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Solar Energy 84 (2010) 1706–1716

Heat extraction from salinity-gradient solar ponds using heat pipeheat exchangers

Sura Tundee a,*, Pradit Terdtoon a, Phrut Sakulchangsatjatai a, Randeep Singh b,**,Aliakbar Akbarzadeh b

a Department of Mechanical Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai 50200, Thailandb Energy Conservation and Renewable Energy Group, School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University,

Bundoora East Campus, Bundoora, Victoria 3083, Australia

Received 1 September 2009; received in revised form 25 March 2010; accepted 13 April 2010Available online 17 July 2010

Communicated by: Associate editor Yogi Goswami

Abstract

This paper presents the results of experimental and theoretical analysis on the heat extraction process from solar pond by using theheat pipe heat exchanger. In order to conduct research work, a small scale experimental solar pond with an area of 7.0 m2 and a depth of1.5 m was built at Khon Kaen in North-Eastern Thailand (16�270N102�E). Heat was successfully extracted from the lower convectivezone (LCZ) of the solar pond by using a heat pipe heat exchanger made from 60 copper tubes with 21 mm inside diameter and22 mm outside diameter. The length of the evaporator and condenser section was 800 mm and 200 mm respectively. R134a was usedas the heat transfer fluid in the experiment. The theoretical model was formulated for the solar pond heat extraction on the basis ofthe energy conservation equations and by using the solar radiation data for the above location. Numerical methods were used to solvethe modeling equations. In the analysis, the performance of heat exchanger is investigated by varying the velocity of inlet air used toextract heat from the condenser end of the heat pipe heat exchanger (HPHE). Air velocity was found to have a significant influenceon the effectiveness of heat pipe heat exchanger. In the present investigation, there was an increase in effectiveness by 43% as the air veloc-ity was decreased from 5 m/s to 1 m/s. The results obtained from the theoretical model showed good agreement with the experimentaldata.� 2010 Elsevier Ltd. All rights reserved.

Keywords: Solar pond; Thermosyphon; Heat pipe heat exchanger; Heat recovery; Renewable energy

1. Introduction

Solar pond is a simple and low cost thermal energy storagesystem which collects incident solar radiation and stores it inthe form of sensible heat of saline water for a relative longperiod of time (seasonal storage). The first investigation onthe solar pond was conducted by Kalecsinsky (1902). Inthe study, the solar-heated natural salt water lake known

0038-092X/$ - see front matter � 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2010.04.010

* Corresponding author. Tel.: +66 43338869; fax: +66 43338870.** Corresponding author. Tel.: +61 399256024; fax: +61 399256108.

E-mail addresses: suratundee2000@yahoo.com (S. Tundee), randeep.singh@rmit.edu.au (R. Singh).

as Lake Madoc located at 42�440N, 28�450E in Transylvaniawas considered. This lake showed temperatures as high as70 �C at a depth of 1.32 m in the summer season. The mini-mal temperature was 26 �C during early spring. Followingthis study, the idea of solar energy collection was furtherdeveloped by using artificially created salinity-gradient solarponds.

A typical salinity-gradient solar pond generally consistsof three regions namely the upper convective zone (UCZ),the middle non-convective zone (NCZ), and the lower con-vective zone (LCZ) as shown in Fig. 1. The upper convec-tive zone is the topmost layer of the solar pond which isrelatively thin and consists almost entirely of fresh water

Nomenclature

A area (m2)C heat capacity (J/kg)Cp specific heat capacity (J/kg K)E rate of solar irradiance absorption per unit vol-

ume of water (W/m3)h convection heat transfer coefficient (W/m2 K)H average daily solar irradiance (MJ/m2 day)Io solar intensity just penetrating the surface of the

pond (W/m2)Ix solar intensity available at depth x (W/m2)j 1–4 (different ranges of wavelength as per Ta-

ble 1)k thermal conductivity (W/m K)L latent heat of evaporation of water (J/kg)l thickness of the solar pond zone (m)LCZ lower convective zonem�a air mass flow rate (kg/s)NCZ non-convective zoneNTU number of heat transfer units for heat pipe heat

exchangern number of thermosyphonsP perimeter (m)Patm atmosphere pressure (Pa)Pv saturation vapour pressure corresponding to

surface water temperature (Pa)P1 partial pressure of water vapour in air (Pa)q rate of heat loss per unit area (W/m2)qext heat extracted from the lower convective zone of

solar pond by HPHE (W)Qtot total heat transferred by heat pipe heat exchan-

ger (W)Qmax maximum possible heat that can be transferred

by heat exchanger (W)Rh relative humidity (%)S salt concentration (kg/m3)T temperature (K)t time (s)U overall heat transfer coefficient (W/m2 K)UCZ upper convective zoneV wind speed (m/s)x distance from the surface of the solar pond (m)Ztot total thermal resistance of the HPHE (K/W)

Dt time difference (s)

DT temperature difference (K)

Dx thickness of horizontal layers (m)

