Evacuated tube solar heat pipe collector model and associated tests

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Evacuated tube solar heat pipe collector model and associated testsFarzad Jafarkazemiand Hossein AbdiCitation: J. Renewable Sustainable Energy 4, 023101 (2012); doi: 10.1063/1.3690958View online: http://dx.doi.org/10.1063/1.3690958View Table of Contents: http://jrse.aip.org/resource/1/JRSEBH/v4/i2Published by theAmerican Institute of Physics.Related ArticlesTheoretical and experimental investigation of Alfa type bio mass Stirling engine with effect of regeneratoreffectiveness, heat transfer, and properties of working fluidJ. Renewable Sustainable Energy 4, 043126 (2012)Performance analysis and parametric optimum criteria of the nanothermoelectric engine with a single-levelquantum dot at maximum powerJ. Appl. Phys. 111, 094318 (2012)Optimization of power and efficiency of thermoelectric devices with asymmetric thermal contactsJ. Appl. Phys. 111, 024509 (2012)Performance of copper coated two stroke spark ignition engine with methanol-blended gasoline with catalyticconverterJ. Renewable Sustainable Energy 4, 013102 (2012)

A high performance thermoacoustic engineJ. Appl. Phys. 110, 093519 (2011)Additional information on J Renewable Sustainable EnergyJournal Homepage: http://jrse.aip.org/Journal Information: http://jrse.aip.org/about/about_the_journalTop downloads: http://jrse.aip.org/features/most_downloadedInformation for Authors: http://jrse.aip.org/authors

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Evacuated tube solar heat pipe collector model andassociated tests

Farzad Jafarkazemia) and Hossein Abdib)

Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University,P.O. Box 1584743311, Tehran, Iran

(Received 10 December 2011; accepted 8 February 2012; published online 6 March 2012)

In this paper, an evacuated solar heat pipe collector is investigated theoretically

and experimentally. Heat transfer formulas were used for theoretical modeling, and

a test method was adopted from ISO 9806-1 to compare the theoretical model with

the experimental results. The collector efficiency and useful heat gain were com-

pared between the theoretical and experimental methods. The effect of the working

fluid flow rates and collector area were also investigated and discussed. The com-

parison shows that the theoretical model is in good agreement with the experimen-

tal results and is capable of predicting the efficiency, useful heat gain, and working

fluid outlet temperature of an evacuated heat pipe collector with good accuracy.VC 2012 American Institute of Physics.[http://dx.doi.org/10.1063/1.3690958]

I. INTRODUCTION

Currently, most of the global energy demand is met by fossil fuels, but the massive exploi-

tation of fossil fuels leads to a real threat to the environment from global warming and acidifi-

cation of the water cycle. Rapidly increasing energy requirements, reduced availability of tradi-

tional sources of energy, and environmental pollution have forced scientists to search for

alternative energy sources. Sun and wind are among those energy resources that are effectively

unlimited and are available in abundant amounts and all over the world at no cost.

The average solar irradiation for the whole of Iran is approximately 5.3 kWh per square

meter per day, and it is even higher in the central part of the country. The amount of useful so-

lar radiation hours in Iran exceeds 2800 h per year.1

To convert the solar radiation energy into a more usable or storable form, solar collectors

are used. These devices constitute the core of solar heating systems and are available in differ-

ent forms and designs. Evacuated solar heat pipe collectors represent a novel design concept

that has a low loss coefficient.

The literature contains studies on evacuated and heat pipe solar collectors and the effect of

different parameters on their performance. Mahdjuri2 first introduced a tubular evacuated solar

collector with rectangular performance characteristics. He introduced a heat pipe cycle to trans-

fer heat from the absorber to the water tubing. Ortabasi and Fehlner3 used a solar thermal heat

pipe collector based on an internal cusp concentrator. The performance of the collector was

compared to that of an evacuated, selectively coated flat-plate absorber equipped with flow-

through heat transfer. Garg et al.4 have discussed the state of the art for evacuated tubular solar

energy collectors. They have also attempted to analyze the optical and thermal behavior of this

evacuated collector. Ezekwe5 employed a mathematical model to analyze and compare solar

energy systems that useheat pipe absorbers with systems that use conventional solar collectors.

