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Heat Transfer in Flat-Plate Solar Air-Heating Collectors

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Heat Transfer in Flat-Plate Solar Air-Heating Collectors Advanced Computational Methods in Heat Transfer VI, C.A. Brebbia & B. Sunden (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-818-X Heat transfer in flat-plate solar air-heating collectors Y. Nassar & E. Sergievsky Abstract All energy systems involve processes of heat transfer. Solar energy is obviously a field where heat transfer plays crucial role. Solar collector represents a heat exchanger, in which receive solar radiation, transform it to heat and transfer this heat to the working fluid in the collector's channel The radiation and convection heat transfer processes inside the collectors depend on the temperatures of the collector components and on the hydrodynamic characteristics of the working fluid. Economically, solar energy systems are at best marginal in most cases. In order to realize the potential of solar energy, a combination of better design and performance and of environmental considerations would be necessary. This paper describes the thermal behavior of several types of flat-plate solar air-heating collectors. 1 Introduction Nowadays the problem of utilization of solar energy is very important. By economic estimations, for the regions of annual incident solar radiation not less than 4300 MJ/m^ pear a year (i.e. lower 60 latitude), it will be possible to cover - by using an effective flat-plate solar collector- up to 25% energy demand in hot water supply systems and up to 75% in space heating systems. Solar collector is the main element of any thermal solar system. Besides of large number of scientific publications, on the problem of solar energy utilization, for today there is no common satisfactory technique to evaluate the thermal behaviors of solar systems, especially the local characteristics of the solar collector. By calculating the effective of solar collectors, considering all characteristics constant Advanced Computational Methods in Heat Transfer VI, C.A. Brebbia & B. Sunden (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-818-X 576 Advanced Computational Methods in Heat Transfer VI by the length direction (x), such as, over all heating loss UL, connective and radiative heat transfer coefficients a?, a,,... etc., which resulting to get unexactly information and to complicate the evaluation of economic effect of using solar energy. 2 Heat transfer in flat-plate solar air-heating collectors Very little works considered the thermal characteristics of solar collectors as a function of the length direction [10], the variation of results obtained by itegration method Hottel and Whillier [3] and by our offered model plotted in figure 1. *t \J \J r/r o o A p*n PQ J O U 0) pmmM! jwj Jo O/: U A % !^w fc 340 cx __ ~ \ § 320 % v If 'Vi. i nn tr ;r Tg Taout Tarn Tp Figure 1: Comparison between the results obtained by integration method and by finite difference method, for a flat-plate solar air-heating collector first type with one glass cover Where Tp, Tg, Tarn are the average temperatures of absorber plate Glass cover and air and Taout is the outlet air temperature [K]. The classical approach of treating the heat transfer processes in flat-plate solar collectors is documented in all modern textbooks of solar energy, eg. Duffie & Beckman [2], Kreider & Krieth [6], Meinel & Meinel [7], Klein [5] and Zvirin & Aronov [11]. The theory is based on calculating the heat losses through the various components of the collectors, and representing the heat fluxes between two nodes j, k as (Xj-k(Tj-Tk), where a is an effective heat transfer coefficient (by convective, conduction or radiation). Figure 2 is a schematic of heat transfer balance for a single-glazed collector type Jf° 1 (the extension to multi-glazed and to other types is straightforward). The radiation coefficients are written as: (i) i i -i Advanced Computational Methods in Heat Transfer VI, C.A. Brebbia & B. Sunden (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-818-X Advanced Computational Methods in Heat Transfer VI 577 (2) where: 7 is the temperature and £ is the emissivity; the subscribes p, g, <%> and sky indicated to the absorber plate, glass cover, ambient and effective sky, given by empirical correlation [11], as: 7^ = 0,0552.7^ or 7^ = 7^-6 (K) (3) L_ \_ULJ^i I glass covet Inlet air ir pass channe absorbr pbte Useful Ene^y qu Figure 2. Schema of the heat balance in a solar collector. The conduction coefficient in the case, of the backside insulation (of thickness Axb and thermal conductivity A,b) is expressed as A (4) Ax, Another convection correlation is used for determining the heat losses to the ambient by free and forced convection under the effects of wind with velocity V* [4]: <%<% =2,8 + 3,0.