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Developing a theoretical model to investigate thermal performance of a thin membrane heat-pipe solar collector
Applied Thermal Engineering 25 (2005) 899–915 www.elsevier.com/locate/apthermeng
Developing a theoretical model to investigate thermal performance of a thin membrane heat-pipe solar collector S.B. Riffat, X. Zhao *, P.S. Doherty School of the Built Environment, The University of Nottingham, Nottingham, NG7 2RD, UK Received 17 September 2003; accepted 7 August 2004
Abstract A thin membrane heat-pipe solar collector was designed and constructed to allow heat from solar radiation to be collected at a relatively high efficiency while keeping the capital cost low. A theoretical model incorporating a set of heat balance equations was developed to analyse heat transfer processes occurring in separate regions of the collector, i.e., the top cover, absorber and condenser/manifold areas, and examine their relationship. The thermal performance of the collector was investigated using the theoretical model. The modelling predictions were validated using the experimental data from a referred source. The test efficiency was found to be in the range 40–70%, which is a bitter lower than the values predicted by modelling. The factors influencing these results were investigated. 2004 Elsevier Ltd. All rights reserved. Keywords: Heat pipes; Solar collector; Thin; Membrane; Efficiency; Testing; Simulation
1. Introduction Solar collectors transform solar radiation into thermal energy. There are several types of solar collector available for practical applications, including evacuated tubes, flat plate solar collectors and parabolic dish collectors. *
Corresponding author. Tel.: +44 115 846 7873; fax: +44 115 951 3159. E-mail address: [email protected] (X. Zhao).
1359-4311/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.08.010
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Nomenclature A Cp d Fv h In k V L m n Nu Pr Q r R t x d q g g
area (m2) specific heat (J/kg C) diameter (m) frictional resistance coefficient of the vapour flow in the heat pipe convection heat transfer coefficient (W/m2 C) global solar irradiation (W/m2) thermal conductivity (W/m C) volume flow rate (m3/s) length (m) mass flow rate (kg/s) number of the heat pipes included Nusselt number Prandtl number heat (W) radius (m) heat resistance (m2 C/W) temperature (C) general external parameter thickness (m) density of air (kg/m3) collector thermal efficiency—term 1 collector thermal efficiency—term 2
Subscripts a ambient ab absorber abs absorption adia adiabatic section av average cl cooling liquid con condenser cond condensation section dw downside wall eq equivalent evap evaporation section hp heat pipe hy hydraulic i inside inc incident radiation ins insulation layer
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lim max o ref tc tra
901
limit maximum outside reflection top cover transmission
Heat pipes are devices of high thermal conductance, which transfer thermal energy by twophase circulation of fluid, and can easily be integrated into most types of solar collector. The basic difference in thermal performance between a heat-pipe solar collector and a conventional one lies in the heat-transfer processes from the absorber tube wall to the energy-transporting fluid. In the case with a heat pipe, the process is evaporation–condensation–convection, while for conventional solar collectors, heat transfer occurs only in the absorber plate. Thus, solar collectors with heat pipes have a lower thermal mass, resulting in a reduction of start-up time. A feature that makes heat pipes an attractive for use in solar collectors is their ability to operate like a thermal-diode, i.e., the flow of the heat is in one direction only. This minimizes heat loss from the transporting fluid, e.g., water, when incident radiation is low. Furthermore, when the maximum design temperature of the collector is reached, additional heat transfer can be prevented. This would prevent over-heating of the circulating fluid, a common problem in many applications of solar collectors [3,6]. One of the first studies of heat pipes in solar applications was carried out by Bienert and Wol [3]. In this case, the evaporator end of a heat pipe was inserted in a flat-plate collector, and the condenser protruded into a water manifold attached to the upper end of the collector. The results of this investigation were neither conclusive nor optimistic. Since then, numerous studies have been carried out, including theoretical analysis and calculation [10,19,17,11], experimental testing [1,21,20,26,29,8,22], combined investigation involving theoretical analysis and experimental trials [9,12,13,15,16], as well as applications in practice [4,2,5,18]. Most of these studies involved the investigation of the thermal performance of various types of heat-pipe solar collectors by analytical, numerical or experimental methods with the aim of establishing suitable structures or system layouts, as well as optimum operating conditions for high efficiency. Of the existing collector designs, evacuated tube and flat-plate collectors are most widely used, and the former is usually found to be more efficient for high temperature applications. Flat-plate heat-pipe solar collectors, on the other hand, have their own set of advantages, including simpler structure, lower cost, easier manufacture and simple operation. The lower efficiency of flat-plate collectors is mainly due to the heat loss via the cover surface due to conduction and convection. Standard flat-plate collectors have typical efficiencies of 50% or less [22], while evacuated devices have efficiencies of about 50–80% [21,20,29]. It would be desirable to develop a new structure for flat plate collectors that would overcome heat loss problems and allow a high efficiency to be achieved, while its capital cost still remains low. This paper introduces a novel flat plate heat pipe solar collector, termed as Ôthin membrane heat pipe solar collectorÕ. This collector is expected to achieve a higher efficiency, but with relatively lower capital cost, compared to normal flat plat heat pipe solar collectors. One prototype of such
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kind of collector was constructed, and an analytical model that is able to simulate heat transfer processes occurring in the collector and calculate its efficiency, was developed based at the prototype structure. The model applied heat balance and heat resistance network method, which is a new approach in collector thermal performance analyses. Simulation on the performance of the collector was carried out, and the results were used to estimate its efficiency and determine the relation between efficiency and general external parameter, (tmean ta)/In.
2. Prototype set-up A prototype thin membrane heat-pipe solar collector was designed to collect and distribute heat by means of vaporisation and condensation of a heat transfer fluid. It comprised mainly of an evacuated housing containing an absorber, a reservoir at the lower end of the collector and a condenser panel on the top end of the collector. A micro-pore insulation material, attained with an aluminium/foam plastic tray, was fitted beneath the absorber panel to reduce downward heat loss. A clear acrylic cover was mounted on the top of the evacuated housing, creating an enclosed space where a vacuum could be maintained to eliminate convection/conduction heat loss. Fig. 1 shows schematically the structure of such a prototype collector [23]. The main body of the collector comprised two plates separated by a thin evaporation gap. The plates were ÔspotÕ welded together creating mini-channels (ribs) running parallel across the width of the absorber, as shown in Fig. 2. Each mini-channel was considered to be a single
Fig. 1. Schematic diagram of the ÔnormalÕ thin membrane heat pipe solar collector.
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ribs
Fig. 2. Schematic showing the cross section of the plate heat pipe (enlarged).
ÔminiatureÕ heat pipe, as has previously been investigated by Riffat et al. [24] using an analytical and numerical model. The miniature heat pipes connected the evaporation section to the condensation section of the collector to enable the flow of vapour refrigerant and condensed liquid refrigerant. In this collector, the absorber comprised 22 mini-channels (ribs). The previous analytical investigation showed such a single pipe had a heat transport capacity of 50 W when it was operated at 80 C and installed with the inclination of 60 relative to the horizontal. Thus the whole panel would have an overall heat transport capacity of 1100 W, which is much higher than the actual solar input (<250 W) [30]. This analysis demonstrates that the heat pipes selected allow the received solar energy to be transported without restriction under the given operation conditions. This collector used a coating material, called Maxorb-Nickel foil, on its absorber surfaces. The material has a solar absorptivity of 0.95–0.99, and a long-wave emittance of 0.08–0.11 [27]. These are very favourable for solar absorption and act to enhance collector efficiency. Since the plate and so called Ôheat pipesÕ are actually the same pieces of material, the capital cost of the heat pipe panel is low. Furthermore, as the space between the top cover and absorber plate is intended to be evacuated, the collector heat loss to the surroundings could be reduced and its efficiency is expected to be high. The thermal properties of acrylic plate are illustrated in Table 1, and the design parameters of the absorber/channels are shown in Table 2. In the manufacturing, deformation appeared in the top cover when the space between the cover and absorber plate was evacuated. To recover the shape of the cover, an inert gas, argon, was introduced into the space after evacuation was complete. Photographs of the prototype collector are shown in Fig. 3. The length of the condenser was chosen as 100 mm for the prototype module. However, this parameter could be set at different values.
