Plate Heat Pipe

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International Journal of Low Carbon Technologies 1/1

Analysis of a plate heat pipe solarcollector

Jorge Facão and Armando C. Oliveira

Faculty of Engineering, University of Porto (Dept.Mec.Eng.), Rua Dr. Roberto Frias, 4200-465

Porto, Portugal

Abstract The thermal behaviour of a plate heat pipe solar collector was analysed numerically and

experimentally. The numerical model is based on energy balance equations assuming a quasi-steady

state condition. The major simplification was that the temperature in the heat pipe was considered to

be uniform and equal to the saturation temperature. This assumption is not far from the truth, since

heat pipes are considered as isothermal devices. A small-scale solar collector, with an aperture area of

about 0.1 m2, was experimentally tested during the summer season in Porto. Two types of tests were

made: the first was the determination of the instantaneous efficiency curve and the second was thedetermination of the collector time constant, a measure of its thermal inertia. Results showed a

collector optical efficiency of 64% and an overall loss coefficient of 5.5 W/(m2K), for a non-selective

surface coating. There was a good agreement between numerical and experimental results.

Keywords plate heat pipe solar collector; model; experiment

Nomenclature

A area [m2]

c p pressure specific heat [J/(KgK)]

F ¢ collector efficiency factor

h heat transfer coefficient [W/(m2K)]

I incident solar radiation on collector tilted surface [W/m2]

Q.

useful energy gain [W]

m.

mass flow rate [kg/s]

T temperature [K]

U overall heat loss coefficient [W/(m2K)]

Greek Letters

a absorptance

e emissivity

h collector efficiency

t transmittance

s Stefan-Boltzmann constant [W/m2 /K4]

Subscripts

a ambientback back

c cover

cond condenser



fm fluid mean = (inlet + outlet)/2

in inlet

out outlet

p plate

p-c plate to coversat saturation

sky sky

w wind

1. Introduction

Heat pipes are devices that can transfer large quantities of heat. Since they use the

latent heat of vaporization, the difference between the temperature of the two heat

sources is small. The manufacturing process consists in inserting a small quantityof fluid (e.g. water) in an evacuated closed pipe with a wick. Inside the heat pipe

there are only liquid and vapour. The temperature of the fluid is the saturation tem-

perature, between triple and critical point.

Heat pipes can be used to provide a uniform temperature, generating isothermal

surfaces. They can be used for temperature control in electronic applications, to cool

processors and as thermal diodes. They have the advantage of being silent, operat-

ing independently of gravity, not needing servicing and having no moving parts. In

addition, freezing of the heat pipe is not destructive [1]. They exist in several geome-

tries: pipes, plates, with annular or rectangular sections.Since the advent of heat pipes in 1960, their importance in solar applications

such as solar collectors for domestic water heating, space heating, and cooling of

buildings has received increasing attention [2]. A heat-pipe solar collector operates

like a thermal diode where the flow of heat is in one direction only [3]. Whenever

the temperature of the storage tank is higher than condenser temperature, the

heat pipe stops, preventing the circulation of storage tank fluid to the solar

collector.

Bienert and Wolf [4] carried out one of the first studies of heat pipes in solar col-

lectors, in 1976. Their results were neither conclusive nor optimistic. The water

manifold was so bulky that the energy collected and lost easily offseted any advan-

tages the heat pipe may have had. Ramsey et al. [5] obtained a collector efficiency

of 50% at 300°C for a selective coated heat pipe collector using single axis track-

ing parabolic trough concentrator. Ortabasi and Fehlner [6] analysed a heat pipe con-

centrator solar collector with selective surface, cusp mirror and vacuum insulation.