Greek letters

e emissivityh angles of refraction (rad)gj fraction of solar radiation having absorption

coefficient lj

q density (kg/m3)r Stefan–Boltzmann’s constant (=5.67 � 10�8 W/

m2 K4)lj absorption coefficient for jth portion of solar

spectrum (m�1)n effectiveness of heat exchanger (%)

Subscripts

a airai air inletao air outletamb ambientc coldconv convectione evaporationeff effectivef final/last layer of the NCZg groundh hothh hydrostatic heighti number of layerl lower convective zonemin minimummax maximumn non-convective zoner radiations solar pondsi sinksky sky conditionssl sides of lower convective zonesn sides of non-convective zoneso sourcesu sides of upper convective zonetot totalt 1, 2, 3, . . . (index for time interval Dt)u upper convective zonew water

S. Tundee et al. / Solar Energy 84 (2010) 1706–1716 1707

or water with low salinity. The non-convective zone is theportion just below the upper convective zone that showsan increasing salt concentration with respect to the ponddepth. This layer acts as heat insulation and thus minimizesheat losses from the bottom high saline layer. The lowerconvective zone has the highest percentage of salinity with-out any concentration gradient unlike NCZ. For suffi-

ciently high concentration gradient in NCZ, theconvective current will be suppressed in this region whichhelps to store the absorbed thermal energy in the bottomportion (LCZ) of the pond. Fig. 1 also presents a character-istic salinity and temperature profiles in the salinity-gradi-ent solar pond. When solar radiation is incident on thesolar pond, a part of the radiation is reflected back from

Fig. 1. Salinity gradient solar pond.

1708 S. Tundee et al. / Solar Energy 84 (2010) 1706–1716

the top surface while most of the incident sunlight is trans-mitted inside through the top surface of the UCZ. The frac-tion of the transmitted radiation is first rapidly absorbed inthe surface layer. However, this absorbed heat is lost to theatmosphere by convection and radiation heat transfer. Theremaining radiation is then subsequently absorbed in themiddle NCZ and bottom LCZ before the rest of the radia-tion reaches the bottom of the pond. In the LCZ, theabsorbed solar energy is converted to heat and stored assensible heat in high concentration brine. Since there areno heat losses by convection from the bottom layer, thetemperature of this layer can rise substantially. The tem-perature difference between the top and the bottom of thesolar ponds can be as high as 50–60 �C. Thermal energystored in the solar pond can be utilized for heating of build-ings (hydrophonic), power production and desalinationpurposes (Akbarzadeh et al., 2005).

Heat absorbed in the solar pond can be extracted by dif-ferent means for utilization in various thermal applications.In this area, investigation on the heat extraction systemshas been conducted by number of researchers. Jaefarzadeh(2000) studied the heat extraction from the solar pond withan area of 4 m2 and a depth of 1.1 m by using in-pond heatexchangers with water as the working fluid. In this investi-gation, a system of internal and external heat exchangerswas used. The internal heat exchanger was installed inthe LCZ that helps to extract heat from the bottom ofthe pond by using circulating fresh water and transfer itto the water to air heat exchanger placed externally tothe pond. It was concluded that the solar pond can deliverheat either continuously with low efficiency or intermit-tently with relatively high thermal efficiency.

Andrew and Akbarzadeh (2005) propose an alternativemethod to enhance the thermal efficiency of the solar pondby extracting heat from the non-convecting gradient layerin addition to the lower convective zone. A theoreticalanalysis of combined NCZ and LCZ heat extraction sug-gested that this method has the potential to increase theoverall energy efficiency of the pond by up to 50% as com-pared to the conventional method of heat extraction fromLCZ only. In the analysis, heat exchanger was assumed tobe single phase type with water as the working fluid.

From the literature survey, it is evident that the heatextraction from the solar ponds is generally performed bymeans of single-phase heat transfer using sensible heat gain

by the liquid working fluid which is mostly water. The cur-rent method of heat extraction suffers from two main lim-itations. Firstly, the active circulation of the working fluidinside the in-pond heat exchanger requires pumping powerwhich is not very sustainable in the remote area applica-tions where solar ponds are most viable. Secondly, single-phase heat exchangers are bulky in size and are requiredto handle large mass flow rates of heat transfer fluid inorder to transfer kilowatt range heat provided by the solarponds. In this regard, two phase heat transfer systems (Leeet al., 2006; Huang et al., 2001; Hussein, 2002; Shiraishiet al., 1981; Lee and Bedrossian, 1978; Chyng et al.,2003; Esen, 2004) based on the latent heat of evaporationof the liquid working fluid can be considered as an advan-tage due to its passive mode of operation and relativelyhigh heat transfer capacity with reasonable system size. Tillnow, such a heat exchanger is not utilized for the solarpond heat extraction purposes. Therefore, the currentresearch investigates the potential and viability of heatextraction from the lower convective zone of the solar pondby using system of two-phase gravity-assisted thermosy-phons as the heat exchanger. In the study, the theoreticalmodel of solar pond heat extraction by using thermosy-phons is discussed and elaborated. Also, the outcomes ofthe thermal simulation are compared to the experimentaldata obtained from the artificially constructed salinity-gra-dient solar pond.