Table 1 Specifications of the top covers and their solar optical and thermal parameters Cover condition
1. Single acrylic cover with an evacuated chamber 2. Single acrylic cover with an un-evacuated chamber
Parameter stc (transmit.)
stc (absorpt.)
reftc (reflectivity)
etc (emmitance)
U (W/m2 K) R (m2 K/W)
0.8
0.08
0.12
0.88
5.9 1
0.8
0.08
0.12
0.88
5.90.18
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Table 2 Parameters of the heat pipes and absorber panel Absorpvity of absorber surface, aab
0.95
Reflectivity of absorber surface, refab Emmitance of absorber surface, eab Absorber area, Aab
0.05 0.1 0.24
Unshaded absorber area, Aab,r Heat resistance of top cover inner surface, Rtc,i, m2. K/W Heat resistance of top cover outer surface, Rtc,o, m2. K/W Thermal conductivity of insulation layer 1, kins1, W/m K Thickness of insulation layer 1, dins1, m Thermal conductivity of insulation layer 2, kins2, W/m K Thickness of insulation layer 2, dins2, m
0.233 0.12 0.06 0.005 0.025 0.046 0.005
Thermal conductivity of bottom plate, kdw, W/m K Thickness of bottom plate, ddw, m Number of heat pipes Equivalent diameter of heat pipe (inner) dhp, m Length of evaporator levap, m Length of condenser lcon, m Thermal conductivity of heat pipe wall, khp, W/m K Thickness of heat pipe wall, dhp, m Thermal conductivity of liquid film on heat pipe inner wall, Kw, W/m K Equivalent diameter of vapour column in evaporator dvap,evap, m Equivalent diameter of vapour column in condenser dvap,con, m
0.0015 0.0015 22 0.002 1 0.1 43 0.001 0.68 0.00196 0.0019
Fig. 3. The prototype thin membrane heat-pipe solar collector.
3. Analytical model set-up The analytical model focused on heat transfer problems existed in the prototype heat pipe solar collector. In fact, heat transfers exist in three major parts of the collector prototype, i.e., the top cover, the absorber (evaporator plate) and the condenser/manifold, as shown schematically in Fig. 4. These heat transfers finally achieve balance themselves and are inter-linked by a distributed
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Fig. 4. Schematic diagram showing relation of heat balances in different parts of a solar collector.
temperature profile. In the modelling development, a few assumptions were made in order to simplify solution solving process, including: • A steady state condition has achieved and heat balance exists in each component and whole area of the collector prototype. • The absorber has uniform temperature distribution over its surface area, supposed that a uniform heat input is exerted onto it. • There is no heat loss on the edge area of the absorber where the top cover and the bottom chamber are covered, due to a good insulation applied.
3.1. Heat transfer process in the top cover For a given collector area and total solar irradiation, the heat striking the top cover surface is part absorbed by the cover, part transmitting through the cover and reaching the absorber, and the remaining is reflected to atmosphere. This heat transfer process can be expressed as Qinc ¼ Qabc þ Qref þ Qtra
ð1Þ
The absorbed heat will be dispersed to the surroundings or (and) absorber by ways of convection, conduction or radiation, to achieve a heat balance relative to the top cover. This balance may be expressed as Qabc ¼ Qtc–ab þ Qtc–a
ð2Þ
Heat dissipation to the surroundings occurs mainly by the combined effect of conduction and convection. However, Heat transfer between the top cover and absorber may be complex. If the absorber chamber were perfectly evacuated, heat transfer between the top cover and absorber would only be induced by radiation. If the chamber were not evacuated, heat transfer between the top cover and the absorber will be a combined effect of conduction, convection and radiation.
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The above items, i.e., Qabc, Qref, Qtra, Qtc–ab and Qtc–a, can be calculated using basic heat radiation & convection equations given by Yang and Tao [28]. 3.2. Heat transfer process in the absorber (evaporator) plate Part of the heat reaching the absorber plate will be transferred to the working fluid through the miniature heat pipes formed by the spot welded flat plates, and this will cause the liquid to vaporise. This is therefore termed the effective heat input. The remainder will be dispersed to the environment through the top cover and bottom casings, resulting in heat losses due to conduction, convection and radiation. The heat losses include upward and downward losses. The upward loss refers to heat transfer between the absorber and the top cover, which has been mentioned in Eq. (2), and the downward loss can be expressed as Qdw–a ¼ Aab ðtab ta Þ=ðdab =k ab þ dins =k ins þ ddw =k dw þ 1=ha Þ
ð3Þ
There are temperature differentials in the absorber area, which result in heat transmission from the plate area to the channels, or from one part to another part of the plate area. However, these differentials are small as the plate and channels are made into an integrated body using stainless steel, a good heat conductor. In order to simplify the thermal analysis, the differentials are considered to be negligible and thus the absorber surface is assumed to be at the same temperature over the whole area. In this situation, actual heat obtained by the absorber (evaporator) plate is then expressed as Qab ¼ Qtra Qab–tc Qdw–a
ð4Þ
The heat obtained should be transferred to the heat pipes, causing evaporation of the operating fluid inside the pipes. However, if the heat transport capacity of the heat pipes is not large enough to transport such an amount of heat, then part of the heat will be dispersed to the surroundings via the top cover and the metal surface of the chamber, resulting in a change of temperature over the absorber area. To investigate the heat transfer of a heat pipe solar collector, it is necessary to determine its heat transport limitation. The limit of the heat transport capacity for a single heat pipe may be determined using the analytical model developed by Riffat et al. [24]. The maximum heat transport capacity of the collector may then be obtained as Qmax ¼ nQlim
ð5Þ
Where n is the number of heat pipes included. If Qab is less than Qmax, then the heat obtained will be transported without any restriction. However, if Qmax is less than Qab, then part of the obtained heat will be dispersed to the surroundings, resulting in reduced heat transportation from the absorber to condenser. In this case, the temperature of the absorber surface would be adjusted automatically until a new thermo-equilibrium is achieved.
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3.3. Heat transfer processes in the condensers and manifold The heat obtained from the absorber, Qab, will be transported to the cooling fluid passing across manifold through evaporation and condensation of the working fluid in the heat pipes. There are several heat resistances in this process, namely, the evaporator wall resistance, the equivalent resistance of the working fluid and wick in the evaporator, the vapour flow resistance, the equivalent resistance of the working fluid and wick in the condenser, and the condenser wall resistance. These resistances can be calculated using the equations given by Dunn and Reay [7]. The total resistance would be the sum of the individual resistances. For a single heat pipe, heat transportation from the evaporator outer surface to the condenser outer surface may be written as Qhp;i ¼ pr2hp ðthp;evap thp;cond Þ=Rhp
ð6Þ
The heat will be transferred to the cooling liquid by heat conduction through the manifold wall, and heat convection between the manifold wall and the cooling liquid. The cooling liquid will be heated when flowing through the manifold channel, which is tightly fixed to the heat pipe condensers. For an inlet temperature given as t0, a temperature increase Dt1, (t1 t0), will be achieved after the fluid passes around the first heat pipe due to heat absorption from the pipe. The fluid temperature increases gradually along the flow direction due to continuous heat transfer from the parallel-array of heat pipes. The heat transfer between a single heat pipe and the cooling liquid may be expressed as Qcon;i ¼
Acon;i ðthp;cond ðti1 þ ti Þ=2Þ ¼ C p;cl mcl ðti ti1 Þ ¼ Qhp;i dcon 1 þ k con hcl
ð7Þ
hcl is the convective heat transfer coefficient of the cooling fluid, which is largely dependent on the velocity of fluid passing over the surface, and the cross-sectional area, as well as the geometry of the flow channel. For the collector indicated above, the flow of the cooling liquid flow and the manifold geometry are shown schematically in Fig. 5. The flow may be treated as half of the annular flow. To solve for the convective heat transfer coefficient, hcon, the channel needs to be treated as an annular geometry rather than a semi-annular one, and correspondingly, heat flow from the inner wall needs to be doubled to comply with this treatment. Heat transfer through the outer walls was negligible as a satisfactory insulation was provided. For both situations, calculation of hcl could be carried out using the annular flow model [14], as shown schematically in Fig. 6. hcl Dhy;con k con
ð8Þ
Dhy;con ¼ Do;con Di;con
ð9Þ
Nucl ¼
Di,con is the hydraulic diameter of the internal wall of the flow channel, and Do,con is that of the external wall of the flow channel. For the situation shown in Fig. 6, If b > (a2 a1), then: Do;con ¼ a2 Di;con ¼ a1
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b Heat pipe panel a1 a2
Manifold Cooling fluid
Fig. 5. Schematic diagram showing cooling liquid flow and manifold geometry in the thin membrane heat pipe solar collector.