Vries et al. [7] developed a resistance analogue model for heat pipe and conven-

tional solar collector. They concluded that the performance of the heat pipe collec-

tor used without fluid circulation control was as good as that of a conventional

collector used with control. Hull [8] showed theoretically that arrays with less than

10 heat pipes connected to a single manifold, had a significantly lower efficiencythan a similar conventional open-loop thermosyphon hot water heater, based on the

same plate area. Akyurt [9] compared the thermal behaviour of two conventional

thermosyphon collectors with a heat pipe solar collector. This one had an efficiency

2 J. Facão and A. C. Oliveira




50% higher than the conventional collectors. Bong [3] presented a theoretical model

for the determination of the efficiency, the heat removal factor, and the outlet water

temperature of a single collector and an array of flat-pipe heat-pipe collectors. The

model was validated by testing 16 heat pipe collectors. The results showed an optical

efficiency of 44% and an overall heat loss coefficient of 2.85 W/(m2K). El-Nasr andEl-Haggar [10] designed and tested a wickless solar collector using R11, acetone

and water as working fluids at different charging pressures, under the climatic con-

ditions of Cairo, Egypt. Ismail and Abodgderah [11] presented a comparative theo-

retical and experimental analysis of a heat pipe solar collector. The theoretical model

for the heat pipe solar collector was based on the method by Duffie and Beckman

[12], modified to include heat pipes for energy transportation. The working fluid in

the heat pipes was methanol. The condenser was wickless and inclined 15 deg more

than the inclination of evaporators, to facilitate condensate return. The instantaneous

efficiency was higher than the one of a conventional collector, when the heat pipesreached their operating temperatures. Ghaddar and Nasr [13] investigated experi-

mentally the performance of a heat pipe solar collector using R11 as a working

fluid in Beirut, Lebanon. The instantaneous efficiency varied from 60 to 20%.

Mathioulakis and Belessiotis [1] investigated theoretically and experimentally the

performance of a solar hot water system with an integrated heat pipe. The system

used a wickless gravity assisted heat pipe with ethanol as working fluid. The

condenser was inserted directly inside the tank. They got an instantaneous efficiency

up to 60%.

All the solar collectors reported in the previous paragraph were made with circu-lar heat pipes, and some were evacuated. The collector analysed in this work uses

a plate heat pipe manufactured by Thermacore Europe Ltd (UK). The plate was

coated with black paint (Nextel 3101c10), with emissivity and absorptance for solar

radiation of approximately 0.96 in a wide spectrum of wavelength – non selective

coating. The condenser was implemented under the plate through a rectangular

section channel – see figure 1. The water that circulates in the channel is in direct

contact with the plate, minimizing the thermal resistance. The plate was encased in

a 434mm ¥ 325mm ¥ 100mm aluminium box with 50mm of rock wool insulation.

The cover was a window glass (354mm ¥ 250mm) placed at 20mm from the plate

heat pipe. Figure 2 shows a view of the solar collector.

2. Energy balance model

The model assumes a quasi-steady state condition in each collector component. The

major simplification was that the temperature in the plate heat pipe was considered

to be uniform and equal to the saturation temperature. This assumption is not far

from the truth, since heat pipes are considered as isothermal devices.

The energy balance equation on the glass cover is:

(1)a s

e e

e s c

sat c

c p

p c sat c c c sky w c a I T T

h T T T T h T T +-

+ -+ -( ) = -( ) + -( )-

4 44 4

1 11

Analysis of a plate heat pipe solar collector 3






Figure 1. Plate heat pipe representation and dimensions.

Figure 2. View of plate heat pipe solar collector.



The energy balance equation on the plate is:

(2)

The energy balance on the condenser is:

(3)

A non-linear system of equations has to be solved, with 3 equations and 3

unknown variables: Tsat, Tc and Tout. The model was implemented in the EES [14]

computer environment. Tin, Ta and I are considered to be known.

The useful heat collected can be given by

(4)

Difficulties in knowing directly the plate temperature, Tp, make it more conve-

nient to present the efficiency as a function of fluid temperature, Tf . Since Tf < Tp,

a factor less than unity, F¢ – collector efficiency factor, is needed. This factor repre-

sents the ratio of the actual useful energy gain to the useful gain that would result

if the collector absorbing surface was at the fluid temperature, and

(5)

This equation is known in the literature as the Hottel-Whillier-Bliss equation, [16],[17]. The collector efficiency expresses the fraction of incident energy that is col-

lected by the working fluid:

(6)

Figure 3 shows the simulated instantaneous efficiency of the solar collector. It was

obtained by varying the different model inputs: Tin, Ta and I. The heat transfer coef-

ficient in the condenser, hcond, was calculated using the study of Shah and London