2. Experimental setup

In the present experimental work, solar pond with anarea of 7 m2 and a depth of 1.5 m was built at RajamangalaUniversity of Technology in north east of Thailand(16�270N102�E). The built solar pond was used to charac-terize the daily temperature variations and possible heatextraction rate from the salinity-gradient solar ponds.Fig. 2 illustrates various zones in the solar pond and theirthicknesses. In this case, the pond was built above groundwith concrete walls 20 cm thick. The temperature measure-ments were taken at different locations along the inner con-crete wall of the pond, as indicated in the Fig. 2, by usingK-type thermocouples with an accuracy of ±0.5 �C. Thesethermocouples were equally spaced at 0.05 m interval withthe starting point at 0.05 m and end point at 1.45 m fromthe bottom surface of the pond. The temperature distribu-tions at these regions were recorded at 5 min time intervalby using the data acquisition system connected to thesethermocouples. For monitoring and processing the outputdata, the data acquisition unit was connected to a com-puter system. The solar radiation intensity (in W/m2) inci-dent on the horizontal surface was measured at an intervalof 10 min by using a 105HP type pyranometer with anuncertainty of ±5% of the output reading. In order torecord the density profile for the solar pond, samples ofthe saline water was extracted from different depths ofthe pond using simple gravity assisted siphoning technique.

UCZ

NCZ

LCZ

Concrete slab

Computer System

Data LoggerSignal from

thermocouples

30 cm

60 cm

70 cm

20 cm

Thermocoupleslined along the depth

of the solar pond

Blower

HPHE

Sun

TLCZ

Tai

Tao

Cold Air Warm Air

Fig. 2. Experimental setup showing different zones of solar pond their dimensions, pond heat extraction system and associated data acquisition facilities.

S. Tundee et al. / Solar Energy 84 (2010) 1706–1716 1709

Density was measured using DMA 35N Density meterfrom Anton Paar which has an accuracy of ±1 kg/m3.

The schematic of the heat extraction system, as shown inFig. 2, is composed of heat pipe heat exchanger (HPHE),blower and air flow duct. A system of internal heat exchan-ger based on the two phase thermosyphons (gravityassisted heat pipes) was designed for removing heat fromthe LCZ of the solar pond. The heat pipe heat exchanger(HPHE) consisted of 60 thermosyphons which were madefrom copper tube with an internal diameter of 21 mmand external diameter of 22 mm. Each tube has evaporatorand condenser length of 80 cm and 20 cm respectively.R134a was used as the heat transfer fluid inside the ther-mosyphon. The HPHE was inclined at 60� to the verticalthat provide a favourable tilt for superior thermal perfor-mance of the thermosyphon as well as for integrating theheat exchanger inside the lower convective zone. Tiltingthe HPHE at such an angle helps to provide heat transferaccess at the evaporator and condenser sections and alsoinstallation of the unit in the heat storage section of thepond. It should be noted that the performance of the ther-mosyphon is very much dependent on the tilt angle. Forproper return of the condensate to the evaporation section,the tilt angle should be higher (more than 45�). On theother hand, 90� tilt increases the chances of entrainmentand blockage of condensation area with liquid film. Keep-ing all these factors into account, 60� tilt was consideredoptimum for the present experimental setup. In order toextract heat transferred by the HPHE from the LCZ, a var-iable speed blower was used for circulation the ambient airthrough the HPHE condenser. The air temperature at theinlet and outlet of the HPHE condenser and volume flow

rate were measured to determine the heat extraction rate.A vane type anemometer with ±0.3 m/s accuracy was usedto measure the mean velocity of air passing through theblower.

On the basis of the error analysis, it was observed thatthe uncertainties associated with the experimental resultswere higher at the lower flow velocities of the air throughthe blower due to the lower quantities of extracted heat.For the minimum experimental air velocity of 1 m/s, themaximum uncertainty for the heat extracted from the solarpond and effectiveness of the heat pipe heat exchanger was±5.1% and ±7.2% respectively.

3. Theoretical analysis of solar pond heat extraction

3.1. Solar pond analysis

A one-dimensional mathematical model based on theenergy conservation for three zones of the pond namelyUCZ, NCZ and LCZ as shown in Fig. 3 was used to pre-dict the thermal characteristics of the experimental solarpond. The model outcomes were validated by using testdata obtained from the constructed solar pond. In themodel, it was assumed that the upper convective zoneand lower convective zone are fully mixed. The tempera-ture variations inside the solar pond depend on the solarradiation intensity incident on the horizontal surface, theclimatic conditions of the place, the structure and geometryof the pond and the rate of heat extraction.