Qe Di
Do Fig. 6. Annular channel flow model.
However, if b/(a2 a1) < 10 then: Di;con ¼
2a1 b ða1 þ bÞ
Do;con ¼
2a2 b a2 þ b
Cooling liquid flow in the manifold is fully developed laminar flow, which has a Reynolds number less than 400 due to its very low velocity and the relatively large cross-sectional area. For this case, Nuo may be obtained from Table 3 [14]. For a single heat pipe, given the inlet temperature ti1, the outlet temperature ti may be obtained by solving Eq. (7). For the whole condenser/manifold configuration, the overall heat transfer may be expressed as Qcon ¼ Qcon;1 þ Qcon;2 þ þ Qcon;n ¼ C p;cl mcl ðtn t0 Þ
ð10Þ
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Table 3 Nusselt number Di/Do
Nuo
0 0.05 0.10 0.25 0.50 1.00
3.66 4.06 4.11 4.23 4.43 4.86
Qcon should be equal to Qob according to the principle of heat balance. Eqs. (6)–(10) may be used to obtain solutions for the outlet temperature and the mean temperature of the cooling water, as well as the temperatures in different parts of the heat pipe panel. 3.4. Numerical procedure The three heat processes described above are actually inter-linked by a well-developed temperature layout. The numerical procedure used for the solution solving is indicated as follows: 1. Given the collector configuration, geometrical and thermodynamic parameters of the collector unit are determined; 2. Given the incident radiation and ambient temperature, the heat striking the absorber is determined. 3. Given the manifold configuration, as well as the cooling liquid flow condition, geometrical, thermodynamic and flow parameters of the cooling fluid are determined; 4. Assuming an absorber temperature ts, heat analysis is carried out as follows: • Heat balance of the top cover may be analysed using Eqs. (1) and (2), which results in solution solving of the inner surface temperature of top cover tci. • Heat balance of the absorber (evaporator) plate may be analysed using Eqs. (3)–(5), which results in solution solving of the absorber heat gain, Qobt. • Heat balance of the heat pipes, and condenser/manifold pair may be analysed using Eqs. (6)–(10), which results in solution solving of the heat gain of the cooling water passing through the manifold, as well as the temperature layout in different areas of collector. 5. If (Qobt Qcon)/Qobt > 0.5% (error allowance), then increase ts by 0.1 C, and return to step 4 for re-calculation. 6. If (Qobt Qcon)/Qobt < 0.5% (error allowance), then decrease ts by 0.1 C, and return to step 4 for a re-calculation. 7. If 0.5% (Qobt Qcon)/Qobt 0.5%, heat balances in the whole system, as well as different areas of the system, are achieved. 8. The cooling water temperature at the outlet and different points along the flow channel, as well as the temperatures at different areas of the collector, may be calculated. 9. Program stops.
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4. Results and discussion 4.1. Efficiency calculation The data obtained by running the computer program described in Section 3 could be used to evaluate the thermal performance of a solar collector. For a solar collector, its performance is usually evaluated using efficiency g, which is defined as the ratio of heat taken from the manifold by the cooling liquid and the incident irradiation striking the collector absorber. g varies with a number of external parameters, including global solar irradiation In, ambient temperature ta, as well as cooling fluid inlet temperature t0 and mass flow rate m. These parameters may be grouped by a specially-defined parameter, termed (tmean ta)/In, whereby tmean is the average temperature of the cooling fluid and may be written as ðt0 þ tn Þ 2 g is usually expressed as the function of (tmean ta)/In, as follows: tmean ta g ¼ g0 a1 In tmean ¼
ð11Þ
ð12Þ
where g0, a1 are the collector character parameters. 4.2. Simulation results Simulation was carried out for the thin membrane heat pipe solar collector by assuming a certain operating parameters. The assumed parameters were coincident with the actual testing conditions in order to facilitate comparison between theoretical and experimental results, as shown in Table 4. g–(tmean ta)/In relations for the collector with/without evacuation treatment were investigated using the computer model developed, and the results are shown in Fig. 7. It was found that the single acrylic with an un-evacuated chamber has the much lower efficiency (62–38%) than the evacuated case (75–68%). For the both cases, g decreased while (tmean ta)/In increased. The relation of g and (tmean ta)/In was approximately linear. 4.3. Experimental results The prototype collector was tested at the laboratory of Fraunhofer Institute for Solar Energy System (ISE) in Germany, by complying with the European Standard of prEN 12975: 1999 [25]. Table 4 Summary of the external parameters In, W/m2 ta, C Mcl, kg/h tin,cl, C
1033 19.1 30.1 17.1
1033 19.9 30 17.2
1027 20.3 30 17.4
998 21.3 30.1 54.9
1031 22.5 30.1 55.0
949 17.7 30.1 79.4
962 18.3 30.2 79.5
968 18.9 30 79.7
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Efficiency - (t mean -ta)/In relation - Comparison of different covers 80 75 70
Efficiency, %
65 60 55 50 45 Evacuated chamber
40 Un-evacuated chamber
35 30 -0.01
0
0.01
0.02
0.03 0.04 (tmean-ta)/In, oC.m 2/W
0.05
0.06
0.07
Fig. 7. g–(tmean ta)/In relation—simulation results.
The collector had a gross area of 0.4 m2, of which 0.255 m2 was the absorber area, and the rest was the condensation area. The absorber area was not completely utilised because of the edge effect, and the un-shadowed area was only 0.233 m2. An outdoor climate was created in the laboratory. The wind speed was measured at the middle area of the collector module, 5 cm above the transparent cover, and adjusted to 3 m/s using a ventilator. Optical bulbs were scatter-distributed at the dome area to simulate the global solar irradiation. Water was used as the cooling liquid, and passed through the collector manifold at a rate of 30 kg/h during the test period. Test conditions and results were summarised in Table 5. The efficiencies were calculated using the results obtained, and are shown in Fig. 8. The characteristic parameters indicating the collector performance are given as: g0 = 0.70094; a1 = 4.604. 4.4. Comparison of the modelling and experimental results Comparison was carried out between the modelling and experimental results for the thin membrane heat-pipe solar collector. The results of these comparisons are summarised in Fig. 9. It was found that the experimental efficiencies were lower than the predicted results for the evacuated case, but higher than those for the case of the single acrylic cover with an un-evacuated chamber. The reason for this was investigated, and it was found that the evacuation of the chamber was not well processed. This resulted in reduced efficiencies compared to the modelling results because the theoretical analysis assumed that the chamber was completely evacuated. The top cover was deformed during processing an evacuation and to recover its shape, the chamber
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Table 5 Test results for the thin membrane heat pipe solar collector In, W/m2
Idiffuse, W/m2
ta, C
mcl, kg/h
tin,cl, C
tout,cl, C
tout,cl tin,cl, C
tmean, C
(tmean ta)/In, C m2/W
g
1033 1033 1027 998 1031 949 962 968
85 87 90 121 135 110 109 110
19.1 19.9 20.3 21.3 22.5 17.7 18.3 18.9
30.1 30 30 30.1 30.1 30.1 30.2 30
17.1 17.2 17.4 54.9 55 79.4 79.5 79.7
21.8 22.1 22.2 58.6 58.8 81.8 82.1 82.3
4.7 4.9 4.8 3.7 3.8 2.4 2.5 2.6
19.5 19.7 19.8 56.7 56.9 80.6 80.8 81.0
0.0003 0.0002 0.0005 0.0335 0.0333 0.0663 0.0649 0.0642
0.6847 0.7073 0.7006 0.5561 0.5578 0.3869 0.3944 0.4040
Efficiency - (tmean-ta)/Inrelation - test results
80 70 60
y = -460.4x + 70.094 R2 = 0.9926
Efficiency, %
50 40 30 20 10 0 -0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
(tmean-ta)/In, oC.m 2/W
Fig. 8. g–(tmean ta)/In relation—test results.
was filled with an inert gas, argon, after evacuation. Filling resulted in reduced efficiencies compared to the evacuated treatment, but still provide higher efficiency values than the un-evacuated or un-filled cases.
