Heat and Mass Transfer in Tray Drying - Tiffany Robinson · Heat and Mass Transfer in Tray Drying Group # 11: Sami Marchand ... “Fundamentals of Momentum, Heat, and Mass Transfer.”

10/8/2014 LOUISIANA STATE UNIVERSITY 1

Heat and Mass Transfer in Tray Drying

Group # 11: Sami Marchand (GL), Chase Kairdolf (WR),

Tiffany Robinson (OR)

Instructor: Dr. Wetzel

Objective: The objective of this experiment is to exhibit how

accurately the theory of heat and mass transfer matches the

practice of drying used coffee grounds in a tray dryer.

Heat Transfer


Mass Transfer


The Drying Process

Settling period

Constant rate

Falling rate

Time

Moisture

Content

[1] “Air Drying” available via http://www.nzifst.org.nz/unitoperations/drying5.htm [Retrieved 9-22-2014.]

[1]

http://www.nzifst.org.nz/unitoperations/drying5.htm

• The exchange of energy between a surface

and an adjacent fluid. [5]

Forced convection- an external agent forces a

fluid to flow past a solid surface


Heat Transfer

[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat, and Mass Transfer.” Fifth

ed., Wiley, (2008).

Heat Transfer Theoretical Calculations



ed., Wiley, (2008).

ℎ =𝑘

𝐿0.664𝑅𝑒1/2𝑃𝑟1/3

𝑁𝑢𝐿 =ℎ𝐿

𝑘= 0.664𝑅𝑒𝐿

1/2𝑃𝑟1/3 [5]

Heat Transfer Expectations


ℎ =𝑘

𝐿0.664𝑅𝑒1/2𝑃𝑟1/3

[5]


ed., Wiley, (2008).

Heat Transfer Equation


ℎ =𝑞

2𝐴Δ𝑇

ℎ= convective heat transfer coefficient in 𝑊

𝑚2𝐾

𝑞= rate of heat transfer in 𝑊

𝐴= heat transfer area in 𝑚2

Δ𝑇= temperature gradient between surface and fluid in 𝐾


ed., Wiley, (2008).

[5]

Heat Transfer Equation


ℎ =𝑞

2𝐴Δ𝑇

ℎ= convective heat transfer coefficient in 𝑊

𝑚2𝐾

𝑞= rate of heat transfer in 𝑊

𝐴= heat transfer area in 𝑚2

Δ𝑇= temperature gradient between surface and fluid in 𝐾

𝑞 =Δ𝑚𝛌𝑣

𝑡

Δ𝑚= change in mass in 𝑔

𝛌𝑣= heat of vaporization in 𝐽

𝑔

𝑡= time in 𝑠

[5]


ed., Wiley, (2008).

• Convective mass transfer is the transport of

material between boundary surface and a

moving fluid. [5]


Mass Transfer


ed., Wiley, (2008).

Mass Transfer Theoretical Calculations


𝑘𝑐 = 0.664𝐷𝐴𝐵𝐿

𝑅𝑒1/2𝑆𝑐1/3

[5]

𝑆ℎ𝐿 =𝑘𝑐𝐿

𝐷𝐴𝐵= 0.664𝑅𝑒𝐿

1/2𝑆𝑐1/3


ed., Wiley, (2008).

𝑘𝑐 = 0.664𝐷𝐴𝐵𝐿

𝑅𝑒1/2𝑆𝑐1/3

Mass Transfer Expectations


[5]


ed., Wiley, (2008).


𝑘𝑐 =𝑚

𝐴 𝐶𝐴𝑆 − 𝐶𝐴∞ 𝑘𝑐= convective mass transfer coefficient in

𝑚

𝑠

𝑚 = rate of mass transfer in 𝑘𝑔 𝐻2𝑂

𝑠

𝐴= mass transfer area in 𝑚2

𝐶𝐴𝑆= concentration of water at the surface in 𝑘𝑔 𝐻2𝑂

𝑚3

𝐶𝐴∞= concentration of water in the bulk stream in 𝑘𝑔 𝐻2𝑂

𝑚3

[5]

Mass Transfer Equation


ed., Wiley, (2008).