Zambolin and Del Col6 and Fischeret al.7 tested different collectors with standard testing meth-

ods, such as EN, ISO, and ASHRAE. EN 12975-2 (Ref. 8) standard is the latest standard in

these series. Ng et al.9 conducted performance tests under steady state conditions for two types

a)Author to whom correspondence should be addressed. Electronic mail: [email protected]. Tel.: 0098(912)

3499232. Fax: 0098(21)66572717.b)

Electronic mail: [email protected].

1941-7012/2012/4(2)/023101/13/$30.00 VC 2012 American Institute of Physics4, 023101-1

JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 4, 023101 (2012)

http://dx.doi.org/10.1063/1.3690958http://dx.doi.org/10.1063/1.3690958http://dx.doi.org/10.1063/1.3690958http://dx.doi.org/10.1063/1.3690958http://dx.doi.org/10.1063/1.3690958http://dx.doi.org/10.1063/1.3690958http://dx.doi.org/10.1063/1.3690958


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of evacuated tube solar heat pipe collectors. A theoretical model was also presented to predict

the collector efficiency. Azad10 designed and constructed a heat pipe solar collector and meas-

ured its performance in an outdoor test facility. The thermal behavior was investigated theoreti-

cally and experimentally. The theoretical model was based on the effectiveness-NTU method.

Ayompeet al.11

presented year-round energy performance monitoring results for two solar waterheaters (SWHs) with flat plate and heat pipe evacuated tube collectors (ETCs). The energy pe r-

formance of the two systems was compared on a daily, monthly, and yearly basis. Hayek et al.12

conducted an experimental investigation of the overall performance of two kinds of evacuated

tube solar collectors, specifically, the water-in-glass tube and the heat-pipe designs. Jafarkazemi

et al.13 reviewed the international standards for determining the thermal performance of solar

thermal collectors and solar water heating systems and introduced the details of a test center

which was under construction in Iran. Badaret al.14 investigated the overall heat loss coefficient

(U-value) of a vacuum tube solar collector experimentally and theoretically with regard to the

pressure of the remaining gas inside the evacuated glass envelope. Tang et al.15

constructed and

tested two sets of water-in-glass evacuated tube SWH for performance comparative study. Both

SWHs were identical in all aspects but had different collector tilt-angle from the horizon with

the one inclined at 22 and the other at 46. Zambolin and Del Col16 introduced an improved

procedure for the experimental characterization of optical efficiency in evacuated tube solar col-lectors. The new method does not require a minimum number of data points for each data subset

and thus it is less demanding in terms of required number of tests.

In this study, an evacuated heat pipe solar collector with a circular fin and a dry condenser

has been theoretically modeled by heat transfer formulas, and its efficiency and heat gain dia-

grams are compared with the results of experimental tests. The test procedure was adapted

from the ISO 9806-1 (Ref. 17) test procedure. Additionally, the variation of the working (cool-

ing) fluid flow rate and its effect on the efficiency and useful heat gain has been discussed, and

the experimental and theoretical results are also presented.

II. THERMAL ANALYSIS

The heat pipe is a device with very high thermal conductance. The main components of

the heat pipe are the evaporator, the condenser, and the contained working fluid. When theevaporator is heated, the working fluid is evaporated as it absorbs an amount of heat equivalent

to its latent heat of vaporization. In the condenser section, the working fluid vapor is condensed

by a cooling fluid. The method of condensate return is dependent on the heat pipe structure.

Condensate return techniques include capillary force and gravity, among others. This cycle con-

tinues as the evaporator is heated.18,19 A solar heat pipe collector consists of a row of heat

pipes that are connected to a manifold on the top that transfers the heat produced in the pipes

to the working fluid. A schematic of a wickless heat pipe that uses gravity for condensate return

and an evacuated heat pipe collector schematic are shown in Figs. 1and2, respectively.

In this study, an evacuated tube solar collector with a heat pipe has been modeled. The con-

denser part of the collector in the manifold was of the dry type. There are many advantages to the

use of heat pipes for solar thermal applications. They have no moving parts, and if the condenser is

of the dry type, maintenance difficulties are reduced because a damaged heat pipe can be changed

while the working fluid is circulating. Moreover, leakage problems are reduced because of the indi-rect contact between the heat pipe and the condenser.9 Water was chosen as the working (cooling)

fluid because the local ambient temperature did not drop below its freezing point during the test. For

simplicity, the following assumptions were made in the theoretical model:

The collector absorber area is always at a uniform temperature. The temperature gradient across the absorber thickness and over its perimeter is neglected. Because the evaporator section is subjected to a constant heat flux and the phase change occurs

at a constant temperature, the temperature gradient along the longitudinal direction is negligible. The thermal contact resistance between the absorber area and the evaporator tube and between

the condenser section and the condenser manifold is neglected. The connection of the evaporator and the condenser of the heat pipe is assumed to be adiabatic.