5. Conclusions A thin membrane heat-pipe solar collector was designed and constructed. The collector comprised of two sheets of stainless steel ÔspotÕ welded along the length and parallel-arrayed at the
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Comparison of testing and modelling results the thin membrane heat pipe solar collector 80 70 60
Efficiency, %
50 40 testing
30
evacuated chamber single glass, unevacuated chamber
20 10 0 -0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
(tmean-ta)/In, oC.m2/W
Fig. 9. Comparison of testing and modelling results.
width, creating mini-channels (ribs) running parallel along the width of the absorber. These were termed ÔminiatureÕ heat pipes. This design would reduce the capital cost of the heat pipe panel compared to normal, flat-plate heat-pipe solar collectors. Furthermore, since the space between the top cover and absorber plate was evacuated, or filled with an inert gas, the efficiency of this type of collector was expected to be high. A theoretical model was developed to analyse the heat transfer occurring in the collector. The heat processes in different areas of the collectors were investigated, and these were linked by a set of heat balance equations. The thermal performance of the thin membrane heat-pipe solar collector was investigated using the computer model developed. The simulation results were used to determine the collector efficiency g, which is defined as the ratio of heat taken from the manifold by the cooling liquid and the incident irradiation striking the collector absorber. It was found that the efficiency varies with the external conditions, i.e., global solar irradiation In, ambient temperature ta, as well as cooling fluid inlet temperature t0 and mass flow rate m, for the given collector structure. The external conditions can be grouped by an item specified as (tmean ta)/In. Overall, g was found to decrease with increasing of (tmean ta)/In. The relationship can be expressed by linear equations. The modelling predictions were validated using the experimental data from a referred source. The test efficiency was found to be in the range of 40%–70%, which is lower than the values predicted by modelling for the evacuated case, but higher than the values predicted for the case of a single glass cover with an un-evacuated chamber. The reason for this was that the chamber was filled with an inert gas, argon, after being evacuated, and this has a larger heat resistance than air,
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but still gave rise to an extra conductive or/and convective heat loss compared to the evacuated situation. This treatment was not taken into account in modelling development and processing.
Acknowledgment The authors would like to acknowledge the financial support provided for this research by the European Commission, under the Joule Craft Programme.
References [1] R. Bairamov, K. Toiliev, Heat pipe in solar collectors, in: D.A. Ray (Ed.), Advances in Heat Pipe Technology, Pergamon Press, Oxford, 1981. [2] A. Balzar et al., A solar cooker using vacuum-tube collectors with integrated heat pipes, Solar Energy 58 (1996) 63–68. [3] W.B. Bienert, D.A. Wolf, Heat pipe applied to flat-plate solar collectors, Final Report COO/2604-76/1, 1976. [4] T.Y. Bong et al., Thermal performance of a flat-plate heat pipe collector array, Solar Energy 50 (6) (1993) 491– 498. [5] W. Chun et al., An experimental study of the utilization of heat pipes for solar water heaters, Applied Thermal Engineering 19 (1999) 807–817. [6] H.F.W. DeVriers, W. Kamminga, J.C. Franken, Fluid circulation control in conventional and heat pipe planar solar collectors, Solar Energy 24 (1980) 209–213. [7] P.D. Dunn, D.A. Reay, Heat pipes, third ed., Pergamon Press, New York, 1982. [8] M.A. El-nasr et al., Performance of a wickless heat pipe solar collector, Energy Source 15 (1993) 513–522. [9] D.M. Ernst, Cost-effective solar collectors using heat pipes, Final Technical Report, DOE/CS/34099-4, 1981. [10] R.D. Franken, in: Proc. ISES. New Delhi, 1979, pp. 885. [11] H.M.S. Hussein, et al., Optimisation of a wickless heat pipe flat plate solar collector, Energy Converstion and Management 40 (1999) 1949–1961. [12] K.A.R. Ismail, M.M. Abogderah, Comparative study between flat plate solar collector with heat pipes and commercial conventional unit, IV congresso latino americano de transferencia de calor y material, La Serena, Chile, 1991, pp. 229–332. [13] K.A.R. Ismail, M.M. Abogderah, Thermal and numerical analysis of heat pipe solar collector, in: Proceedings of the Second Renewable Energy Congress, Reading, UK, vol. 2, 1992, pp. 862–866. [14] P. Incropera Frank, P. De Witt David, Fundamentals of Heat and Mass Transfer, third ed., John Wiley & Sons, Inc., Singapore, 1997, pp. 502–503. [15] K.A.R. Ismail, M.M. Abogderah, Residential solar collector with heat pipes, 8th Heat Pipe Conference, Beijing, China, 1992, pp. 531–534. [16] K.A.R. Ismail, M.M. Abogderah, Performance of a heat pipe solar collector, Journal of Solar Energy Engineering 120 (1998) 51–59. [17] W.D. Lu, H.F. Guo, Performance of a gravity assisted heat pipe solar collector, International Journal of Solar Energy 3 (1984) 1–11. [18] E. Mathioulakis et al., A new heat-pipe type solar domestic hot water system, Solar Energy 72 (1) (2002) 13–20. [19] U. Ortabasi, F. Fehlner, Cusp mirror-heat-pipe evacuated tubular solar thermal collector, Solar Energy 24 (1979) 477–489. [20] J.W. Ramsey, Experimental evaluation of a cylindrical parabolic solar collector. ASME paper 76-WA/HT-13 8, 1986. [21] J. Ribot, R.D. McConnell, Testing and analysis of a heat pipe solar collector, ASME Journal of Solar Energy Engineering 105 (1983) 440–445.
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[22] S.B. Riffat, P.S. Doherty, E.I. Abdel Aziz, Performance testing of different types of liquid flat plate collectors, International Journal of Energy Research 24 (2000) 1203–1215. [23] S.B. Riffat, X. Zhao, P.S. Doherty, Structure optimisation and performance simulation of a novel thin membrane heat pipe solar collector using a mathematical model, International Journal of Ambient Energy 23 (1) (2002) 3–16. [24] S.B. Riffat, X. Zhao, P.S. Doherty, Analytical and numerical simulation of the thermal performance of ÔminiÕ gravitational and ÔmicroÕ gravitational heat pipes, Applied Thermal Engineering 22 (2002) 1047–1068. [25] Rommel Matthias, Tests of the thin membrane heat pipe solar collector, Fraunhofer Institut Solare Energiesysteme, November 2000. [26] M. Terpstra, J. Van Veen, Heat Pipes: Construction and Application. A Study of Patents and Patent Applications, Elsevier Applied Science, New York, 1987. [27] W.K.A. Yagoub, A review of coating materials for a novel membrane heat pipe solar panel, Report to project coordinator, University of Nottingham, May 1999. [28] S. Yang, W. Tao, in: Heat Transfer, China High Education Press, Beijing, China, 1998, pp. 162–165. [29] M.A. Zanardi, Numerical and experimental analysis of a cylindrical parabolic solar collector with a heat pipe. Ph.D dissertation, Department of Mechanical Engineering, Campinas State University, Brazil, 1989. [30] X. Zhao, Investigation of a Novel Heat Pipe Solar Collector/CHP System, Ph.D thesis, The University of Nottingham, UK, 2003, pp. 47–62.