𝑘𝑐 =𝑚


𝑚

𝑠


𝑠



𝑚3


𝑚3

[5]

𝐶𝐴𝑆 =𝑃𝐴𝑅𝑇

𝑃𝐴= vapor pressure of water in 𝑃𝑎

𝑅= gas constant in 𝑃𝑎∗𝑚3

𝑘𝑔 𝐻2𝑂∗𝐾

𝑇= temperature of water in 𝐾


𝑘𝑐 =𝑚


𝑚

𝑠


𝑠



𝑚3


𝑚3

[5]

𝐶𝐴𝑆 =𝑃𝐴𝑅𝑇

𝐶𝐴∞ = ℎ𝐴𝜌𝑎𝑖𝑟

ℎ𝐴= moisture content in 𝑘𝑔 𝐻2𝑂

𝑘𝑔 𝑑𝑟𝑦 𝑎𝑖𝑟

𝜌𝑎𝑖𝑟= density of air in 𝑘𝑔 𝑑𝑟𝑦 𝑎𝑖𝑟

𝑚3

𝑃𝐴= vapor pressure of water in 𝑃𝑎

𝑅= gas constant in 𝑃𝑎∗𝑚3


𝑇= temperature of water in 𝐾

[2]

[2] Felder, R. M., and R. W. Rousseau, “Elementary Principles of Chemical Processes,” Third ed., Wiley,

(2005).


Experiment


Velocity 0.5

𝑚

𝑠 (low)

1.45 𝑚

𝑠 (high)

Heat Supply 1000 𝑊 (low)

2500 𝑊 (high)


Heat Transfer Results

• Experimental results 1.6

times larger than theory

• Uncertainty propagation

ranged from 35-55%

• Temperature not constant

over tray

Heat Transfer Results


At a 95% confidence interval Nusselt and

Reynolds do not correlate

Flat Plate Correlation Experimental

Log(Nu) = -1.57 + 1.06*Log(Re)

Flat Plate Correlation Theoretical

Log(Nu) = -0.226 + 0.499*Log(Re)

Mass Transfer Results


• Experimental results 1.2

times larger than theory

• Uncertainty propagation

ranged from 33-51%

• Temperature not constant

over tray

Mass Transfer Results


At a 95% confidence interval Sherwood and

Reynolds do not correlate

Flat Plate Correlation Experimental

Log(Sh) = -0.858 + 0.737*Log(Re)

Flat Plate Correlation Theoretical

Log(Sh) = -0.190 + 0.4867*Log(Re)

Confidence Intervals


Experimental

Theoretical

Corrections for Inconsistencies


A B C D E

Top View


jD = mass transfer

jH = heat transfer

Effect of Parameters


Heat Transfer Mass Transfer

All parameters are significant

Conclusion The practice of drying used coffee grounds in a

convective tray dryer does not accurately adhere to the

theory of heat and mass transfer based on our results.


References [1] “Air Drying” available via http://www.nzifst.org.nz/unitoperations/drying5.htm

[Retrieved 9-22-2014.]

[2] Felder, R. M., and R. W. Rousseau, “Elementary Principles of Chemical

Processes,” Third ed., Wiley, (2005).

[3] McCabe, W. L., J. C. Smith, and P. Harriott, “Unit Operations of Chemical

Engineering.” Seventh ed., McGraw-Hill, (2005).

[4] “The Performance of a Tray Dryer” available via http://www-

unix.ecs.umass.edu/~rlaurenc/che401/stations/dryer/drying.html [Retrieved 9-29-

2014.]