Using Cartesian system of coordinates, x is measured aspositive downward with the origin (x = 0) at the surface ofthe pond. The general one-dimensional transient equation

UCZ

NCZ

LCZ

qe qconv qr

Io

qg

qext

qsl

qsn

qsu

ll

ln

lu Tu

f

1

i-1

i

i+1

Δxi-1

Δxi

Δxi+1

Tl

xi-1/2xi+1/2 xi

ulI

nu llI +

Fig. 3. Mathematical model of the solar pond showing details of the three zones and the sub-layers for numerical analysis.

1710 S. Tundee et al. / Solar Energy 84 (2010) 1706–1716

for temperature T in the conducting (non-convecting) zoneof the pond can be given as (Rubin et al., 1984):

qCp@T@t¼ @

@xk@T@x

� �þ Eðx; tÞ ð1Þ

The energy source term, E(x, t), appearing in Eq. (1)represents the rate of solar energy absorption by the fluidper unit volume, and can be expressed as follows:

E ¼ � @Ix

@xð2Þ

The thermophysical properties of the saline water interms of temperature (T) in Kelvin and salt concentration(S) in kg/m3 are given by (Wang and Akbarzadeh, 1982)as below:

kw ¼ 0:5553� 0:0000813S þ 0:0008ðT � 20Þ ð3Þqw ¼ 998þ 0:65S � 0:4ðT � 20Þ ð4ÞCpw ¼ 4180þ 4:396S þ 0:0048S2 ð5Þ

Table 1Values for g and l for different range of wavelength as used in Eq. (6).

j Wavelength (lm) g l

1 0.2–0.6 0.237 0.0322 0.6–0.75 0.193 0.453 0.75–0.9 0.167 34 0.9–1.2 0.179 35

3.1.1. Absorption of solar radiation in solar pond

Solar radiation is one of the most important parametersfor estimating the temperature in the solar pond. For thesolar pond, the thermal performance is largely dependenton the nature of light absorption in the body of water inthe solar pond. The solar irradiance that penetrates the

pond surface decays exponentially with the depth (x) asthe energy is absorbed by fluid layers. The rate of decayis a function of the wavelength of the radiation and canbe expressed for the whole spectrum of wavelength by ser-ies of exponential functions (Rubin et al., 1984) as follows:

Ix

Io¼X4

j¼1

gj exp�ljx

cos h

� �ð6Þ

Table 1 gives the values for g and l for different range ofwavelength.

A simplified equation for light absorption in water isgiven by (Wang and Akbarzadeh, 1982) as:

Ix

Io¼ 0:36� 0:08 ln x for 0:01 m < x < 10 m ð7Þ

Fig. 4 presents the graph for the extent of the solarenergy absorption inside the pond with the depth by usingEqs. (6) and (7). As evident from the trends, the predictions

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Ix/IoD

epth

(m)

Equation (6)Equation (7)

Fig. 4. Variation of radiation intensity with depth inside water ascalculated on the basis of two different correlations given by Eqs. (6)and (7).

S. Tundee et al. / Solar Energy 84 (2010) 1706–1716 1711

made by the two correlations is quite close. It is noted thatthe absorption of the incident radiation shows an initialsharp and then slow trend with respect to the depth ofthe pond. At a depth of 1 m, only 36% of the radiationentering the pond is available while at a depth of 2 m thisvalue is reduced to 30%. Solar radiation intensity has adirect effect on the temperature of the pond. In this study,the meteorological data used was recorded at Khon Kaenin Thailand. Table 2 presents the monthly average of dailysolar radiation on horizontal surface and ambient temper-ature based on recorded data.

3.1.2. Energy balance for the upper convective zone (UCZ)

Due to convection, the UCZ zone can be assumed tohave a uniform temperature Tu. The UCZ is treated as asingle layer with the constant thermophysical propertiesof the fluid throughout the thickness of the layer. Theenergy flows in the solar pond is in the form of heat, thus,the heat balance as shown in Fig. 3 can be written as:

quCpulu@T u

@t¼ ðIo � IluÞ þ ku

@T@x

����x¼lu

� qu ð8Þ

Table 2Metrological data for Khon Kaen Thailand based on the monthlyaverage.

Month Insolation,H (MJ/m2 day)

Tamb

(�C)Tmin

(�C)Tmax

(�C)V(m/s)

Rh

(%)

January 15.6 26.18 18.4 30.6 8.5 56February 16.8 27.41 19.8 32 6.4 54March 17.8 30.4 23.6 34.4 7.9 55April 18.7 31.05 25.5 34.1 6.9 61May 19.2 30.29 25.8 32.6 7.5 70June 19.6 30.04 26 32.1 7.9 72July 19.2 29.26 25.7 31.2 8.1 76August 18.9 28.91 25.3 30.8 7.4 77September 18.5 28.46 24.9 30.3 8.5 76October 18.1 28.53 23.9 30.7 9.3 70November 17.6 26.86 20.7 29.8 10.1 62December 17.4 25.34 28.2 29 9.5 58

where qu is the rate of total heat loss per unit area from thepond due to convection, evaporation, radiation as well asheat losses through the wall (Kurt et al., 2000) as expressedbelow:

qu ¼ qconv þ qe þ qr þ qsu ð9Þ

The convective heat loss from pond surface is given by

qconv ¼ hconvðT u � T ambÞ ð10Þ

where convection heat transfer coefficient is determinedfrom

hconv ¼ 5:7þ 3:8V ð11Þ

where V is the average monthly wind speed at Khon KaenThailand as recorded in Table 2.