023101-2 F. Jafarkazemi and H. Abdi J. Renewable Sustainable Energy 4, 023101 (2012)



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The thermal resistance model that has been used is shown in Fig. 3. In the figure, I repre-

sents the solar radiation that reaches the collector surface, and I (sa) represents the radiation

that reaches the absorber. A small part of the gained heat is wasted by radiation, which is

shown by Q loss.rad. The useful heat gain, Qu, is calculated by subtracting the heat pipe collector

heat gain, Qhp, from the manifold heat loss from the top of the collector, Qloss,ma. Rloss,radis the

radiation thermal resistance, which can be calculated and represented as follows:

Rloss;rad TpTa

erT4p T4a Ar

: (1)

The evaporator thermal resistance is represented by Rhp and is a combination of three resistan-

ces. These resistances are the circular fin resistance, the copper pipe resistance, and the boiling

film condensation resistance inside the evaporator pipe. Thus, Rhp may be written as follows20:

RhplnDo;fin=Di;fin

2pkfinLevap

lnDo;evap=Di;evap

2pkevapLevap

1

hhpAevap; (2)

where

hhp 0:555gqlql qvk

3lhfg

llTpTkDevap

14

: (3)

Rcond,w is considered to be the thermal resistance of the condenser section, which is the sum of

the condensing film resistance in the condenser, the condenser copper pipe section, and the dry

manifold condenser resistance. The thermal contact resistance in the dry condenser is assumed

to be negligible. Rcond,wmay be written as:20

Rcond;w 1

hcondAcond

lnDo;cond=Di;cond

2pkcondLcond

lnDo;ma=Di;ma

2pkmaLma; (4)

FIG. 1. Heat pipe schematic.

023101-3 Evacuated tube solar heat pipe collector J. Renewable Sustainable Energy 4, 023101 (2012)



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where

hhp 0:555gqlql qvk

3lhfg

llTpTkDcond

14

: (5)

The manifold resistance is also calculated by the common heat transfer formulas, as

1/UmaAma,loss.

The heat transfer balance is written using the thermal resistance model shown in Fig. 3, as

follows:

_qin _qloss;rad _qhp _qloss;rad _qu _qloss;ma: (6)

The expressions for the temperatures, resistances, and radiation are used in Eq. (6), and it yields

the following:

FIG. 2. Evacuated heat pipe collector schematic.

FIG. 3. Thermal resistance model for an evacuated heat pipe collector.




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IsaArTpTa

Rrad _qu

TfTaRloss;ma

: (7)

To simplify the derivation process, Rcond;w=Rrad is replaced by Rcrand Rhp=Rrad is replaced by

Rhr. From the thermal resistance model, the following expression may be written:

_qhp TpTf

RhpRcond;w; (8)

_qhp _qu _qloss;ma _quTfTaRloss;ma

: (9)

Using the energy balance in the thermal resistance model and Eqs. (8) and (9) to simplify the

useful heat gain equation, the following may be written,

_qu IsaAr

1Rhr Rcr

TfTa

1RhrRcr

1

Rrad

1

Rloss;ma1RhrRcr : (10)

Equation(10)may be written as

_qu F0ArIsa ULTfTa; (11)

where

F0 1

1RhrRcr; (12)

and

UL 1

RradAr

1

Rloss;maArF0: (13)

The collector heat removal factor can be calculated by the following equation:21

FR _mCp

ArUL1exp

ULArF0

_mCp

: (14)

FR is similar to heat exchanger effectiveness and is defined as the ratio of the actual heat trans-

fer to the maximum possible heat transfer. The maximum possible heat transfer occurs when

the collector is at the working fluid inlet temperature.21

The actual collector useful heat gain may be calculated from the following:

_qu ArFRIsa ULTf;iTa: (15)

By incorporating the useful heat gain value, the heat gain of the working fluid in the manifold

can be expressed as _qu _mCpTfTo, where To represents the outlet temperature of theworking fluid and will be determined.