[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat,

and Mass Transfer.” Fifth ed., Wiley, (2008).


http://www.nzifst.org.nz/unitoperations/drying5.htm

http://www-unix.ecs.umass.edu/~rlaurenc/che401/stations/dryer/drying.html



Appendix Contents • Appendix I

– Raw data (H/H, L/H, L/L, H/L)

• Appendix II

– Dimensionless groups

• Appendix III

– Design of experiment

• Appendix IV

– Values of constants

• Appendix V

– Values of heat/mass transfer coefficients

• Appendix VI

– Side by side confidence plots


Appendix I Raw Data for High_High


High/High 1.45 m/s 2500W

Time (min) Mass (g) T1(°C) T2(°C) T3(°C) T4(°C) T ∞ (°C) T wet bulb (°F)T dry bulb (°F)

0 1518.1 24.8 24.7 23.8 24.8 23.3

5 1512.3

10 1506.2 26.1 26.3 24.8 27.2

15 1501.1

20 1495.3 26.4 26.2 25.4 27.3

25 1489.7

30 1483.6 25.6 26.4 25.4 27.3 27.4 68 76

35 1477.4

40 1470.8 27.4 27.5 25.9 27.7

45 1465.6

50 1459.7 28.4 26.7 25.6 27

55 1453.4

60 1447.3 28.9 27.2 25.5 27.8 27.5

65 1440.3

70 1434.2 28.1 26.3 26.1 27.5 29

75 1428.9

55 66.4 Averages 27.46667 26.71667 25.65 27.43333 26.8 68 76

SLOPE 1.207273 Tray Ave. 26.81667

Appendix Contents

Appendix I Raw Data for High_High Continued


Run 1 (1.45 m/s) 2500 W 1.45 2500 W Heat of Vaporization (J/g) 2435 1046.99

T wet (F/C) 68 20.00 80 1048.3

T dry (F/C) 76 24.44 85 1045.5

Vapor pressure water at 26.8C (mmHg) 26.45398932 T infinity (average of constant drying) 27.96666667 82.34

Vapor pressure water at 26.8C (Pascals) 3526.90851 T surface (average of constant drying) 26.81666667 80.27

Ca inf (kg mois/m^3) 0.01560 0.0133

Cas (kg mois/m^3)) 0.02546 P/RT Specific Heat, cp (J/kg K) 1006.356

300 1006.3

Density of air 1.173 301.1166667 320 1007.3

300 1.1769 dynamic viscosity (Pa s) 0.00001851576

320 1.1032 300 0.000018464

320 0.000019391

change in mass (g/min) 1.207272727 k conductivity (W/m K) 0.0263262625

constant drying region starts at 20 minutes 300 0.02624

320 0.027785

kinematic viscosity air (m^2/s) 0.00001579441 Prandtl number 0.708

300 0.000015689

320 0.000017577

301.1166667

Reynolds number 35344.776

Diffusivity (m2/s) 0.00002573818

Scmidt number 0.614

Linear Interpolation

Slope of line

Antoine's

Appendix Contents

Appendix I Raw Data for High_High Continued


h k Re Nu Sh

7.60724 0.007092 Theoretical 35345 111.2496 106.0814

194.1814 0.0186 Experimental 35345 2839.743 278.2268

jH jD

Theoretical 0.00353 0.003532

Experimental 0.090117 0.009263

Chilton-Colburn Analogy

Heat and Mass Transfer Coefficients

Theoretical

Experimental

Reynolds/Nusselt/Sherwood

Appendix Contents


Appendix I Raw Data for Low_High

Low/High 0.5m/s 2500W


0 1428.9

5 1425.1 30.6 30.7 29.8 30.1 35.6 71 77

10 1421.4

15 1417.7 32.5 34 32 32.4 40.4

20 1413.3

25 1409.2 32.4 33.9 31.5 32.2 40.6

30 1405.5

35 1401.2 32.2 33.7 33 32.4 41.1 70 78

40 1396.4

45 1391.9 34.1 34.8 33.7 33.9 39.7

50 1387.3

55 1383.4 33.4 34.4 33.2 33.6 38.6

60 1377.4 68.5 77.5

65 1372.9 33.7 33.4 31.9 32.7 39

70 1368.1

75 1363.5 33.4 34.5 32.5 33.4 37.5

55 49.8 Averages 33.16 34.04 32.66 32.96 39.28571429 69.83333 77.5

SLOPE 0.905455 Tray Ave. 33.205

Appendix Contents

Appendix I Raw Data for Low_High Continued


0.5 2500 W Heat of Vaporization (J/g) 2409

T wet (F/C) 69.83333333 21.02 80 1048.3

T dry (F/C) 77.5 25.28 85 1045.5

Vapor pressure water at 33.2C (mmHg) 38.1701561 T infinity (average of constant drying) 39.41666667