Developing a theoretical model to investigate thermal performance of a thin membrane heat-pipe solar collector S.B. Riffat, X. Zhao *, P.S. Doherty School of the Built Environment, The University of Nottingham, Nottingham, NG7 2RD, UK Received 17 September 2003; accepted 7 August 2004
Abstract A thin membrane heat-pipe solar collector was designed and constructed to allow heat from solar radiation to be collected at a relatively high efficiency while keeping the capital cost low. A theoretical model incorporating a set of heat balance equations was developed to analyse heat transfer processes occurring in separate regions of the collector, i.e., the top cover, absorber and condenser/manifold areas, and examine their relationship. The thermal performance of the collector was investigated using the theoretical model. The modelling predictions were validated using the experimental data from a referred source. The test efficiency was found to be in the range 40–70%, which is a bitter lower than the values predicted by modelling. The factors influencing these results were investigated. 2004 Elsevier Ltd. All rights reserved. Keywords: Heat pipes; Solar collector; Thin; Membrane; Efficiency; Testing; Simulation
1. Introduction Solar collectors transform solar radiation into thermal energy. There are several types of solar collector available for practical applications, including evacuated tubes, flat plate solar collectors and parabolic dish collectors. *
Corresponding author. Tel.: +44 115 846 7873; fax: +44 115 951 3159. E-mail address: [email protected] (X. Zhao).
1359-4311/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.08.010
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Nomenclature A Cp d Fv h In k V L m n Nu Pr Q r R t x d q g g
area (m2) specific heat (J/kg C) diameter (m) frictional resistance coefficient of the vapour flow in the heat pipe convection heat transfer coefficient (W/m2 C) global solar irradiation (W/m2) thermal conductivity (W/m C) volume flow rate (m3/s) length (m) mass flow rate (kg/s) number of the heat pipes included Nusselt number Prandtl number heat (W) radius (m) heat resistance (m2 C/W) temperature (C) general external parameter thickness (m) density of air (kg/m3) collector thermal efficiency—term 1 collector thermal efficiency—term 2
Subscripts a ambient ab absorber abs absorption adia adiabatic section av average cl cooling liquid con condenser cond condensation section dw downside wall eq equivalent evap evaporation section hp heat pipe hy hydraulic i inside inc incident radiation ins insulation layer
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lim max o ref tc tra
901
limit maximum outside reflection top cover transmission
Heat pipes are devices of high thermal conductance, which transfer thermal energy by twophase circulation of fluid, and can easily be integrated into most types of solar collector. The basic difference in thermal performance between a heat-pipe solar collector and a conventional one lies in the heat-transfer processes from the absorber tube wall to the energy-transporting fluid. In the case with a heat pipe, the process is evaporation–condensation–convection, while for conventional solar collectors, heat transfer occurs only in the absorber plate. Thus, solar collectors with heat pipes have a lower thermal mass, resulting in a reduction of start-up time. A feature that makes heat pipes an attractive for use in solar collectors is their ability to operate like a thermal-diode, i.e., the flow of the heat is in one direction only. This minimizes heat loss from the transporting fluid, e.g., water, when incident radiation is low. Furthermore, when the maximum design temperature of the collector is reached, additional heat transfer can be prevented. This would prevent over-heating of the circulating fluid, a common problem in many applications of solar collectors [3,6]. One of the first studies of heat pipes in solar applications was carried out by Bienert and Wol [3]. In this case, the evaporator end of a heat pipe was inserted in a flat-plate collector, and the condenser protruded into a water manifold attached to the upper end of the collector. The results of this investigation were neither conclusive nor optimistic. Since then, numerous studies have been carried out, including theoretical analysis and calculation [10,19,17,11], experimental testing [1,21,20,26,29,8,22], combined investigation involving theoretical analysis and experimental trials [9,12,13,15,16], as well as applications in practice [4,2,5,18]. Most of these studies involved the investigation of the thermal performance of various types of heat-pipe solar collectors by analytical, numerical or experimental methods with the aim of establishing suitable structures or system layouts, as well as optimum operating conditions for high efficiency. Of the existing collector designs, evacuated tube and flat-plate collectors are most widely used, and the former is usually found to be more efficient for high temperature applications. Flat-plate heat-pipe solar collectors, on the other hand, have their own set of advantages, including simpler structure, lower cost, easier manufacture and simple operation. The lower efficiency of flat-plate collectors is mainly due to the heat loss via the cover surface due to conduction and convection. Standard flat-plate collectors have typical efficiencies of 50% or less [22], while evacuated devices have efficiencies of about 50–80% [21,20,29]. It would be desirable to develop a new structure for flat plate collectors that would overcome heat loss problems and allow a high efficiency to be achieved, while its capital cost still remains low. This paper introduces a novel flat plate heat pipe solar collector, termed as Ôthin membrane heat pipe solar collectorÕ. This collector is expected to achieve a higher efficiency, but with relatively lower capital cost, compared to normal flat plat heat pipe solar collectors. One prototype of such
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kind of collector was constructed, and an analytical model that is able to simulate heat transfer processes occurring in the collector and calculate its efficiency, was developed based at the prototype structure. The model applied heat balance and heat resistance network method, which is a new approach in collector thermal performance analyses. Simulation on the performance of the collector was carried out, and the results were used to estimate its efficiency and determine the relation between efficiency and general external parameter, (tmean ta)/In.
2. Prototype set-up A prototype thin membrane heat-pipe solar collector was designed to collect and distribute heat by means of vaporisation and condensation of a heat transfer fluid. It comprised mainly of an evacuated housing containing an absorber, a reservoir at the lower end of the collector and a condenser panel on the top end of the collector. A micro-pore insulation material, attained with an aluminium/foam plastic tray, was fitted beneath the absorber panel to reduce downward heat loss. A clear acrylic cover was mounted on the top of the evacuated housing, creating an enclosed space where a vacuum could be maintained to eliminate convection/conduction heat loss. Fig. 1 shows schematically the structure of such a prototype collector [23]. The main body of the collector comprised two plates separated by a thin evaporation gap. The plates were ÔspotÕ welded together creating mini-channels (ribs) running parallel across the width of the absorber, as shown in Fig. 2. Each mini-channel was considered to be a single
Fig. 1. Schematic diagram of the ÔnormalÕ thin membrane heat pipe solar collector.
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ribs
Fig. 2. Schematic showing the cross section of the plate heat pipe (enlarged).
ÔminiatureÕ heat pipe, as has previously been investigated by Riffat et al. [24] using an analytical and numerical model. The miniature heat pipes connected the evaporation section to the condensation section of the collector to enable the flow of vapour refrigerant and condensed liquid refrigerant. In this collector, the absorber comprised 22 mini-channels (ribs). The previous analytical investigation showed such a single pipe had a heat transport capacity of 50 W when it was operated at 80 C and installed with the inclination of 60 relative to the horizontal. Thus the whole panel would have an overall heat transport capacity of 1100 W, which is much higher than the actual solar input (<250 W) [30]. This analysis demonstrates that the heat pipes selected allow the received solar energy to be transported without restriction under the given operation conditions. This collector used a coating material, called Maxorb-Nickel foil, on its absorber surfaces. The material has a solar absorptivity of 0.95–0.99, and a long-wave emittance of 0.08–0.11 [27]. These are very favourable for solar absorption and act to enhance collector efficiency. Since the plate and so called Ôheat pipesÕ are actually the same pieces of material, the capital cost of the heat pipe panel is low. Furthermore, as the space between the top cover and absorber plate is intended to be evacuated, the collector heat loss to the surroundings could be reduced and its efficiency is expected to be high. The thermal properties of acrylic plate are illustrated in Table 1, and the design parameters of the absorber/channels are shown in Table 2. In the manufacturing, deformation appeared in the top cover when the space between the cover and absorber plate was evacuated. To recover the shape of the cover, an inert gas, argon, was introduced into the space after evacuation was complete. Photographs of the prototype collector are shown in Fig. 3. The length of the condenser was chosen as 100 mm for the prototype module. However, this parameter could be set at different values.
