Analysis of a Plate Heat Pipe Solar Collector

SET 2004 - International Conference on Sustainable Energy Technologies Nottingham, UK, 28-30 June 2004 Page 1 of 5 Analysis of a Plate Heat Pipe Solar Collector Jorge Facão and Armando C Oliveira Faculty of Engineering, University of Porto (DeptMecEng 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 quasisteady 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 01 m 2, 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 the determination 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 55 W/(m 2 K, 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 [m 2 ] c p pressure specific heat [J/(KgK] F collector efficiency factor h heat transfer coefficient [W/(m 2 K] I incident solar radiation on collector tilted surface [W/m 2 ] Q m useful energy gain [W] mass flow rate [kg/s] T temperature [K] U overall heat loss coefficient [W/(m 2 K] Greek letters α absorptance ε emissivity η collector efficiency τ transmittance σ Stefan-Boltzmann constant [W/m 2 /K 4 ] Subscripts a ambient back back c cover cond condenser fm fluid mean = (inlet+outlet/2 in inlet out outlet p plate p-c plate to cover sat 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 quantity of fluid (eg 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 temperature, 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, operating 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 geometries: 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 collectors, in 1976 Their results were neither conclusive nor optimistic The water manifold was so bulky that the energy collected and lost easily offseted any advantages the heat pipe may have had Ramsey et al [5] obtained a collector

SET2004 International Conference on Sustainable Energy Technologies Nottingham, UK, 28-30 June 2004 Page 2 of 5 efficiency of 50% at 300ºC for a selective coated heat pipe collector using single axis tracking parabolic trough concentrator Ortabasi and Feher [6] analysed a heat pipe concentrator solar collector with selective surface, cusp mirror and vacuum insulation Vries et al [7] developed a resistance analogue model for heat pipe and conventional solar collector They concluded that the performance of the heat pipe collector 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 efficiency than 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 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 285 W/(m 2 K El-Nasr and El-Haggar [10] designed and tested a wickless solar collector using R11, acetone and water as working fluids at different charging pressures, under the climatic conditions of Cairo, Egypt Ismail and Abodgderah [11] presented a comparative theoretical 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 pipes reached their operating temperatures Ghaddar and Nasr [13] investigated experimentally 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 circular 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 096 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 434 mm x 325 mm x 100 mm aluminium box with 50 mm of rock wool insulation The cover was a window glass (354 mm x 250 mm placed at 20 mm from the plate heat pipe Figure 2 shows a view of the solar collector Figure 1 Plate heat pipe representation and dimensions Figure 2 View of plate heat pipe 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

SET2004 International Conference on Sustainable Energy Technologies Nottingham, UK, 28-30 June 2004 Page 3 of 5 is: The energy balance equation on the glass cover 4 4 Tsat Tc αci + σ + hp c Tc = 1 1 + 1 εc ε p = εσ T 4 T 4 + h T T (1 ( ( c c sky w c a The energy balance equation on the plate is: 4 4 Tsat Tc ατ p ciac = σap + hp cap Tc + 1 1 + 1 εc ε p T T T T + Uback Aback Ta + Acondhcond T T ( ( sat in sat out ( The energy balance on the condenser is: ( p out in cond cond sat out ( Tin Ta ( Ta Uback ( Tin Ta ( T T mc T T = A h A cond out a (2 (3 A non-linear system of equations has to be solved, with 3 equations and 3 unknown variables: T sat, T c and T out The model was implemented in the EES [14] computer environment T in, T a and I are considered to be known The useful heat collected can be given by ( ( τα ( Q= mc T T = IA UA T T p out in c p p a (4 Difficulties in knowing directly the plate temperature, T p, make it more convenient to present the efficiency as a function of fluid temperature, T f Since T f <T p, a factor less than unity, F - collector efficiency factor, is needed This factor represents 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 heat transfer coefficient in the condenser, h cond, was calculated using the study of Shah and London [15] Note that efficiency characteristics (F τ c α 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 7-8 W/(m 2 K η 07 06 05 04 03 02 01 η = 068-611(T fm /I 0 0 001 002 003 004 005 006 007 008 (T fm /I [ºCm 2 /W] Figure 3 Collector efficiency obtained with the model 3 PERFORMANCE TESTS The collector was tested in open circuit in outdoor conditions, according to the Portuguese 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 20 g/s/m 2 (0019 kg/s and measured with an ultra-low rate flowmeter accuracy of +-3% To stabilise the pressure and flow rate at collector inlet, an atmospheric pressure tank was used see figure 4 representing the experimental facility for solar collector testing The inlet and outlet water temperature was measured with calibrated type T thermocouples The solar radiation was measured with a Kipp & Zonen pyranometer, with a sensitivity of 1320 V/(Wm² and a maximum error of ±5% The ambient air temperature was measured with an Mo 1000 sensor with a maximum error of 046ºC The data acquisition system used a data logger HP 34970A and HP VEE as software Pyranometer ( τα c p ' ( fm a Q= F' IA F UA T T (5 Solar collector 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 collected by the working fluid: ( fm Ta Q F ' U T η = = F '( τcαp (6 IA I Figure 3 shows the simulated instantaneous efficiency of the solar collector It was obtained by varying the different model inputs: T in, T a and I The Tin Heater m T a Tank Figure 4 Experimental facility for solar collector testing