Vapor pressure water at 33.2C (Pascals) 5088.935614 T surface (average of constant drying) 33.205

Ca inf (kg mois/m^3) 0.01583 0.014


300 1006.3

Density of air 1.1306 312.5666667 320 1007.3


320 1.1032 300 0.000018464

320 0.000019391



320 0.027785


300 0.000015689

320 0.000017577

312.5666667



Scmidt number 0.656

Antoine's

Linear

Interpolation

Slope of line

Appendix Contents

Appendix I Raw Data for Low_High Continued


h k Re Nu Sh

4.460621 0.004119 Theoretical 11407 63.11246 61.60968

26.66517 0.007076 Experimental 11407 377.2804 105.8516

jH jD

Theoretical 0.006206 0.006217


Theoretical

Experimental


Heat and Mass Transfer Coefficients Reynolds/Nusselt/Sherwood

Appendix Contents


Appendix I Raw Data for Low_Low

Low/Low 0.5m/s 1000W


0 1059.4 22.5 22.2 21.9 21.9 24.3

5 1057.6 69.8 77

10 1055.6 24.9 23.4 22.7 22.1 25.4

15 1053

20 1051.1 24.1 23.6 23 23.3 25.6

25 1049.1

30 1046.9 25.4 23.7 23.2 23.9 25.4

35 1044.5

40 1042.5 24.7 23.8 23.4 23.8 25.6

45 1040.5

50 1038.2 25.8 24.2 23.4 24 25.3

55 1036.1

60 1033.8 25.2 24.6 23.8 24.5 25.4

65 1031.3

70 1030.1 23.9 23.9 23.3 24.1 25.2

75 1028.6

55 22.5 Averages 24.85 23.96667 23.35 23.93333 25.275 69.8 77

SLOPE 0.409091 Tray Ave. 24.025

Appendix Contents

Appendix I Raw Data for Low_Low Continued


0.5 1000W Heat of Vaporization (J/g) 2441

T wet (F/C) 69.8 21.00 75 1051.1

T dry (F/C) 77 25.00 80 1048.3

Vapor pressure water at 24C (mmHg) 22.409968 T infinity (average of constant drying) 25.41666667

Vapor pressure water at 24C (Pascals) 2987.75001 T surface (average of constant drying) 24.025

Ca inf (kg mois/m^3) 0.01680 0.0142


280 1005.7

Density of air 1.1830 298.5666667 300 1006.3


300 1.1769 280 0.000017503

300 0.000018468



300 0.02624


280 0.000013876

300 0.000015689

298.5666667



Scmidt number 0.601

Antoine's

Linear

Interpolation

Slope of line

Appendix Contents

Appendix I Raw Data for Low_Low Continued


h k Re Nu Sh

4.468515 0.00419 Theoretical 12372 65.84536 62.33782

54.50665 0.01274 Experimental 12372 803.1773 189.5438

jH jD

Theoretical0.005967 0.00597

Experimental0.07279 0.018151

Theoretical

Experimental



Appendix Contents

Appendix I Raw Data for High_Low


High/Low 1.45 m/s 1000W


0 1117.4

5 1111.8 23.4 22.9 22.6 23.4 24

10 1106.8

15 1103.9 22.4 22.7 22.3 22.8 24

20 1098.8 68 75.5

25 1095.1 22.5 22.2 21.8 22.5 24.1

30 1091

35 1087.2 22.8 22.7 21.7 22.5 23.9

40 1084.4

45 1080.6 23 22 21.5 22 23.8

50 1076.9

55 1073.3 22.1 21.9 21.4 21.9 23.9

60 1071.3

65 1067.7 22.9 22.2 21.5 22.1 23.9

70 1063.1

75 1059.4 22.5 22.2 21.9 21.9 24.3

55 39.4 Averages 22.66 22.2 21.58 22.2 23.94285714 68 75.5

SLOPE 0.716364 Tray Ave. 22.16

Appendix Contents


Appendix I Raw Data for High_Low Continued

1.45 1000W Heat of Vaporization (J/g) 2445

T wet (F/C) 68 20.00 75 1051.1

T dry (F/C) 75.5 24.17 80 1048.3

Vapor pressure water at 24C (mmHg) 20.6368645 T infinity (average of constant drying) 23.98333333