Table 1 Specifications of the top covers and their solar optical and thermal parameters Cover condition
1. Single acrylic cover with an evacuated chamber 2. Single acrylic cover with an un-evacuated chamber
Parameter stc (transmit.)
stc (absorpt.)
reftc (reflectivity)
etc (emmitance)
U (W/m2 K) R (m2 K/W)
0.8
0.08
0.12
0.88
5.9 1
0.8
0.08
0.12
0.88
5.90.18
904
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Table 2 Parameters of the heat pipes and absorber panel Absorpvity of absorber surface, aab
0.95
Reflectivity of absorber surface, refab Emmitance of absorber surface, eab Absorber area, Aab
0.05 0.1 0.24
Unshaded absorber area, Aab,r Heat resistance of top cover inner surface, Rtc,i, m2. K/W Heat resistance of top cover outer surface, Rtc,o, m2. K/W Thermal conductivity of insulation layer 1, kins1, W/m K Thickness of insulation layer 1, dins1, m Thermal conductivity of insulation layer 2, kins2, W/m K Thickness of insulation layer 2, dins2, m
0.233 0.12 0.06 0.005 0.025 0.046 0.005
Thermal conductivity of bottom plate, kdw, W/m K Thickness of bottom plate, ddw, m Number of heat pipes Equivalent diameter of heat pipe (inner) dhp, m Length of evaporator levap, m Length of condenser lcon, m Thermal conductivity of heat pipe wall, khp, W/m K Thickness of heat pipe wall, dhp, m Thermal conductivity of liquid film on heat pipe inner wall, Kw, W/m K Equivalent diameter of vapour column in evaporator dvap,evap, m Equivalent diameter of vapour column in condenser dvap,con, m
0.0015 0.0015 22 0.002 1 0.1 43 0.001 0.68 0.00196 0.0019
Fig. 3. The prototype thin membrane heat-pipe solar collector.
3. Analytical model set-up The analytical model focused on heat transfer problems existed in the prototype heat pipe solar collector. In fact, heat transfers exist in three major parts of the collector prototype, i.e., the top cover, the absorber (evaporator plate) and the condenser/manifold, as shown schematically in Fig. 4. These heat transfers finally achieve balance themselves and are inter-linked by a distributed
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Fig. 4. Schematic diagram showing relation of heat balances in different parts of a solar collector.
temperature profile. In the modelling development, a few assumptions were made in order to simplify solution solving process, including: • A steady state condition has achieved and heat balance exists in each component and whole area of the collector prototype. • The absorber has uniform temperature distribution over its surface area, supposed that a uniform heat input is exerted onto it. • There is no heat loss on the edge area of the absorber where the top cover and the bottom chamber are covered, due to a good insulation applied.
3.1. Heat transfer process in the top cover For a given collector area and total solar irradiation, the heat striking the top cover surface is part absorbed by the cover, part transmitting through the cover and reaching the absorber, and the remaining is reflected to atmosphere. This heat transfer process can be expressed as Qinc ¼ Qabc þ Qref þ Qtra
ð1Þ
The absorbed heat will be dispersed to the surroundings or (and) absorber by ways of convection, conduction or radiation, to achieve a heat balance relative to the top cover. This balance may be expressed as Qabc ¼ Qtc–ab þ Qtc–a
ð2Þ
Heat dissipation to the surroundings occurs mainly by the combined effect of conduction and convection. However, Heat transfer between the top cover and absorber may be complex. If the absorber chamber were perfectly evacuated, heat transfer between the top cover and absorber would only be induced by radiation. If the chamber were not evacuated, heat transfer between the top cover and the absorber will be a combined effect of conduction, convection and radiation.
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The above items, i.e., Qabc, Qref, Qtra, Qtc–ab and Qtc–a, can be calculated using basic heat radiation & convection equations given by Yang and Tao [28]. 3.2. Heat transfer process in the absorber (evaporator) plate Part of the heat reaching the absorber plate will be transferred to the working fluid through the miniature heat pipes formed by the spot welded flat plates, and this will cause the liquid to vaporise. This is therefore termed the effective heat input. The remainder will be dispersed to the environment through the top cover and bottom casings, resulting in heat losses due to conduction, convection and radiation. The heat losses include upward and downward losses. The upward loss refers to heat transfer between the absorber and the top cover, which has been mentioned in Eq. (2), and the downward loss can be expressed as Qdw–a ¼ Aab ðtab ta Þ=ðdab =k ab þ dins =k ins þ ddw =k dw þ 1=ha Þ
ð3Þ
There are temperature differentials in the absorber area, which result in heat transmission from the plate area to the channels, or from one part to another part of the plate area. However, these differentials are small as the plate and channels are made into an integrated body using stainless steel, a good heat conductor. In order to simplify the thermal analysis, the differentials are considered to be negligible and thus the absorber surface is assumed to be at the same temperature over the whole area. In this situation, actual heat obtained by the absorber (evaporator) plate is then expressed as Qab ¼ Qtra Qab–tc Qdw–a
ð4Þ
The heat obtained should be transferred to the heat pipes, causing evaporation of the operating fluid inside the pipes. However, if the heat transport capacity of the heat pipes is not large enough to transport such an amount of heat, then part of the heat will be dispersed to the surroundings via the top cover and the metal surface of the chamber, resulting in a change of temperature over the absorber area. To investigate the heat transfer of a heat pipe solar collector, it is necessary to determine its heat transport limitation. The limit of the heat transport capacity for a single heat pipe may be determined using the analytical model developed by Riffat et al. [24]. The maximum heat transport capacity of the collector may then be obtained as Qmax ¼ nQlim
ð5Þ
Where n is the number of heat pipes included. If Qab is less than Qmax, then the heat obtained will be transported without any restriction. However, if Qmax is less than Qab, then part of the obtained heat will be dispersed to the surroundings, resulting in reduced heat transportation from the absorber to condenser. In this case, the temperature of the absorber surface would be adjusted automatically until a new thermo-equilibrium is achieved.
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3.3. Heat transfer processes in the condensers and manifold The heat obtained from the absorber, Qab, will be transported to the cooling fluid passing across manifold through evaporation and condensation of the working fluid in the heat pipes. There are several heat resistances in this process, namely, the evaporator wall resistance, the equivalent resistance of the working fluid and wick in the evaporator, the vapour flow resistance, the equivalent resistance of the working fluid and wick in the condenser, and the condenser wall resistance. These resistances can be calculated using the equations given by Dunn and Reay [7]. The total resistance would be the sum of the individual resistances. For a single heat pipe, heat transportation from the evaporator outer surface to the condenser outer surface may be written as Qhp;i ¼ pr2hp ðthp;evap thp;cond Þ=Rhp
ð6Þ
The heat will be transferred to the cooling liquid by heat conduction through the manifold wall, and heat convection between the manifold wall and the cooling liquid. The cooling liquid will be heated when flowing through the manifold channel, which is tightly fixed to the heat pipe condensers. For an inlet temperature given as t0, a temperature increase Dt1, (t1 t0), will be achieved after the fluid passes around the first heat pipe due to heat absorption from the pipe. The fluid temperature increases gradually along the flow direction due to continuous heat transfer from the parallel-array of heat pipes. The heat transfer between a single heat pipe and the cooling liquid may be expressed as Qcon;i ¼
Acon;i ðthp;cond ðti1 þ ti Þ=2Þ ¼ C p;cl mcl ðti ti1 Þ ¼ Qhp;i dcon 1 þ k con hcl
ð7Þ
hcl is the convective heat transfer coefficient of the cooling fluid, which is largely dependent on the velocity of fluid passing over the surface, and the cross-sectional area, as well as the geometry of the flow channel. For the collector indicated above, the flow of the cooling liquid flow and the manifold geometry are shown schematically in Fig. 5. The flow may be treated as half of the annular flow. To solve for the convective heat transfer coefficient, hcon, the channel needs to be treated as an annular geometry rather than a semi-annular one, and correspondingly, heat flow from the inner wall needs to be doubled to comply with this treatment. Heat transfer through the outer walls was negligible as a satisfactory insulation was provided. For both situations, calculation of hcl could be carried out using the annular flow model [14], as shown schematically in Fig. 6. hcl Dhy;con k con
ð8Þ
Dhy;con ¼ Do;con Di;con
ð9Þ
Nucl ¼
Di,con is the hydraulic diameter of the internal wall of the flow channel, and Do,con is that of the external wall of the flow channel. For the situation shown in Fig. 6, If b > (a2 a1), then: Do;con ¼ a2 Di;con ¼ a1
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b Heat pipe panel a1 a2
Manifold Cooling fluid
Fig. 5. Schematic diagram showing cooling liquid flow and manifold geometry in the thin membrane heat pipe solar collector.
