Theoretical Analysis of Overall Heat Loss Coefficient in a Flat Plate Solar Collector with an In-Built Energy Storage Using a Phase Change Material R. Sivakumar and V. Sivaramakrishnan Abstract Flat Plate Solar Heater is one of the most widely used devices to harness solar energy available in abundance. The collector efficiency can be improved by reducing the overall losses. Efficiency of the collector depends on overall loss coefficient which is the sum of Top loss, Bottom loss, and Edge loss. The present theoretical analysis is on Overall Heat Loss Coefficient of a solar collector with and without in-built Phase Change Material (PCM). Theoretical results show a reduction in overall loss coefficient with decrease in distance between the absorber plate and PCM surface, and decrease in mean absorber plate temperature. Keywords PCM Top loss coefficient Overall loss coefficient and efficiency Nomenclature A c Collector area (m 2 ) c p Specific heat capacity (Jkg 1 k 1 ) I Intensity of solar radiation (Wm 2 ) S Solar radiation reaching the absorber plate (Wm 2 ) L Number of glass covers M Mass flow rate (Kgs 1 ) T Temperature (K) R. Sivakumar (*) Department of Mechanical Engineering, MAM College of Engineering and Technology, 621 105 Tiruchirapalli, TamilNadu, India e-mail: ramalingam.sivakumar@gmail.com V. Sivaramakrishnan Department of Mechanical Engineering, Roever Engineering College, 621 212 Perambalur, TamilNadu, India e-mail: vsmp1967@yahoo.com S. Sathiyamoorthy et al. (eds.), Emerging Trends in Science, Engineering and Technology, Lecture Notes in Mechanical Engineering, DOI: 10.1007/978-81-322-1007-8_13, Springer India 2012 145
146 R. Sivakumar and V. Sivaramakrishnan h w Wind loss coefficient (Wm 2 K 1 ) U L Overall heat loss coefficient (Wm 2 K 1 ) U T Top loss coefficient (Wm 2 K 1 ) U B Bottom loss coefficient (Wm 2 K 1 ) U E Edge loss coefficient (Wm 2 K 1 ) Q T Top heat loss (W) Q B Bottom heat loss (W) Q E Edge heat loss (W) Q o Is the heat loss (W) Qu Useful heat energy collected (W) FR Collector heat removal factor F Collector efficiency factor Greek α Absorptive τ Transitivity η Efficiency σ Stefan Boltzmann s constant = (5.67 10 8 Wm 2 K 4 ) β Collector tilt angle Subscripts a Ambient c Collector i Inlet o Outlet g Glass cover p Absorber plate 1 Introduction Time delay in availability of solar energy and utility of solar energy reiterates the need for use of Phase Change Materials (PCM) in Thermal Energy Storage Systems (TES). A conventional liquid flat plate collector consists of an absorber plate, tube, transparent cover, insulation, and collector box. The advantages are: it utilizes both diffused and direct component of solar radiation, does not require orientation towards sun, and requires minimum maintenance. The disadvantages are: it has no optical concentration, hence heat is lost from large area and low efficiency as a result, and can be used only during day time. A natural circulation solar water heater works on the principle of conduction, convection and radiation, and flow is because of density difference developed in the heater. A forced circulation solar water heater is provided with a pump to circulate water at a constant flow rate. The above mentioned Flat plate solar water heaters have limitation of usage only during sun shine. An inbuilt storage of heat in the Solar water heater by
Theoretical Analysis of Overall Heat Loss Coefficient 147 Table 1 Properties of Phase change materials considered [6] PCM Melting Heat of fusion Thermal Density kg/m 3 Specific heat point o C kj/kg conductivity solid, liquid Wm 1 K 1 capacity solid, liquid in kjkg 1 K 1 Paraffin wax Sunoco P116 50 190 0.21 930, 830 2.1, 2.1 Glauber s salt Na 2 SO 4. 32 251 2.25 1,460, 1,330 1.73, 3.3 10H 2 O Fig. 1 Energy balance of a flat plate collector adapted from Garg 1987 [2] providing PCM under the absorber surface enables charging of heat during sunshine and discharge of heat to water even during night time. The properties of PCMs studies are given in Table 1 [1]. The volume changes of the PCMs on melting would also necessitate special volume design of the containers. This necessitates the provision of the expansion volume gap between the absorber plate and the top surface of the solid PCM in the storage tank. More the distance between the absorber plate surface and PCM surface, more will be the resistance to heat transfer by radiation and convection mode. This resistance tends to increase the average absorber plate