The evaporative heat loss is given by

qe ¼LhconvðP v � P1Þ

1:6CP P atmð12Þ

where

P1 ¼ Rh exp 18:403� 3885

T amb þ 230

� �ð13Þ

where Rh is the monthly average relative humidity at KhonKaen Thailand as recorded in Table 2.

P v ¼ exp 18:403� 3885

T u þ 230

� �ð14Þ

The radiation heat loss is given by

qr ¼ ewr T 4u � T 4

sky

� �ð15Þ

where ew is the emissivity of water which is assumed to be0.83 and r is the Stefan–Boltzmann’s constant (5.67 �10�8 W/m2 K4).

Sky temperature is given by (Kurt et al., 2000) as:

T sky ¼ T amb � 0:55þ 0:061ffiffiffiffiffiffiffiP1

p� �0:25

ð16Þ

qsu is the rate of heat loss from the side walls of upper con-vective zone per unit area of the pond given by:

qsu ¼PAs

luUsuðT u � T ambÞ ð17Þ

where Usu is the overall heat transfer coefficient from fluidinside the upper convective zone to the ambient.

The heat balance for upper convective zone in non-dif-ferential form can be written as

quCpuluT tþDt

u � T tu

� Dt

¼ I tjx¼0 � I tjx¼lu

� � k1

2

T tu � T t

1Dx1

2

!� qt

u

ð18Þ

where t is the time, Dt is the time increment and T1 is thetemperature of the first layer of the NCZ as defined inFig. 3.

From the above equation, the UCZ layer temperaturecan be obtained as follow:

1712 S. Tundee et al. / Solar Energy 84 (2010) 1706–1716

T tþDtu ¼T t

uþDt

quCpuluI tjx¼0� I tjx¼lu

� þk1

2

T tu�T t

1Dx1

2

!�qt

u

( )

ð19Þwhere qt

u is obtained from Eq. (9) by considering the corre-sponding values evaluated at time, t.

3.1.3. Energy balance for the non-convective zone (NCZ)

The energy balance for the NCZ as shown in Fig. 3 isgoverned by the heat diffusion equation and expressed byEq. (1). However, here this layer is also subjected to someheat losses through the wall surrounding it. This rate ofheat loss is assumed to be proportional to the temperaturedifference between the water in non-convective zone andthe ambient temperature.

The NCZ is divided into different layers for which theenergy equation is formulated below. Fig. 3 shows the divi-sion of the NCZ with the temperature in the first layerdenoted by T1 and in the last layer by Tf.

Thus, the energy balance for any layer i other than thefirst layer, 1 and the last layer, f as shown in Fig. 3 canbe written in the non-differential form as:

qiCPiDxiT tþDt

i � T ti

Dt¼ ki�1

2

T ti�1 � T t

i

�12ðDxi�1 þ DxiÞ

� kiþ12

�T t

i � T tiþ1

�12ðDxi þ Dxiþ1Þ

þ Ixi�1

2ð Þ� Ix

iþ12ð Þ

�

� PAs

DxiU sl T ti � T t

amb

� ð20Þ

Hence, the NCZ layer temperature can be expressed as:

T tþDti ¼ T t

iþDt

qiCpi

ki�12

1

Dx2i

T ti�1�T t

i

�� kiþ1

2

1

Dx2i

T ti�T t

iþ1

��

þ 1

Dxi½Ixði�1

2Þ� Ixðiþ1

2�� P

AsUsl T t

i�T tamb

� �ð21Þ

The above equation can be utilized to calculate the tem-perature at node i at time t + Dt when the temperature isknown for node i � 1, i and i + 1 at time t.

3.1.4. Energy balance for the lower convective zone (LCZ)

Heat balance for LCZ as shown in Fig. 3 can be writtenas:

qlCplll@T l

@t¼ Iluþln þ k fþ1

2ð Þ@T@x

����x¼luþln

� qsl � qg � qext

ð22Þwhere, Iluþln is the solar intensity available at lu þ ln depth,qsl is the rate of heat loss per unit area through side walls ofLCZ, qg is the heat loss per unit area through the pond bot-tom to the ground and qext is the rate of heat extraction perunit area of the solar pond by thermosyphons heatexchanger.