Qe Di
Do Fig. 6. Annular channel flow model.
However, if b/(a2 a1) < 10 then: Di;con ¼
2a1 b ða1 þ bÞ
Do;con ¼
2a2 b a2 þ b
Cooling liquid flow in the manifold is fully developed laminar flow, which has a Reynolds number less than 400 due to its very low velocity and the relatively large cross-sectional area. For this case, Nuo may be obtained from Table 3 [14]. For a single heat pipe, given the inlet temperature ti1, the outlet temperature ti may be obtained by solving Eq. (7). For the whole condenser/manifold configuration, the overall heat transfer may be expressed as Qcon ¼ Qcon;1 þ Qcon;2 þ þ Qcon;n ¼ C p;cl mcl ðtn t0 Þ
ð10Þ
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Table 3 Nusselt number Di/Do
Nuo
0 0.05 0.10 0.25 0.50 1.00
3.66 4.06 4.11 4.23 4.43 4.86
Qcon should be equal to Qob according to the principle of heat balance. Eqs. (6)–(10) may be used to obtain solutions for the outlet temperature and the mean temperature of the cooling water, as well as the temperatures in different parts of the heat pipe panel. 3.4. Numerical procedure The three heat processes described above are actually inter-linked by a well-developed temperature layout. The numerical procedure used for the solution solving is indicated as follows: 1. Given the collector configuration, geometrical and thermodynamic parameters of the collector unit are determined; 2. Given the incident radiation and ambient temperature, the heat striking the absorber is determined. 3. Given the manifold configuration, as well as the cooling liquid flow condition, geometrical, thermodynamic and flow parameters of the cooling fluid are determined; 4. Assuming an absorber temperature ts, heat analysis is carried out as follows: • Heat balance of the top cover may be analysed using Eqs. (1) and (2), which results in solution solving of the inner surface temperature of top cover tci. • Heat balance of the absorber (evaporator) plate may be analysed using Eqs. (3)–(5), which results in solution solving of the absorber heat gain, Qobt. • Heat balance of the heat pipes, and condenser/manifold pair may be analysed using Eqs. (6)–(10), which results in solution solving of the heat gain of the cooling water passing through the manifold, as well as the temperature layout in different areas of collector. 5. If (Qobt Qcon)/Qobt > 0.5% (error allowance), then increase ts by 0.1 C, and return to step 4 for re-calculation. 6. If (Qobt Qcon)/Qobt < 0.5% (error allowance), then decrease ts by 0.1 C, and return to step 4 for a re-calculation. 7. If 0.5% (Qobt Qcon)/Qobt 0.5%, heat balances in the whole system, as well as different areas of the system, are achieved. 8. The cooling water temperature at the outlet and different points along the flow channel, as well as the temperatures at different areas of the collector, may be calculated. 9. Program stops.
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4. Results and discussion 4.1. Efficiency calculation The data obtained by running the computer program described in Section 3 could be used to evaluate the thermal performance of a solar collector. For a solar collector, its performance is usually evaluated using efficiency g, which is defined as the ratio of heat taken from the manifold by the cooling liquid and the incident irradiation striking the collector absorber. g varies with a number of external parameters, including global solar irradiation In, ambient temperature ta, as well as cooling fluid inlet temperature t0 and mass flow rate m. These parameters may be grouped by a specially-defined parameter, termed (tmean ta)/In, whereby tmean is the average temperature of the cooling fluid and may be written as ðt0 þ tn Þ 2 g is usually expressed as the function of (tmean ta)/In, as follows: tmean ta g ¼ g0 a1 In tmean ¼
ð11Þ
ð12Þ
where g0, a1 are the collector character parameters. 4.2. Simulation results Simulation was carried out for the thin membrane heat pipe solar collector by assuming a certain operating parameters. The assumed parameters were coincident with the actual testing conditions in order to facilitate comparison between theoretical and experimental results, as shown in Table 4. g–(tmean ta)/In relations for the collector with/without evacuation treatment were investigated using the computer model developed, and the results are shown in Fig. 7. It was found that the single acrylic with an un-evacuated chamber has the much lower efficiency (62–38%) than the evacuated case (75–68%). For the both cases, g decreased while (tmean ta)/In increased. The relation of g and (tmean ta)/In was approximately linear. 4.3. Experimental results The prototype collector was tested at the laboratory of Fraunhofer Institute for Solar Energy System (ISE) in Germany, by complying with the European Standard of prEN 12975: 1999 [25]. Table 4 Summary of the external parameters In, W/m2 ta, C Mcl, kg/h tin,cl, C
1033 19.1 30.1 17.1
1033 19.9 30 17.2
1027 20.3 30 17.4
998 21.3 30.1 54.9
1031 22.5 30.1 55.0
949 17.7 30.1 79.4
962 18.3 30.2 79.5
968 18.9 30 79.7
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Efficiency - (t mean -ta)/In relation - Comparison of different covers 80 75 70
Efficiency, %
65 60 55 50 45 Evacuated chamber
40 Un-evacuated chamber
35 30 -0.01
0
0.01
0.02
0.03 0.04 (tmean-ta)/In, oC.m 2/W
0.05
0.06
0.07
Fig. 7. g–(tmean ta)/In relation—simulation results.
The collector had a gross area of 0.4 m2, of which 0.255 m2 was the absorber area, and the rest was the condensation area. The absorber area was not completely utilised because of the edge effect, and the un-shadowed area was only 0.233 m2. An outdoor climate was created in the laboratory. The wind speed was measured at the middle area of the collector module, 5 cm above the transparent cover, and adjusted to 3 m/s using a ventilator. Optical bulbs were scatter-distributed at the dome area to simulate the global solar irradiation. Water was used as the cooling liquid, and passed through the collector manifold at a rate of 30 kg/h during the test period. Test conditions and results were summarised in Table 5. The efficiencies were calculated using the results obtained, and are shown in Fig. 8. The characteristic parameters indicating the collector performance are given as: g0 = 0.70094; a1 = 4.604. 4.4. Comparison of the modelling and experimental results Comparison was carried out between the modelling and experimental results for the thin membrane heat-pipe solar collector. The results of these comparisons are summarised in Fig. 9. It was found that the experimental efficiencies were lower than the predicted results for the evacuated case, but higher than those for the case of the single acrylic cover with an un-evacuated chamber. The reason for this was investigated, and it was found that the evacuation of the chamber was not well processed. This resulted in reduced efficiencies compared to the modelling results because the theoretical analysis assumed that the chamber was completely evacuated. The top cover was deformed during processing an evacuation and to recover its shape, the chamber
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Table 5 Test results for the thin membrane heat pipe solar collector In, W/m2
Idiffuse, W/m2
ta, C
mcl, kg/h
tin,cl, C
tout,cl, C
tout,cl tin,cl, C
tmean, C
(tmean ta)/In, C m2/W
g
1033 1033 1027 998 1031 949 962 968
85 87 90 121 135 110 109 110
19.1 19.9 20.3 21.3 22.5 17.7 18.3 18.9
30.1 30 30 30.1 30.1 30.1 30.2 30
17.1 17.2 17.4 54.9 55 79.4 79.5 79.7
21.8 22.1 22.2 58.6 58.8 81.8 82.1 82.3
4.7 4.9 4.8 3.7 3.8 2.4 2.5 2.6
19.5 19.7 19.8 56.7 56.9 80.6 80.8 81.0
0.0003 0.0002 0.0005 0.0335 0.0333 0.0663 0.0649 0.0642
0.6847 0.7073 0.7006 0.5561 0.5578 0.3869 0.3944 0.4040
Efficiency - (tmean-ta)/Inrelation - test results
80 70 60
y = -460.4x + 70.094 R2 = 0.9926
Efficiency, %
50 40 30 20 10 0 -0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
(tmean-ta)/In, oC.m 2/W
Fig. 8. g–(tmean ta)/In relation—test results.
was filled with an inert gas, argon, after evacuation. Filling resulted in reduced efficiencies compared to the evacuated treatment, but still provide higher efficiency values than the un-evacuated or un-filled cases.