^(m/j) (5) Where the heat convection coefficients are taken from appropriate correlation for the Nusselt number Nu, for example: Nu% = 0,0233. Re ^ . Pr^ for turbulent flow; Nuy, = 0,332. Re*P . Pr^'^ for laminar flow (6) where Re% = ; u/is the local velocity of the working fluid However, the above maintained eqn (6) only for fully hydrodynamic developed turbulent or laminar flow, without accounting the entrance length, which presented Advanced Computational Methods in Heat Transfer VI, C.A. Brebbia & B. Sunden (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-818-X 578 Advanced Computational Methods in Heat Transfer VI approximately 40-50% of the channel length [1], in where Mussel number is higher than the fully developed region, not accounting the effect of temperatures variations of the upper and lower plates and not accounting the effect of the turbulence intensity, which increase the convective coefficient by 50% in the intervals of 8-9% turbulence intensity [8]. In the case of solar collectors formula for Nusselt number must be taking into account of variation of temperatures of walls and the relation of turbulence intensity by the length of the channel of solar collector. So the task of this paper is, to obtain a relationship between all these factors and Nusselt number. To achieve this aim the following tasks were setting up: 1. Realization of experimental and numerical investigations, to obtain the local characteristics fields of velocity, temperature and turbulence intensity through the length of the channel flat-plate solar air-heating collector. 2. Development of a technique to calculate flow and heat exchange parameters in the channel 3. Evaluation of thermal behavior of flat-plate solar air-heating collectors. 3 Experimental approach Experiment was setup on aerodynamic open type installation (figure 3), to obtain the fields of speed, turbulence intensity, temperature of air flowing through the channel model of solar collector, and temperatures of solar collector's elements The measurements was collected using hot-wire and thermonanometer and block measurement from DISA. The obtained results used, furthermore to prove the reliability of the offered mathematical models, used to evaluate Nusselt's number and as boundary conditions for solving k-e turbulent model. 2 glass co' air flow Co 5 absorber plate £:insulation be Figure 3: Experimental installation, where 1 radiation source; 2 fan; 3 model flat- plate air-heating solar collector; 4 sensor of measurement; 5 measurement block; 6 IBM computer, 7 aerodynamic channel Advanced Computational Methods in Heat Transfer VI, C.A. Brebbia & B. Sunden (Editors) © 2000 WIT Press, www.witpreAdvancess.com,d ISBNComputationa 1-85312-818-Xl Method s in Heat Transfer VI 579 4 Numerical approach Experimental results shown, that the specialty of heat transfer in solar collectors are: 1. The upper and lower walls of the solar collector' s channel are different. 2. There is a large turbulence intensity at the inlet of the channel, and its damped not only by the thickness of the sublayer, but also by the length direction of the channel. 3. Inlet Reynold's number Ren approximately 10*. The problem of the calculation the temperatures of solar collector's elements, that there are not enough information about the mechanism heat exchange in the air channel. To understanding the heat transfer processes in solar collectors, we used complex PHOENICS, a working sheet file Ql was written down under our conditions, the obtained results plotted in figure 4, 5. 40 60 80 100 1 20 Air te m perature, [c ] Figure 4: Two dimensional temperature behavior of air flowing through the channel of flat-plate solar air heating collector first type obtained via PHOENICS. Figure 5: Two dimensional turbulence intensity evaluation of air flowing through the channel of flat-plate solar air heating collector first type obtained via PHOENICS. Advanced Computational Methods in Heat Transfer VI, C.A. Brebbia & B. Sunden (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-818-X 580 Advanced Computational Methods in Heat Transfer VI Nassar [9] developed a model for Nusselt's number as functions of variation of the temperatures of die upper and lower walls and turbulence intensity (Tu) by the length direction the channel, which found as: (7) (8) Tux%(x) = 7w/«%-exp (9) J U where NupX is the local Nusselt number of the absorber plate; NugX is the local Nusselt number of the glass cover; Ntt^x = 0,0233. Re ^ .Pr^; L channel length; Tuin% , Tux% is the inlet ant local turbulence intensity receptively; \Ke Tu = .J ; where 7T, 7 and V are the impulsion velocities in x,y and z coordinates, Ke is the kinetic energy and U« is velocity We investigated the reliability of these equations in the regions of and 0. !%<Tu%<14%. 34567 Channel length x = 0,081 .X Figure 6: Comparison of convective heat transfer coefficient by using: 1, 2. our offered model; 3. experiment; 4. Nu^ =0,0233Re£* .Pr°'* and 5.
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