Vapor pressure water at 24C (Pascals) 2751.355652 T surface (average of constant drying) 22.16

Ca inf (kg mois/m^3) 0.01546 0.013


280 1005.7

Density of air 1.1890 297.1333333 300 1006.3


300 1.1769 280 0.000017503

300 0.000018468



300 0.02624


280 0.000013876

300 0.000015689

297.1333333



Scmidt number 0.596

Antoine's

Linear

Interpolation

Slope of line

Appendix Contents

Appendix I Raw Data for High_Low Continued


h k Re Nu Sh

7.609973 0.007145 Theoretical 36182 112.6207 106.306

72.95075 0.023816 Experimental 36182 1079.605 354.3418

jH jD

Theoretical 0.003488 0.003491



Theoretical

Experimental


Appendix Contents

Appendix II Dimensionless Groups


𝑁𝑢 =𝐿ℎ

𝑘

𝑃𝑟 =𝑐𝑝𝜇

𝑘

𝑗𝐷 =𝑘𝑐𝑣∞

𝑆𝑐 2/3 𝑗𝐻 =ℎ

𝜌𝑣∞𝑐𝑝𝑃𝑟 2/3

𝑆ℎ = 𝑘𝑐𝐿

𝐷𝐴𝐵

𝑆𝑐 = 𝜇

𝐷𝐴𝐵𝜌

𝑅𝑒 =𝐷𝑉𝜌

𝜇

Appendix Contents

Appendix III Design of Experiment


Heat DOE

Mass DOE

Velocity Heat Run Y1 Y2 Divisor Result Effects

- - 54.50665005 127.4574 348.3039 4 87.07598 AVE

+ - 72.95075269 220.8465 185.9603 2 92.98014 V

- + 26.66517397 18.4441 93.38913 2 46.69456 H

+ + 194.1813581 167.5162 149.0721 2 74.53604 VH

Velocity Heat Run Y1 Y2 Divisor Result Effects

- - 0.012739505 0.036555 0.062232 4 0.015558 AVE

+ - 0.023815814 0.025677 0.0226 2 0.0113 V

- + 0.007076433 0.011076 -0.01088 2 -0.00544 H

+ + 0.018600131 0.011524 0.000447 2 0.000224 VH

Appendix Contents

Appendix IV Values of Constants


𝑅= 0.46189 in 𝑃𝑎∗𝑚3


𝑙𝑜𝑔10 𝑃∗ = A −𝐵

𝑇 + 𝐶

Antoine Equation Constants

𝐴= 8.10765

𝐵= 1750.286

𝐶=235.000

Area of tray= 0.109725 𝑚2

Length= 0.385 𝑚2

Width= 0.285 𝑚2

8.314𝑃𝑎 ∗ 𝑚3

𝑚𝑜𝑙 ∗ 𝐾∗1

18

𝑚𝑜𝑙

𝑘𝑔 𝐻2𝑂

Appendix Contents

Appendix V Values of Heat/Mass Transfer Coefficients


h k

7.607240069 0.007091797

194.1813581 0.018600131

High_High


Theoretical

Experimental

h k

4.460620819 0.004118756

26.66517397 0.007076433

Low_High


Theoretical

Experimental

h k

4.468515156 0.004189813

54.50665005 0.012739505

Low_Low

Experimental


Theoretical

h k

7.609973067 0.007144973

72.95075269 0.023815814

High_Low


Theoretical

Experimental

Appendix Contents

Appendix VI Side by Side of Confidence Intervals


Mass Transfer Heat Transfer

Appendix Contents

Documents

Heat and Mass Transfer in Tray Drying - Tiffany Robinson · Heat and Mass Transfer in Tray Drying Group # 11: Sami Marchand ... “Fundamentals of Momentum, Heat, and Mass Transfer.”