Heat Transfer in Flat-Plate Solar Air-Heating Collectors

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-platesola r 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-platesola r 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

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 inflat-plat e 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

(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

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 channelflat-plat esola r 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

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.

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. !%

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.

NUy, =0,0233Re%* .Pr^

4.1 Thermal behavior of flat-platsola r air-heating collector

Since, solar collector is the main element of any solar thermal system, this study considered four types of flat-platesola r air-heating collectors indicated in figure 4. Considering the heat balance of the first type solar collector, the formulas for calculating the local thermal characteristics, such as heat loss coefficient UL and coefficient effectiveness F' , will be found as: (10)

By using finite difference technique, the equations for evaluating air flowing through the collector's cannel, will be written as [9] :

Pf.Tf.Cpf

(hx.rhCp f+lf \Tf (x + Ax, /) for x=0 (13)

2m.Cp f'?

(x, f - 1

for (Kx

582 Advanced Computational Methods in Heat Transfer VI

rTp(x,t)+acg2ffg2(x>*) +

forx=L (15)

Af where: m - mass flow rate, p,X, cp are the density, thermal conductivity and specific heat of the working fluid f, a*, Or convective and effective radiative heat transfer coefficients and the subscribes gi, gz, p and f indicated to the 1" and 2™* glass cover, absorber plate and workingfluid ,A t and Ax are the elementary length for the time and the direction length, Ut and Uy are the top and bottom heating losses, FR is the heat removed factor. For other types documented in [9]. The obtained results via offered model were well satisfactory with the experimental results. So we can recommended these models for engineering calculations.

(i)

—>

(4)

Figure 7: Types of flat-platesola r air-heating collectors considering in the study where 1 glass cover; 2 air gap; 3 air pass channel; 4 absorber plate, 5 insulation bottom.

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 Length, m

Figure 8: Comparison experimental results (•> A ,•) with results obtained by offered

mathematical model (a, A, o), for absorber plate Tpx, glass cover Tgx and air temperature Tax, [C].

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Length m

'Figure 9: Air temperature behaviors for the four types of solar collector considered in the study the numbers refereed to the type of collector.

5 Conclusion

The survey of heat transfer inflat-plat esola r air-heating collectors, presented in this paper, includes basic approaches as well as new methods to calculate, local convective heat transfer coefficient and evaluate the local thermal characteristics of

584 Advanced Computational Methods in Heat Transfer VI solar collector. The heat transfer in flat plate collectors is discussed, and in solar systems for heating liquid and air in domestic applications. The offered mathematical model for calculating the air temperature for the considering types is very important to optimize the dimension of solar collectors, furthermore, to choose the suitable type for a particular application. The obtained results were used to evaluate the economic effect of using the solar air heating collectors in domestic space heating and hot water supply solar system in Russia. Investigation showed, that the cost of such system about 5200$ and will be margined in 8 years, with fraction coefficient about 30%.

References

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SavetsTde issledovanie, Moscow, pp. 64-76, 1980. (Russian). [2] Duffie, J.A. & Beckman, W.A Solar Engineering of Thermal Processes, John Wiley & Sons, New York, pp. 35-72,1991. [3] Hottel, H.C. & Whillier, A. Evaluation of flat-platesola r collector performance,

Trans. oftheASME, 86, pp. 74-79, 1955. [4] Hsieh, J.S. Solar energy engineering, prentie-Hall Inc, New Jersey, 1986. [5] Klein, S.A Calculation offlat-plat e collector loss coefficient, Solar energy, vol. 17, pp. 14-19, 1967. [6] Kreith, F. & Kreider, J.F. Principle of Solar Engineering, McGraw-Hill,

Washington, pp. 112-145, 1978. [7] Meinel, M.P. & Meinel, A.B. Applied Solar Energy, Addison Wesley, New York, pp. 54-71, 1977. [8] Motylevitsh, V.P., Sergievsky, E.D., Znbrin, S.V. & Lukashobitshoc, L.K. Rachot trenia I teploobmena v pagranishnom sloe torbolizirovannovo patoka, V

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(Russian) [10]Rhee, S.J. & Edwards, D.K. Laminar entrance flow in afla tplat e duct with a symmetric suction, Numerical heat transfer, 4, pp. 85-100, 1981. [ll]Zvirin, Y. & Aronov, B. Heat transfer in solar collectors, heat transfer 1998, proceeding of the eleventh intrnational heat transfer conference, eds. J.S. Lee,

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