The instantaneous efficiency of a collector, which is the ratio of the useful energy to the

solar radiation, can be expressed as follows:21

g _qu=ArI FRsa FRULTf;iTa=I: (16)




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III. EXPERIMENTAL TEST AND PROCEDURE

Fig.4shows a schematic of the experimental configuration used for the efficiency and per-

formance evaluation of an evacuated heat pipe collector. The test facility and weather station

are located on the roof of solar energy laboratory building of the Islamic Azad University

South Tehran Branch. The collector tilt angle was set to 45 , facing south. The latitude and lon-

gitude of the test center are 35.6 N and 51.4 E, respectively. A picture from the test facility

is shown in Fig.5.

The test plan for testing the collectors was adopted from ISO 9806-1 because it is known as

an accepted standard in Iran. The specifications of the system components are described below.

The reservoir tank volume was 150 l, and the tank was made of galvanized steel. Calibrated Pt-

100 temperature sensors were used to measure the inlet and outlet fluid temperatures of the col-

lector and the reservoir tank. In order to control the tank fluid temperature, two 2 kW electric

heaters and one 1 kW heater were used. A calibrated flow meter with a range of 20-200 l/h was

used to measure the inlet working fluid flow rate. The heaters were controlled by a solid state

relay (SSR) controller. A proportional integral derivative (PID) temperature controller was used

for this purpose. The pyranometer, ambient temperature probe, and wind velocity sensor are all

calibrated against reference instruments and supplied by Soldata Instruments. The weather datawere logged at intervals of 10 min during the tests. The general specification of the tested collec-

tor, which is a heat pipe solar collector with 19 heat pipes, is presented in Table I.

The test procedure which is used to test the performance and efficiency, according to ISO

9806-1, is as follows. First, the temperature of the reservoir tank is kept constant with the heat-

ers and controller. The water tank temperature is set to different values during each test period.

The minimum temperature is set to the ambient temperature, and the other temperatures are set

higher for the subsequent data points. Using the flow control valve, the flow is set to a constant

rate, and after 10 min, when the outlet temperature is constant, the collector outlet temperature

FIG. 4. Schematic diagram of the test set-up.




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is recorded. This procedure is repeated for five other temperatures in each test period with steps

of approximately 8 C. The test procedure is also repeated for two other flow rates. The time

periods are chosen such that the data points represent times symmetrical to the solar noon. In

this study, the test is performed for two collectors, one with 19 heat pipes and the other with 4

heat pipes. The experimental efficiency and the useful heat gain of each solar collector are

compared to the theoretical calculated values to evaluate the accuracy of the model. The effect

of the three flow rates on the efficiency and heat gain is discussed after the test procedure was

completed.

IV. RESULTS AND DISCUSSION

The test for evaluation of the heat pipe performance was performed in August 2011. The

climate conditions on August 8 and August 15, 2011 when the tests were performed are shown

in Fig.6.

The tests were performed for 19 heat pipes and 4 heat pipes on days 1 and 2, respectively.

The flow rates were set to 0.056, 0.042, and 0.028 kg/s for the 19 heat pipe collector and 0.014,

0.010, and 0.007 kg/s for the 4 heat pipe collector for the tests. These are based on requirement

of ISO 9806-1, which recommends a flow rate of 0.02kg/s/m2 for collector testing. Other flow

rates were chosen to compare the flow rate effect on heat gain and efficiency.

FIG. 5. Test facility.

TABLE I. Specifications of an evacuated collector.

Parameter (unit) Value

Aperture area (m2

) 2.50

Absorber area (m2) 1.78

Emittance 0.07

Tube spacing (m) 0.078

Tube length (m) 1.7

Condenser O.D. (m) 0.024

Condenser length (m) 0.065

Evaporator O.D. (m) 0.008

Absorber absorptance 0.93

Glass cover transmittance 0.90




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The theoretical and experimental efficiencies, useful heat gains and inlet and outlet temper-

atures for the collector with 19 heat pipes and a flow rate of 0.042 kg/s of working fluid is

shown in Table II as an example. For each working fluid flow rate, this table should be madeavailable before processing the data.