temperature and hence the losses. Figure 1 explains the energy balance of a flat plate collector. Solar radiation falling on the glazing cover is partly absorbed, partly reflected and the balance is transmitted through on to the absorber plate. The absorber plate absorbs the radiation and a fraction is reradiated particularly in the long wave length range. The solar radiation that reaches the absorber plate is given by: S = τ g. α p. I The energy losses that take place in a flat plate solar collector are Top loss, Bottom loss, and Edge loss. Top loss is the heat energy from the top surface which is mainly by radiation and convection. Bottom loss is the heat energy lost from the bottom surface of the housing of the collector which is mainly by conduction. (1)
148 R. Sivakumar and V. Sivaramakrishnan Edge loss is the heat energy lost from the sides of the collector which is also mainly by conduction and subsequent convection to the surrounding. Q L = Q T + Q B + Q S (2) ( ) Q L A p U L Tp T a (3) U L = U T + U B + U E (4) Top loss coefficient is calculated using the empirical equation developed by Klein [2], following the basic procedure of Hottel and Woertz: ) 1 N U T = [ ] C a Tp T a e + 1 + h w T p N+ f where C a and f and e and h w are given by: σ ( ) T p + T a ( (Tp 2 + T a 2 [ ] 2N+ f 1+0.133εp [ (ε p + 0. 00591Nh w ) 1 + C a = 520(1 0. 00005β 2 ) f = ( ) 1 + 0. 089h w 0. 1166h w ε p (1 + 0. 07866N) ( e = 0. 43 1 + 100 ) T p The useful heat gained by the absorber plate is given by: Q u = A p S Q L (9) h w = 5. 7 + 3. 8v (10) The bottom loss is assumed to take place one dimensionally through the insulation at the bottom. The bottom loss coefficient is given by U B = K s L s The edge loss is negligible for a very small collector perimeter to area ratio [3]. The loss coefficient decreases with increase in the gap between the absorber plate and the glass cover. A gap width >= 5 cm is recommended for optimum loss coefficient [1]. Double layers of glass cover reduces the loss coefficient by 44 % [1] since glazing cover is transparent to thermal radiation but opaque to long wave radiations from the absorber plate surface. Top loss coefficient increases with increase in emissivity of the absorber plate. Top loss coefficient decreases with increase in ambient temperature and hence efficiency increases. There is no significant effect of tilt angle β of the collector on top loss coefficient. The thermal losses increase as temperature difference between collector and ambient air rises. In order to decrease the thermal losses, the idea proposed is to ε g ] N (5) (6) (7) (8) (11)
Theoretical Analysis of Overall Heat Loss Coefficient 149 place the absorber plate on the surface of the PCM thereby heat transfer takes place by direct conduction and not by radiation and convection mode resulting in reducing the temperature of the absorber plate. The absorber plate should be designed movable upward and downward to always be in contact with the PCM surface as the volume of PCM changes with phase change. The sides along the edges of the absorber plate should designed such that the plate is movable and also leak proof to enable tilting the plane of the Solar water heater. With the increase in absorber plate temperature, simultaneously the value of U T and U L increases at different tilt angle. Thus the value of U T and U L are found increasing due to increased convection and radiation losses [4]. 2 Estimation of Overall Heat Loss Coefficient The present work deals with an analytical method for predicting the heat loss coefficient of Flat plate solar water heaters without PCM and with PCM for inbuilt thermal energy storage with an objective of suggesting ways to reduce the heat loss coefficient. A solar water heater of dimension 0.4 0.8 m with PCM to a depth of 0.1 m is assumed. The insulation thickness assumed is 0.05 m of Polyurethane. The glass cover is one in number and of 0.003 mm thickness. The glazing cover is at a distance of 0.05 m from the absorber plate. The absorber plate material is chosen as copper of thickness 0.00112 m and thermal conductivity 401 Wm 1 K 1. The collector housing is designed with insulation at the bottom and sides by Polyurethane material of thickness 0.05 m to minimize convection heat losses to the surrounding. The emissivity and absorptivity of the glazing cover are taken as 0.1 and transmissibility of the glazing cover is taken as 0.9. The emissivity of the absorber plate is taken as 0.8 and emissivity for