Heat loss from the side walls of LCZ can be obtainedfrom:

qsl ¼PAs

llUslðT l � T ambÞ ð23Þ

Heat loss to the ground is given by:

qg ¼ U gðT l � T gÞ ð24Þ

Energy balance in non-differential from can be writtenas:

qlCplllT tþDt

l � T tl

� Dt

¼ I tjx¼ðluþlnÞ � U g T tl � T t

g

� �� P

AsllUsl T t

l � T tamb

�

þ kfþ12

T tf � T t

lDxf

2

!� qt

ext ð25Þ

Hence, the LCZ layer temperature can be obtained fromEq. (26) as:

T tþDti ¼ T t

i þDt

qlCplllI t

x¼ðluþlnÞ � U g T tl � T t

g

� �n

� PAs

llU sl T tl � T t

amb

� þ kfþ1

2

T tf � T t

lDxf

2

!� qt

ext

)

ð26Þ

3.1.5. Numerical calculation procedure

Computer code was written on the basis of the mathemat-ical approach outlined in the previous section to solve theenergy balance equations for the three layers of the solarpond and obtain the temperature distribution inside eachlayer. The input parameters for the program includes solarpond dimensions, climatic parameters including ambienttemperature and solar radiation intensity as obtained fromthe meteorological data for Khon Kaen, Thailand. Numeri-cal calculations were initialized by assuming the temperatureof the various layer of the solar pond to be equal to the ambi-ent temperature at time, t = 0. Firstly, the code determinesthe value for various internal and external heat transfer coef-ficients and the liquid properties in different layers of thepond on the basis of the initial (i.e. ambient) temperature.The obtained values of various heat transfer coefficientsalong with the values for other climatic parameters were fur-ther used to calculate the temperatures for different layers ofthe solar pond at time interval Dt. Using the same procedure,the code can be used to determine the temperatures of thelayers for any selected time interval or time of the day. Hence,the hourly and daily temperature values as well as the dailysolar pond efficiency can be plotted from the output data.

4. Performance of the experimental solar pond and

comparison with simulation model

The solar pond at Rajamangala University of Technol-ogy, Isan Khon Kaen Campus in Thailand has been

0

20

40

60

80

100

120

140

160

975 1000 1025 1050 1075 1100 1125 1150 1175 1200 1225

Density (kg/m³)

Ele

vatio

n (c

m) Date: 30 June 2008

LCZ

NCZ

UCZ

Fig. 6. Density profile of the water in the solar pond.

0

20

40

60

80

100

120

140

160

20 25 30 35 40 45 50

Temperature (°C)

Elev

atio

n (c

m)

Date: 30 June 2008

LCZ

NCZ

UCZ

Fig. 7. Temperature profile inside the solar pond.

S. Tundee et al. / Solar Energy 84 (2010) 1706–1716 1713

continuously operating since 6 January 2008. Experimentalwork on the heat extraction from the solar pond usingdesigned HPHE system was conducted in the summer ofyear 2008. Fig. 5 shows the seasonal variation of lower con-vective zone temperature, denoted by TLCZ in Fig. 2, sincethe pond started operating. During the 8 month time per-iod plotted on the graph, the pond first showed uniformincrease in the LCZ temperature, since it began opera-tional, until it reached a maximum value of 42 �C on 17June and then it presented steady decline. The minimumLCZ temperature of about 32 �C occurred on 7 February.In the considered time, the ambient temperature variedfrom a minimum of 20 �C on 7 February to the maximumof 35 �C on 21 April. For the solar pond, the rate of heat-ing of LCZ is directly proportional to the incoming solarradiation and inversely proportional to the thickness ofthe LCZ. Here, the LCZ thickness is very importantparameter in the design of the solar pond. Large thicknessof the LCZ is advantageous to increase the heat storagecapacity of the pond whereas small thickness is useful toachieve faster temperature response of the layer with thechanging weather conditions and incoming radiation inten-sity. As shown in Fig. 5, the mathematical model has beenable to predict the pond LCZ temperature quite satisfacto-rily. The differences in the measured and predicted resultsare presumably due to the assumptions made in the formu-lation of the model and under-prediction of the heat lossesfrom the pond to the ambient and ground. In addition tothis, the effect of the weather condition like heavy rainfalland strong winds which is not considered in the presentmodel can magnify the heat losses from the pond therebyreducing the LCZ temperature.

In Fig. 6, density profile in the LCZ, NCZ and UCZ areplotted with respect to the height. It is noted that the den-sity in UCZ and LCZ is fairly constant. The density of theUCZ was close to that of pure water due to continuousflushing of the pond top surface with fresh water from

15

20

25

30

35

40

45

50

03-Jan

23-Jan

12-Feb

03-Mar

23-Mar

12-Apr

02-May M

Time

Tem

pera

ture

(°C

)

Daily m

Daily m

Ambien

Fig. 5. Comparison between measured and calculated t

water supply. For the LCZ, the density was close to satu-rated brine due to continuous charging of the layer withsalt from a salt diffuser. Fig. 7 shows the temperature pro-file in the pond for a typical hot summer day. The density

22-ay

11-Jun

01-Jul

21-Jul

10-Aug

30-Aug

19-Sep

09-Oct

(Date)

ean LCZ (Experiment)

ean LCZ (Model)

t

emperature variations in the lower convective zone.