[15].Note that efficiency characteristics (F¢t ca p and F¢U) are fairly good, with a loss

factor lower than the typical value for non-selective flat-plate collectors (in the range

7–8W/(m2K)).

h t a = ¢( ) -¢ -( )Q̇

IAF

F U T T

I c p

fin a

Q F IA F UA T T c p fin a= ¢ ( ) - ¢ -( )t a

Q mc T T IA UA T T p out in c p p a= -( ) = ( ) - -( )t a

mc T T A hT T T T

T T

T T

A U T T T T

T T

T T

p out in cond cond

sat in sat out

sat in

sat out

cond back

in a out a

in a

out a

-( ) =-( ) - -( )

-( )

-( )

--( ) - -( )

-( )

-( )

ln

ln

a t s

e e

p c c p

sat c

c p

p c p sat c back back sat a

cond cond

sat in sat out

sat in

sat out

A AT T

h A T T U A T T

A hT T T T

T T

T T

= +-

+ -

+ -( ) + -( ) +

-( ) - -( )

-( )

-( )

-

4 4

1 11

ln





3. Performance tests

The collector was tested in open circuit in outdoor conditions, according to the Por-

tuguese Standard NP–1802 [18]. To get results for different inlet temperatures an

electric heater with variable power was used. The nominal mass flow rate was

20g/s/m2 (0.019kg/s) and measured with an ultra-low rate flowmeter – accuracy of

±3%. To stabilise the pressure and flow rate at collector inlet, an atmospheric pre-

ssure tank was used – see figure 4 representing the experimental facility for solarcollector testing. The inlet and outlet water temperature was measured with cali-

brated type T thermocouples. The solar radiation was measured with a Kipp & Zonen

pyranometer, with a sensitivity of 13.20V/(Wm2) and a maximum error of ±5%. The



= 0.68 - 6.11(Tfm

-Ta)/I

0

0.1

0.2

0.3 h

h

0.4

0.5

0.6

0.7

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

(Tfm-Ta)/I [∞Cm2 /W]

Figure 3. Collector efficiency obtained with the model.

Tin

Tout

Heater

Pyranometer

Ta

.

m

Solar collector

Tank

Figure 4. Experimental facility for solar collector testing.



ambient air temperature was measured with an Mo 1000 sensor with a maximum

error of 0.46°C. The data acquisition system used a data logger – HP 34970A – and

HP VEE as software.

Two types of tests were made: the first was the determination of the instantaneous

efficiency curve, for incident angles of direct beam radiation smaller than 30° and

global radiation higher than 630W/m2, and the second was the determination of the

collector time constant, a measure of its thermal inertia.

Figure 5 shows the comparison of measured instantaneous efficiency and model

efficiency. There is a good agreement between numerical and experimental results.

Experimental results confirm the collector good performance: F¢U value of

5.5W/(m2K) compared to 7–8 for a normal flat-plate collector.

The time constant is defined as the time required for the fluid leaving the collec-

tor to change its temperature by (1 - 1/e), or 0.632, of the total difference between

its initial and its final steady-state value, after a change in the incident radiation [12].

The fluid inlet temperature must be controlled near ambient temperature. The time

at which the equality for equation 9 is reached is the time constant:

(9)

Figure 6 shows the time-temperature plot under a sudden reduction of the solar

radiation on the collector to zero. The calculated time constant was equal to 410s

(6min and 50s). This is a low value, which confirms the assumption of quasi-steady

state used in the model.

4. Conclusions

The thermal performance of a plate heat pipe solar collector was evaluated numeri-

cally and experimentally.

T T

T T e

out in

out init in

-( )

-( )= =

,

.1

0 368



fitting = 0.64 - 5.55(Tfm-Ta)/I

R2 = 0.84

model = 0.68 - 6.11(Tfm-Ta)/I

0

0.1

0.2

0.3

h

h

h

0.4

0.5

0.6

0.7

0 0.02 0.04 0.06 0.08

(Tfm-Ta)/I [∞Cm

2

/W]

experiment

exp. fitmodel

Figure 5. Comparison of experimental and model efficiency.



The model involved the solution of a set of non-linear algebraic equations. The

major simplification was that the temperature in the plate heat pipe was considered

uniform.