The collector flow factor, F00, which is the ratio ofFR to F0, is a function of a single vari-

able, the dimensionless collector capacitance rate _mCp=ArULF0. This factor is shown in Fig. 7

for a working fluid flow rate of 0.028 kg/s and a collector with 19 heat pipes. The theoretical

(calculated) collector outlet temperatures and experimental (measured) collector outlet tempera-

tures are shown in Fig. 8. The data points shown correspond to the collectors with both 4 heat

pipes and19 heat pipes and all six flow rates. The predicted values are in good agreement with

the experimental results to within an error of less than 5%, which means that the theoretical

model is acceptable.

Figs.9and10 show the rise in the working fluid temperature for different flow rates. These

figures indicate that the experimental outlet and inlet temperature difference increases as the

working fluid flow rate decreases. Additionally, while the ratio of the temperature difference to

the incident radiation increases, the experimental outlet and inlet temperature difference also

decreases. This result indicates that in order to reach the maximum outlet temperature, the opti-

mum condition is to have a reduced working fluid flow rate and a smaller difference between

the inlet and ambient temperatures. The slopes of the diagrams are nearly the same, which

means that the results do not depend on the collector area or the number of heat pipes.

The theoretical collector heat gain and the experimental results during the testing day for

different flow rates are shown in Figs. 11 and 12. The theoretical and experimental heat gains

are shown by lines and rectangular diagrams, respectively. The model prediction is close in

value to the experimental results at most data points. As expected, when the difference between

the inlet and ambient temperatures increases, the useful heat gain decreases, and vice versa.

FIG. 6. Climate conditions for the two test days (a) August 8 and (b) August 15.

TABLE II. Data table for the collector with 19 heat pipes and a working fluid flow rate of 0.042kg/s.

Time Temp (C) Efficiency (%) Useful heat gain (W) Radiation

Hour Tinlet

Experimental

Toutlet

Theoretical

Toutlet Tamb Theoretical Experimental Theoretical Experimental

I

(W/m2

)

11:25 75.1 77.4 78.69 34.4 46.39 29.67 625.87 400.22 757.9

12:00 67.9 71.4 71.93 36 48.88 42.43 701.57 609.04 806.4

12:25 59.7 63.4 64.01 36.5 50.98 43.76 750.13 643.84 826.6

13:00 52.5 56.7 56.93 37.8 52.76 49.91 772.47 730.85 822.6

13:30 44.7 48.5 49.33 37.7 54.54 44.72 806.50 661.24 830.7

14:10 40.7 44.8 45.19 39.4 55.63 50.72 782.45 713.45 790.2




10/14

FIG. 7. Collector flow factor.

FIG. 8. Theoretical model and comparison with experimental results for outlet temperature.

FIG. 9. Variation in the working fluid temperature in a collector with 19 heat pipes for different flow rates.




11/14

FIG. 10. Variation in the working fluid temperature in a collector with 4 heat pipes for different flow rates.

FIG. 11. Comparison of theoretical and experimental heat gain for a collector with 19 heat pipes.

FIG. 12. Comparison of theoretical and experimental heat gain for a collector with 4 heat pipes.




12/14

This result indicates that more heat can be gained from the collector when the inlet and ambient

temperature difference is kept near zero.

Figs. 13 and 14 show a comparison between the efficiency predicted using the theoretical

model vs. that obtained using the experimental results for the two collectors at different flow

rates. The experimental results are close in value to the predicted results of the model for both

collectors. As the flow rate of the working fluid and the number of heat pipes increase (Fig.

13), efficiency decreases. On the other hand, as shown in Fig. 14, for a collector with smaller

area and reduced working flow rate, the rate of efficiency decrease (slope) is higher. This result

indicates that it is possible to reach higher efficiencies by decreasing the collector aperture

area, but the substantial rate at which the efficiency decreases should be considered. The instan-

taneous efficiency decreases as the ratio of the temperature difference to the incident radiation

increases in both diagrams. The values of FRUL and FR(sa) are estimated for both collectors.FRUL is the slope of the straight regression line, and FR(sa) is the value of the point of intersec-

tion with the y-axis in the region of maximum efficiency. By linear curve fitting of the data

points for the collector with 19 heat pipes, the experimental values of FRUL for flow rates of

0.056, 0.042, and 0.028 kg/s are equal to 3.77, 3.36, and 3.45, respectively, while the theoretical

model yields 1.87, which was approximately constant for all flow rates. The FR(sa) values that

FIG. 13. Predicted efficiency from the theoretical model vs. efficiency determined from the experimental results for the

collector with 19 heat pipes.