Z1, Z9 Convection resistance Z2, Z8 Conduction resistance Z3f, Z3p, Z7 Internal resistance of boiling and condensing

(f denotes film and p denotes pool boiling) Z5 Thermal resistance due to vapour pressure drop Z10 Axially thermal conduction resistance Z4, Z6 Vapour liquid interface resistance

Top of condenser

Bottom of evaporator

Z1

Z2

Z3f

Z3p

Z4

Z5

Z6

Z7

Z8

Z10

Z9

Condensate Vapour

Heat source (Tso)

Heat source (Tsi)

Heat pipe container

Fig. 8. Thermal resistance and their locations.

Tao

Tai

TLCZ

Evaporator Section

Condenser Section

Air Out

Lower Convective Zone

Air In

Fig. 9. Heat pipe heat exchanger (HPHE) installed inside the lowerconvective zone (LCZ) of the solar pond and the associated temperatures.

1714 S. Tundee et al. / Solar Energy 84 (2010) 1706–1716

and temperature profiles in Figs. 6 and 7 are plotted for theperiod before the actual heat extraction from the pond wascommenced.

5. Heat pipe heat exchanger (HPHE) analysis

The gravity assisted heat pipe (thermosyphon) is aneffective heat transfer device that utilises latent heat ofthe working fluid, flowing under the influence of gravity,to transport heat from the source to the sink. As the latentheat of vaporization is relatively high, the thermosyphoncan transfer large quantity of heat with very small end toend temperature differential and thus low thermal resis-tance. In the thermal analysis of the heat pipe heat exchan-ger (HPHE) constructed from 60 thermosyphon tubes,equations and correlations from ESDU (1983) were used.The total thermal resistance (Ztot) of HPHE from heatsource which in this case is the lower convective zone tothe ambient heat sink is related to the actual overall heattransfer (Qtot) as given below:

Qtot ¼DT eff

Ztotð27Þ

where DTeff is effective temperature difference between heatsource and heat sink and defined by:

DT eff ¼ T so � T si � DT hh ð28Þ

In Eq. (28), Tso is heat source temperature, Tsi is the heatsink temperature and DThh is mean temperature differencedue to hydrostatic head of the liquid column in the evapora-tor which is calculated by using formulations from ESDU(1983). The individual thermal resistances that make upthe total thermal resistance from the heat source to the heatsink in the thermosyphon are depicted in Fig. 8. Calculationapproach mentioned in ESDU (1983) is used to determineeach resistance element. Fig. 9 shows the schematic of theheat pipe heat exchanger that was installed for heat extrac-tion from the lower convective zone of the solar pond.

The thermal performance of the heat pipe heat exchan-ger was assessed on the basis of the effectiveness-number oftransfer unit (NTU) method (Kays and London, 1994).For a heat pipe heat exchanger with n rows of heat pipesin the direction of flow, the following effectiveness-NTUequations can be written:

NTU ¼ UAtot

Cmin

ð29Þ

n ¼ 1� expð�NTUÞ ð30Þ

where UAtot is the overall thermal conductance of the ther-mosyphon heat exchanger as calculated in the previous sec-tion, i.e.

UAtot ¼1

Ztotð31Þ

Cmin is equal to heat capacity rate of the cold (Cc) or hot(Ch) fluid, whichever is small. In the present case, the heatcapacity of the lower convective zone is large enough as

compare to the heat capacity of the air flowing throughthe HPHE condenser therefore Cmin represents the heatcapacity of the cold fluid.

Effectiveness of the heat exchanger can also be obtainedfrom:

n ¼ Qtot

Qmax

ð32Þ

The maximum possible heat transfer from the heatexchanger can be expressed as:

Qmax ¼ m�aCpaðT LCZ � T aiÞ ð33Þ

0

10

20

30

40

50

60

0 1 2 3 4 5 6

Mean air velocity (m/s)

Effe

ctiv

enes

s (%

)

Fig. 11. Effect of air velocity on the heat exchanger effectiveness.

S. Tundee et al. / Solar Energy 84 (2010) 1706–1716 1715

6. HPHE results and discussion

It is evident from the Eq. (27) that the thermal perfor-mance of the HPHE is dependent on the solar pond tem-perature. While the solar pond LCZ temperature is low,the thermosyphon will have low thermal performance dueto the high thermal resistance encountered by the workingfluid (R134a) at the low operating temperatures. For highLCZ temperature in solar pond, the HPHE shows superiorthermal performance owing to the improvement in the fig-ure of merit of the working fluid at high temperatures(Dunn and Reay, 1994). As a result, the effectiveness ofthe thermosyphon based heat exchanger for heat extractionfrom LCZ increases at higher pond temperatures. For largequantity of heat extraction from the LCZ, the pond tem-perature will eventually decrease which will result in thecorresponding decrease in the performance of the ther-mosyphon. This cycle is repeated continuously in the heatextraction by two phase thermosyphon heat exchanger.Fig. 10 shows the solar pond LCZ temperature and heatextraction rate by HPHE from the experimental solar pondat Khon Kaen province for 3 h time period. The heatextraction rate showed somewhat cyclic variation withrespect to the time as discussed above. It is noted fromthe graph that the LCZ temperature is fairly constantwhich can be due to small quantity of heat extraction rateas compared to the overall thermal capacity of the pondand remote location of the LCZ temperature measurementpoint from the HPHE evaporator.