SET2004 International Conference on Sustainable Energy Technologies Nottingham, UK, 28-30 June 2004 Page 4 of 5 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 30º and global radiation higher than 630 W/m 2, 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 55 W/(m 2 K compared to 7-8 for a normal flat-plate collector η 07 06 05 04 03 02 01 η fitting = 064-555(T fm /I R 2 = 084 η model = 068-611(T fm /I experiment exp fit model 0 0 002 004 006 008 (T fm /I [ºCm 2 /W] Figure 5 Comparison of experimental and model efficiency The time constant is defined as the time required for the fluid leaving the collector to change its temperature by (1-1/e, or 0632, 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: 1 = = 0368 T T e out, init in (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 410 s (6 min and 50 s 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 numerically and experimentally The model involved the solution of a set of nonlinear 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 55 W/(m 2 K The collector time constant is equal to 6 min and 50 s The simulated efficiency is in good agreement with experimental 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 Temperature [ºC] 44 43 42 41 40 39 38 37 0 100 200 300 400 500 Time [s] Tin Ta Figure 6 Time-temperature plot for a sudden reduction of solar radiation on the collector to zero Acknowledgments 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 partners of the project are also acknowledged REFERENCES [1] Mathioulakis, E, Belessiotis, V 2002 A New heat-pipe solar domestic hot water system Solar Energy Vol 72 No 1 pp13-20 [2] Susheela, N, Sharp, M K 2001 Heat pipe augmented passive solar system for heating of buildings Journal of Energy Engineering Vol 127 No 1 April pp18-36 [3] Bong, T Y, Ng, K C, Bao, H 1993 Thermal performance of flat-plat heat-pipe collector array Solar Energy Vol 50 No 6 pp491-498 [4] Bienert, W B, Wolf, D A 1976 Heat pipes in flat plate solar collectors, ASME paper No 76- WA/Sol-12 [5] Ramsey, J W, Gupta, B P, Knowles, G R 1976 Experimental evaluation of cylindrical parabolic solar collector, ASME paper No 76-WA/HT 13 [6] Ortabasi, U, Feher, F P 1980 Cusp mirrorheat pipe evacuated tubular solar thermal collector Solar Energy Vol 24 pp477-489 [7] Vries, de, H F W, Kamminga, W, Francken, J C 1980 Fluid circulation control in conventional and heat pipe planar solar collectors Solar Energy Vol 24 pp209-213 [8] Hull, J R 1986 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 Vol 108 No 1 pp11-16

SET2004 International Conference on Sustainable Energy Technologies Nottingham, UK, 28-30 June 2004 Page 5 of 5 [9] Akyurt, M 1986 AWSWAH The heat-pipe solar water heater J Engng Appl Sci Vol 3 No 1-2 pp23-28 [10] Nasr, El, Haggar, El 1995 Analysis of a wickless solar collector in Cairo Renewable Energy Vol 5 pp341-344 [11] Ismail, K A R, Abogderah, M M 1998 Performance of a heat pipe solar collector Journal of Solar Energy Engineering, Transactions of the ASME Vol 120 February pp51-59 [12] Duffie, J A, Beckman, W A 1991 Solar Engineering of Thermal Processes, second edition John Wiley & Sons, Inc [13] Ghaddar, N, Nasr, Y 1998 Experimental study of refrigerant charged solar collector International Journal of Energy Research Vol 22 pp625-638 [14] Klein, S A 2004 Enginering Equation Solver F-Chart Software Middleton, USA [15] Shah, R K, London 1978 Laminar flow forced convection in ducts in Supplement 1 to Advances in Heat Transfer edited by Irvine, T F, Hartnett, J P Academic Press New York [16] Hottel, H C, Whillier, W 1955 Evaluation of flat plate solar collector performance Trans Conf Use of Solar Energy Thermal Processes Tuscon AZ [17] Bliss, R W 1959 The derivation of several plate efficiency factors useful in the design of the flat plate solar heat collector Solar Energy Vol 4 pp55-64 [18] NP-1802 1985 Colectores Solares, Determinação da Curva de rendimento Instantâneo