reradiation is 0.18. The flow rate is assumed to be constant as10 kghr 1. Wind velocity is assumed as 3.5 m/s for wind loss calculation. The ambient temperature is assumed. The energy equations that govern heat transfer in the physical system are subjected to the following assumptions: The PCM is homogeneous and isotropic; The thermo physical properties of the PCM and the Heat Transfer Fluid are independent of temperature. However, the thermal conductivities of the liquid and solid phases of the PCM are different; The flow is Newtonian, incompressible, and fully developed dynamically but the local convective heat transfer coefficient for the Heat Transfer Fluid varies along the length of tube for laminar flow; The axial conduction is negligible comparatively to the heat convection in the flow; The effect of natural convection during the melting of PCM is taken into account by using the effective thermal conductivity.
150 R. Sivakumar and V. Sivaramakrishnan 2.1 Estimation of Top Loss Coefficient The fundamental experimental data of Yasin Varol et al 2010 [5] is taken for theoretical analysis of overall loss coefficient. The absorber plate is assumed to be in thermal equilibrium considering the fact that its thermal capacity is small and the calculations of overall heat loss coefficient is a function of average absorber plate temperature. The solar radiation received by the absorber plate is calculated. Maximum possible absorber plate temperature neglecting losses is calculated. Based on the T p maximum value, Loss coefficients are calculated. From the calculated losses, Useful energy transferred through the absorber plate is calculated. From the useful energy calculated, the absorber plate temperature is recalculated and the iteration is continued until repeated values of Loss coefficients have negligible difference. Top loss coefficients is calculated using Eqs.1 10 for (a) Conventional FPSWH, (b) FPSWH using Glauber s salt as PCM with expansion gap of 0.004 m between the PCM surface and absorber plate and (c) FPSWH using Paraffin without expansion gap by providing a movable absorber plate to ensure direct contact with the PCM always. 2.2 Estimation of Bottom Loss Coefficient The bottom loss coefficient varies with temperature of the PCM and the ambient temperature. U B is calculated using Eq. (11) at different time instants for the three cases mentioned above. 3 Results and Discussion The overall loss coefficient has been calculated for a conventional flat plate solar collector and that with a flat plate solar collector with inbuilt PCM storage material which is in direct contact with the absorber plate and the results were compared. 3.1 Variation of Bottom Loss The Bottom loss coefficient is a constant. The change in its value is small and decreases with decrease in solar radiation in the evening. 3.2 Variation of Overall Loss Coefficient The variation of overall loss coefficient illustrated in Fig. 4 with respect to time and variation of solar radiation which is illustrated in Fig. 3.
Theoretical Analysis of Overall Heat Loss Coefficient 151 Fig. 2 Experimental setup adapted from Yasin Varol [5] Fig. 3 Variation of total solar radiation with time in a day It is observed that the overall coefficient is found to vary a little with respect to time till noon for a conventional FPSWH. Its value decreases with decrease in solar radiation in the evening. The loss coefficient is found to be optimum since the absorber plate temperature is about 10 15 C only above the fluid temperature. Since the radiation received by the absorber plate is transferred to the fluid by conduction mode of heat transfer, and the material being Copper of small thickness, the temperature difference between the fluid heated and the absorber plate is small (Fig. 4). It is observed that for FPSWH using Glauber s salt as PCM with expansion gap between the absorber plate and the PCM top surface, the overall loss coefficient is found to vary in a similar trend in comparison with the conventional FPSWH, but the losses are comparatively higher. The reason for this is found to be the expansion gap where radiation takes place by convection and radiation mode. Higher the distance between the Absorber plate surface and the heat gaining fluid, greater is the resistance to heat transfer which results in increasing the average absorber plate temperature to transfer the useful energy available. Increased absorber plate temperature results in increased overall losses.