5. Conclusions A thin membrane heat-pipe solar collector was designed and constructed. The collector comprised of two sheets of stainless steel ÔspotÕ welded along the length and parallel-arrayed at the
S.B. Riffat et al. / Applied Thermal Engineering 25 (2005) 899–915
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Comparison of testing and modelling results the thin membrane heat pipe solar collector 80 70 60
Efficiency, %
50 40 testing
30
evacuated chamber single glass, unevacuated chamber
20 10 0 -0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
(tmean-ta)/In, oC.m2/W
Fig. 9. Comparison of testing and modelling results.
width, creating mini-channels (ribs) running parallel along the width of the absorber. These were termed ÔminiatureÕ heat pipes. This design would reduce the capital cost of the heat pipe panel compared to normal, flat-plate heat-pipe solar collectors. Furthermore, since the space between the top cover and absorber plate was evacuated, or filled with an inert gas, the efficiency of this type of collector was expected to be high. A theoretical model was developed to analyse the heat transfer occurring in the collector. The heat processes in different areas of the collectors were investigated, and these were linked by a set of heat balance equations. The thermal performance of the thin membrane heat-pipe solar collector was investigated using the computer model developed. The simulation results were used to determine the collector efficiency g, which is defined as the ratio of heat taken from the manifold by the cooling liquid and the incident irradiation striking the collector absorber. It was found that the efficiency varies with the external conditions, i.e., global solar irradiation In, ambient temperature ta, as well as cooling fluid inlet temperature t0 and mass flow rate m, for the given collector structure. The external conditions can be grouped by an item specified as (tmean ta)/In. Overall, g was found to decrease with increasing of (tmean ta)/In. The relationship can be expressed by linear equations. The modelling predictions were validated using the experimental data from a referred source. The test efficiency was found to be in the range of 40%–70%, which is lower than the values predicted by modelling for the evacuated case, but higher than the values predicted for the case of a single glass cover with an un-evacuated chamber. The reason for this was that the chamber was filled with an inert gas, argon, after being evacuated, and this has a larger heat resistance than air,
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but still gave rise to an extra conductive or/and convective heat loss compared to the evacuated situation. This treatment was not taken into account in modelling development and processing.
Acknowledgment The authors would like to acknowledge the financial support provided for this research by the European Commission, under the Joule Craft Programme.
References [1] R. Bairamov, K. Toiliev, Heat pipe in solar collectors, in: D.A. Ray (Ed.), Advances in Heat Pipe Technology, Pergamon Press, Oxford, 1981. [2] A. Balzar et al., A solar cooker using vacuum-tube collectors with integrated heat pipes, Solar Energy 58 (1996) 63–68. [3] W.B. Bienert, D.A. Wolf, Heat pipe applied to flat-plate solar collectors, Final Report COO/2604-76/1, 1976. [4] T.Y. Bong et al., Thermal performance of a flat-plate heat pipe collector array, Solar Energy 50 (6) (1993) 491– 498. [5] W. Chun et al., An experimental study of the utilization of heat pipes for solar water heaters, Applied Thermal Engineering 19 (1999) 807–817. [6] H.F.W. DeVriers, W. Kamminga, J.C. Franken, Fluid circulation control in conventional and heat pipe planar solar collectors, Solar Energy 24 (1980) 209–213. [7] P.D. Dunn, D.A. Reay, Heat pipes, third ed., Pergamon Press, New York, 1982. [8] M.A. El-nasr et al., Performance of a wickless heat pipe solar collector, Energy Source 15 (1993) 513–522. [9] D.M. Ernst, Cost-effective solar collectors using heat pipes, Final Technical Report, DOE/CS/34099-4, 1981. [10] R.D. Franken, in: Proc. ISES. New Delhi, 1979, pp. 885. [11] H.M.S. Hussein, et al., Optimisation of a wickless heat pipe flat plate solar collector, Energy Converstion and Management 40 (1999) 1949–1961. [12] K.A.R. Ismail, M.M. Abogderah, Comparative study between flat plate solar collector with heat pipes and commercial conventional unit, IV congresso latino americano de transferencia de calor y material, La Serena, Chile, 1991, pp. 229–332. [13] K.A.R. Ismail, M.M. Abogderah, Thermal and numerical analysis of heat pipe solar collector, in: Proceedings of the Second Renewable Energy Congress, Reading, UK, vol. 2, 1992, pp. 862–866. [14] P. Incropera Frank, P. De Witt David, Fundamentals of Heat and Mass Transfer, third ed., John Wiley & Sons, Inc., Singapore, 1997, pp. 502–503. [15] K.A.R. Ismail, M.M. Abogderah, Residential solar collector with heat pipes, 8th Heat Pipe Conference, Beijing, China, 1992, pp. 531–534. [16] K.A.R. Ismail, M.M. Abogderah, Performance of a heat pipe solar collector, Journal of Solar Energy Engineering 120 (1998) 51–59. [17] W.D. Lu, H.F. Guo, Performance of a gravity assisted heat pipe solar collector, International Journal of Solar Energy 3 (1984) 1–11. [18] E. Mathioulakis et al., A new heat-pipe type solar domestic hot water system, Solar Energy 72 (1) (2002) 13–20. [19] U. Ortabasi, F. Fehlner, Cusp mirror-heat-pipe evacuated tubular solar thermal collector, Solar Energy 24 (1979) 477–489. [20] J.W. Ramsey, Experimental evaluation of a cylindrical parabolic solar collector. ASME paper 76-WA/HT-13 8, 1986. [21] J. Ribot, R.D. McConnell, Testing and analysis of a heat pipe solar collector, ASME Journal of Solar Energy Engineering 105 (1983) 440–445.
S.B. Riffat et al. / Applied Thermal Engineering 25 (2005) 899–915
915
[22] S.B. Riffat, P.S. Doherty, E.I. Abdel Aziz, Performance testing of different types of liquid flat plate collectors, International Journal of Energy Research 24 (2000) 1203–1215. [23] S.B. Riffat, X. Zhao, P.S. Doherty, Structure optimisation and performance simulation of a novel thin membrane heat pipe solar collector using a mathematical model, International Journal of Ambient Energy 23 (1) (2002) 3–16. [24] S.B. Riffat, X. Zhao, P.S. Doherty, Analytical and numerical simulation of the thermal performance of ÔminiÕ gravitational and ÔmicroÕ gravitational heat pipes, Applied Thermal Engineering 22 (2002) 1047–1068. [25] Rommel Matthias, Tests of the thin membrane heat pipe solar collector, Fraunhofer Institut Solare Energiesysteme, November 2000. [26] M. Terpstra, J. Van Veen, Heat Pipes: Construction and Application. A Study of Patents and Patent Applications, Elsevier Applied Science, New York, 1987. [27] W.K.A. Yagoub, A review of coating materials for a novel membrane heat pipe solar panel, Report to project coordinator, University of Nottingham, May 1999. [28] S. Yang, W. Tao, in: Heat Transfer, China High Education Press, Beijing, China, 1998, pp. 162–165. [29] M.A. Zanardi, Numerical and experimental analysis of a cylindrical parabolic solar collector with a heat pipe. Ph.D dissertation, Department of Mechanical Engineering, Campinas State University, Brazil, 1989. [30] X. Zhao, Investigation of a Novel Heat Pipe Solar Collector/CHP System, Ph.D thesis, The University of Nottingham, UK, 2003, pp. 47–62.