.

3,50

4,50

5,50

6,50

7,50

8,50

0,000 0,020 0,040 0,060 0,080 0,100

Nu

(-)

X*(-)

DW-EG-KTH , Q=11 ml/min, Re=143

SiC-ANL, Q=11 ml/min, Re=139

Nu,avg,Shah

0,00000

0,10000

0,20000

0,30000

0,40000

0,50000

0,60000

0,70000

0,80000

0 50 100 150 200

f (-

)

Re (-)

DW-EG-KTH

SiC-ANL

f,Darcy

164

4. CONCLUSIONS

Once all the work has been presented and analyzed, some conclusions can be pointed

out from this thesis:

- Maxwell predicts relative thermal conductivity values with a ± 10% deviation.

- By increasing concentration thermal conductivity is enhanced.

- Absolute thermal conductivity increases with temperature.

- Krieger equation models aggregation effect, though underestimates a little

viscosity, but predict viscosity ratio for nanofluids within ± 15% error.

- Al2O3, CeO2 and SiC nanofluids show good results in heat transfer performance at

test section.

- SiC nanofluids and base fluids consisting of DW-EG-50% mixtures did not

correlated well with friction factor predicted by Darcy equation.

Moreover, it could be a good idea to propose some future works in order to continue

analyzing on this field, such as the following ones:

- Go farther in temperature influence on thermophysical properties of nanofluids.

- Evaluate h coefficient and Nu enhancements against the cost of using nanofluids in

order to study the economic efficiency.

- For weight concentration effect analysis, compare improvements on thermal

conductivity versus penalties on viscosity.

- Deepen on cerium oxide nanofluids heat transfer behavior.

- Analyze the influence of production method and particle size of nanofluids

(including aggregation effect).

165

166

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