A small solar collector was tested and the results showed an optical efficiency of

64% and an overall loss coefficient of 5.5W/(m2K). The collector time constant is

equal to 6min and 50s. The simulated efficiency is in good agreement with experi-mental results. The results indicate a performance for the plate heat pipe collector,

which is better than the one for normal flat-plate collectors (non-selective).

Acknowledgements

The authors wish to thank Fundação para a Ciência e a Tecnologia (P), for the

scholarship of the first author. They also wish to express their gratitude to the

European Commission (DG Research) for partially funding the work done, under

the Hybrid-CHP research project (contract ENK5-CT-2000-00080). The other part-ners of the project are also acknowledged.

References

[1] E. Mathioulakis and V. Belessiotis, ‘A New heat-pipe solar domestic hot water system’, Solar

Energy, 2002, Vol 72, No 1, 13–20.

[2] N. Susheela and M. K. Sharp ‘Heat pipe augmented passive solar system for heating of buildings’,

Journal of Energy Engineering, 2001, Vol 127, No 1, April, 18–36.

[3] T. Y. Bong, K. C. Ng and H. Bao, ‘Thermal performance of flat-plate heat-pipe collector array’,

Solar Energy, 1993, Vol 50, No 6, 491–498.[4] W. B. Bienert and D. A. Wolf, ‘Heat pipes in flat plate solar collectors’, ASME paper, 1976, No 76-

WA/Sol-12.

[5] J. W. Ramsey, B. P. Gupta and G. R. Knowles, ‘Experimental evaluation of cylindrical parabolic

solar collector’, ASME paper, 1976, No 76-WA/HT–13.



37

38

39

40

41

42

43

44

0 100 200 300 400 500

Time [s]

T e m p e r a t u r e [ ∞ C ] Tin

Tout

Ta

Figure 6. Time-temperature plot for a sudden reduction of solar radiation on the collector

to zero.



[6] U. Ortabasi and F. P. Fehlner, ‘Cusp mirror-heat pipe evacuated tubular solar thermal collector’,

Solar Energy, 1980, Vol 24, 477–489.

[7] H. F. W. Vries, de W. Kamminga and J. C. Francken, ‘Fluid circulation control in conventional and

heat pipe planar solar collectors’. Solar Energy, 1980, Vol 24, 209–213.

[8] J. R. Hull, ‘Analysis of heat transfer factors for a heat-pipe absorber array connected to a commom

manifold’. Journal of Solar Energy Engineering, Transactions of the ASME , 1986, Vol 108, No 1,11–16.

[9] M. Akyurt, ‘AWSWAH – The heat-pipe solar water heater’, J. Engng Appl. Sci, 1986, Vol 3, No

1–2, 23–28.

[10] Nasr, El, Haggar, El, ‘Analysis of a wickless solar collector in Cairo’, Renewable Energy, 1995,

Vol 5, 341–344.

[11] K. A. R. Ismail and M. M. Abogderah, ‘Performance of a heat pipe solar collector’, Journal of Solar

Energy Engineering, Transactions of the ASME , 1998, Vol 120, February, 51–59.

[12] J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes, 1991, second edition,

John Wiley & Sons, Inc.

[13] N. Ghaddar and Y. Nasr, ‘Experimental study of refrigerant charged solar collector’, International

Journal of Energy Research, 1998, Vol 22, 625–638.[14] S. A. Klein, Enginering Equation Solver , F-Chart Software, Middleton, USA 2004.

[15] R. K. Shah, ‘Laminar flow forced convection in ducts’, in Supplement 1 to Advances in Heat Trans-

fer , 1978, edited by Irvine, T. F., Hartnett, J. P. Academic Press, New York.

[16] H. C. Hottel and W. Whillier, ‘Evaluation of flat plate solar collector performance’, Trans. Conf.

Use of Solar Energy Thermal Processes, 1955, Tuscon, AZ.

[17] R. W. Bliss, ‘The derivation of several “plate efficiency factors” useful in the design of the flat plate

solar heat collector’, Solar Energy, 1959, Vol 4, 55–64.

[18] NP-1802, Colectores Solares, Determinação da Curva de rendimento Instantâneo, 1985.



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