Fig. 10 also shows the variation of inlet and outlet airtemperature across the HPHE condenser. It is noted fromthe graph that the average temperature of LCZ and tem-perature of inlet air at condenser section was 39.9 �C and28.8 �C respectively. With 60 thermosyphon tubes, the rateof heat extraction was around 100 W on the continuousbasis for a time period of 3 h which resulted in very slightdecrease from 40 �C to 39 �C in the solar pond LCZ tem-perature. It should be noted that the size and simplicityof the heat pipe heat exchanger, which includes only 60thermosyphon tubes without any fins or heat enhancementsurfaces on the evaporator or condenser sides, restricts theheat extraction rate from the LCZ to the stated values. In

0

20

40

60

80

100

120

0 20 40 60 80 100 120 140 160 180 200

Time (minute)

Hea

t ext

ract

ion

(W)

0

10

20

30

40

50

60

Tem

pera

ture

(°C

)

Heat extraction rateAir inlet temperatureAir outlet temperatureLCZ temperature

Fig. 10. Heat extraction rate and related temperature distribution duringheat transfer process from solar pond.

this case, design modifications including increase in theheat transfer area and augmentation in the heat exchangeprocess can improve the extraction rate. However, the pres-ent design of the heat exchanger based on the passivelyoperating thermosyphon provided a sustainable and energyefficient method of extracting heat stored in the solar pond.

Fig. 11 plots the overall heat exchanger effectiveness forcondenser inlet air velocity ranging from 1 to 5 m/s and forsolar pond LCZ temperature of 40 �C. It is noted from theplot that the effectiveness decreases with the increase in theinlet air velocity which is due to the decrease in the temper-ature of the air exiting the HPHE exchanger. As in this casethe heat capacity of the lower convective zone is very high,an increase in the air flow velocity through the HPHE con-denser results in the corresponding decrease in the air out-let temperature which in turn decreases the effectiveness ofthe heat exchanger as per simplified form of Eq. (32) givenbelow.

n ¼ T ao � T ai

T LCZ � T aið34Þ

The investigation showed that the thermal performanceof the thermosyphon heat exchanger can be increased up to43% by decreasing the inlet air velocity from 5 m/s to 1 m/s. The outcome of the simulation approach is comparedwith the experimental results on the basis of effectivenessversus NTU plot in Fig. 12. As evident form the plot, the

00.10.20.30.40.50.60.70.80.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

NTU

Effe

ctiv

enes

s

ModelExp (V=1 m/s)Exp (V=2 m/s)Exp (V=3 m/s)Exp (V=4 m/s)Exp (V=5 m/s)

Fig. 12. Effectiveness versus NTU plot for the heat pipe heat exchanger.

1716 S. Tundee et al. / Solar Energy 84 (2010) 1706–1716

predicted trend showed good agreement with the experi-mentally obtained results. It is noted that the effectivenessand NTU shows increase with the decrease in the inletair velocity which is very typical for the heat exchangers.In the present application the main objective is to extractheat from the pond at high temperature, therefore lowvelocity at the HPHE condenser will provide twofold ben-efit of increase in heat transfer effectiveness and low powerconsumption by the air blower.

7. Conclusions

In this paper, heat extraction from a small-scale solarpond by means of two-phase heat pipe heat exchangerhas been studied. A heat pipe heat exchanger was installedin the lower convective zone of the salinity gradient solarpond to extract heat on the continuous basis. Detailedexperimental and theoretical investigation has been con-ducted on the thermal performance of the salinity-gradientsolar pond and two phase heat extraction system. A math-ematical model to predict the temperature profile for differ-ent zones in the solar pond and to access the thermalperformance of the thermosyphon equipped heat exchan-ger on the basis of the effectiveness-NTU approach hasbeen explained in detail. The small scale thermosyphon(or heat pipe) heat exchanger used for extracting heat fromthe solar pond showed a continuous heat extraction rate ofabout 100 W. As a result, there was a drop in temperatureof lower convective zone from 40 �C to 39 �C in 3 h periodof heat extraction. For the conducted tests, the maximumeffectiveness of 43% for heat exchanger at the air inletvelocity of 1 m/s was achieved. The predicted outcomesfrom the mathematical model showed reasonable agree-ment with the experimental results.

Acknowledgements

The authors would like to express their sincere gratitudefor the support provided by Rajamangala University ofTechnology and Global Cities of RMIT University forundertaking the present research work.

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