FIG. 14. Predicted efficiency from the theoretical model vs. efficiency determined from the experimental results for the

collector with 19 heat pipes.




13/14

are determined from the experimental results are equal to 0.55, 0.52, and 0.51 for flow rates of

0.056, 0.042, and 0.028 kg/s, respectively, while the theoretical model yields 0.56, which was

approximately constant for all flow rates. For the collector with 4 heat pipes, the experimental

value of FRUL for flow rates of 0.014, 0.010, and 0.007 kg/s are 8.86, 8.85, and 10.03, respec-

tively, while the theoretical model yields 8.5,which was approximately constant for all flowrates. The experimental FR(sa) values are 0.73, 0.72, and 0.76 for flow rates of 0.014, 0.010,

and 0.007 kg/s, respectively, while the theoretical model yields 0.79, which was approximately

constant for all flow rates.

V. CONCLUSIONS

In this study, a comparison between the theoretical and experimental results for two collec-

tors with different numbers of heat pipes and different aperture areas were made. The results

led to the following findings.

The theoretical model is in good agreement with the experimental results and is capable of

predicting the efficiency, useful heat gain, and working fluid outlet temperature of an evacuated

tube heat pipe collector with good accuracy.

The effect of the flow rate on the efficiency and heat gain were also discussed theoreticallyand experimentally. It is found that decreasing the flow rate leads to a higher outlet temperature

for an evacuated tube heat pipe collector.

It has been shown that the efficiency of the collector decreases as the ratio of the inlet tem-

perature to the incident radiation increases. It is recommended that the inlet water temperature

is kept as near as possible to the ambient temperature to gain more heat and higher efficiency.

ACKNOWLEDGMENTS

The authors would like to acknowledge the financial support of Islamic Azad University, South

Tehran Branch (under Contract No. B/16/561).

NOMENCLATURE

Ar collector area (m2

)Cp specific heat capacity (J/kg K)

D diameter (m)

F0 collector efficiency factor

F00 collector flow factor

FR collector heat removal factor

h heat transfer coefficient (W/m2 K)

I incident solar radiation (W/m2)

k thermal conductivity (W/m K)

_m mass flow rate (kg/s)

_q heat transfer rate (W)

R resistance (W/K)

t wall thickness (m)

T temperature (K)UL overall heat transfer coefficient of collector (W/m

2 K)

emittance coefficientg efficiency

l dynamic viscosity (N s/m2)

q density (kg/m3)

sa transmittance absorbance product

SUBSCRIPTS

a ambient

cond condenser




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evap evaporator

exp experimental or measured

f working fluid

g gas

hp heat pipei inlet

l liquid

ma manifold

o outlet

p plate

rad radiation

u useful

w wall

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http://dx.doi.org/10.1016/0013-7480(79)90004-4http://dx.doi.org/10.1016/0038-092X(80)90316-3http://dx.doi.org/10.1016/0196-8904(83)90059-6http://dx.doi.org/10.1016/0741-983X(90)90020-3http://dx.doi.org/10.1016/j.solener.2010.04.020http://dx.doi.org/10.1016/j.solener.2003.07.021http://dx.doi.org/10.1243/0954408001530182http://dx.doi.org/10.1016/j.expthermflusci.2008.05.011http://dx.doi.org/10.1016/j.energy.2011.03.034http://dx.doi.org/10.1016/j.egypro.2011.05.071http://dx.doi.org/10.1016/j.solener.2011.04.001http://dx.doi.org/10.1016/j.solener.2011.03.019http://dx.doi.org/10.1016/j.renene.2011.11.011http://dx.doi.org/10.1016/j.renene.2011.11.011http://dx.doi.org/10.1016/j.solener.2011.03.019http://dx.doi.org/10.1016/j.solener.2011.04.001http://dx.doi.org/10.1016/j.egypro.2011.05.071http://dx.doi.org/10.1016/j.energy.2011.03.034http://dx.doi.org/10.1016/j.expthermflusci.2008.05.011http://dx.doi.org/10.1243/0954408001530182http://dx.doi.org/10.1016/j.solener.2003.07.021http://dx.doi.org/10.1016/j.solener.2010.04.020http://dx.doi.org/10.1016/0741-983X(90)90020-3http://dx.doi.org/10.1016/0196-8904(83)90059-6http://dx.doi.org/10.1016/0038-092X(80)90316-3http://dx.doi.org/10.1016/0013-7480(79)90004-4

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