152 R. Sivakumar and V. Sivaramakrishnan Fig. 4 Variation of overall loss coefficient U L with time for three different cases It is observed that for FPSWH using Paraffin wax (Sunoco P116), the heat loss coefficient is very low when compared to the other two cases, since the entire surface of the absorber plate is in direct contact with the PCM which results in pure conduction mode of heat transfer in the beginning. U L increases till the PCM reaches its melting point. Once melting starts, heat transfer takes place by conduction and convection mode. High thermal conductivity and small thickness of the plate in the direction of heat transfer results in absorber plate temperature to be marginally above the melting point of the PCM and the temperature is nearly maintained from there onwards, even though the radiation decreases in the evening because of isothermal property of PCM which is in contact with it. This is the reason for the value of U L not decreasing with decrease in solar radiation. The average value of overall loss coefficient for FPSWH using PCM with expansion gap is greater than that of conventional FPSWH which is marginally greater than that of FPSWH. Higher the area of contact of the fluid with the absorber plate surface, lower is the overall loss coefficient and higher the distance between the absorber plate and the PCM, higher is the overall loss coefficient. 4 Conclusions A theoretical analysis has been done to find the overall losses in three different cases of FPSWH mentioned in the Table 2. The theoretical analysis shows that, the overall loss coefficient increases with increase in average absorber plate temperature. Average absorber plate temperature depends on area of contact of the fluid or the PCM which receives heat from it.
Theoretical Analysis of Overall Heat Loss Coefficient 153 Table 2 Estimated overall loss coefficient at different time period in a day for flat plate solar collector of type Time I Wm 2 Conventional FPSWH PCM1 Nacl 2 PCM2 paraffin sunoco P116 U L U L U L 9:30 AM 950 4.20 4.91 3.433 10:00 AM 1,000 4.21 4.95 3.433 10:30 AM 1,050 4.21 4.97 3.823 11:00 AM 1,100 4.22 5.01 4.023 11:30 AM 1,125 4.19 5.02 4.193 12:00 PM 1,100 4.16 4.99 4.153 12:30 PM 1,100 4.12 4.97 4.123 01:00 PM 1,050 4.05 4.93 4.083 01:30 PM 1,000 3.96 4.86 4.053 02:00 PM 950 4.00 4.82 4.083 02:30 PM 850 3.89 4.72 4.123 03:00 PM 750 3.84 4.61 4.153 03:30 PM 600 3.71 4.39 4.193 04:00 PM 420 3.44 3.88 4.213 (a) conventional (b) having PCM with gap between PCM surface and absorber plate (c) having PCM without gap between PCM surface and absorber plate FPSWH using PCM for inbuilt storage of heat without expansion gap has the entire surface of the absorber plate in direct contact with the heat transfer fluid and hence has least overall loss coefficient. Conventional FPSWH has a portion of the surface of the absorber plate in direct contact with the heat transfer fluid and hence has medium overall loss coefficient. FPSWH using PCM for inbuilt storage of heat with expansion gap has the entire surface of the absorber plate detached from the PCM/the heat transfer fluid and hence has maximum overall loss coefficient. It is concluded that energy efficient FPSWH using PCM for inbuilt energy storage can be provided with a movable absorber plate such that it is always in direct full contact with the PCM top surface. The plate shall move up during expansion of the PCM during melting process and down during contraction of PCM during solidification process. References 1. Agbo SN, Unachukwu GO (2006) Performance evaluation and optimization of the NCERD thermo-siphon solar water heater. Proceedings World Renewable Energy Congress, Florence, pp 19 25 2. Agbo SN, Okoroigwe EC (2007) Analysis of thermal losses in a flat plate collector of a thermo siphon solar water heater. Res J Phys 1:37 45
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