OPTIMIZATION OF PARAMETERS IN SOLAR AIR HEATERS USING ROUGHENED ABSORBERS

Abstract

It has been observed that in solar air heaters the heat transfer coefficient from the absorber plate to air is low. This causes the enhancement of absorber plate temperature, giving rise to high thermal losses to environment and hence poor thermal efficiency of a solar air heater. To improve heat transfer coefficient, one of the methods employed is the introduction of artificial roughness on the absorber plate on the_air side. Rut-the-artificial roughness induces resistance to flow and thereby an increase in pumping power occurs which may offset some of the gain in heat transfer. The roughness and operating parameters -therefore be optimally selected to obtain maximum increase in heat transfer followed by minimum increase in pumping power. So an attempt is made in this direction by a mathematical programming method to optimize the system and operating parameters of a roughened solar air heater by making use of heat transfer and friction factor correlations reported in the literature. Various criteria for the thermohydraulic optimization have been analysed and compared with each other. Effective efficiency as thermohydraulic optimization parameter has been utilized to formulate the problem- in the present studies. „A_b_rief -account on optimization in general and the optimization m.ethod of controlled random search technique based on- quadratic interpolation approach by-which the present problem has been solved in detail are given. A computer programme in FORTRAN-77 used for the solution of pre-sent-probiem h-as been appended with this work for ready -reference_.. The optimization technique is applied to a particular problem of a sotar air heater having roughened absorber plate i.e. a rectangular duct with one of its longer sides (bottom of the absorber plate) roughened. The roughnes-s-elem-ents-provid-ed were circular wires inclined at an angle of attack (a) 40°to 90°. This problem has been experimentally investigated [17]_and their correlations and ranges are used to formulate the present work. The present problem is to optimize effective efficiency which is a function of seven variables [ the relative roughness height ( e/D), aspect ratio-(W/H), Reynolds number (Re), angle of attack ( a ), the height of the duct (H), the temperature rise of the carrier fluid (T0 -T1) and the solar Insolation (I)] as given below: When solar air heater operating in transitionally rough regions (e+< 35), T1 = (e/D)-3°31 • eff (INIFI)M6 (Re)-1-384 [exp {0.040(1-a/60)2}] [H(1-8-5544 T/1 - 86688)]-1.74 T/I + 0.82 =0-.7x1-0--15 (e/D)0.128 (W/H)-0.093(Re)2.835[exp{-0.993(1-a170)2}1/1H3 When solar air heater operating in fully rough regions (e+>35), rieff--= (e/DY1-24 (W/H)°°28 (Re)-°.83 [exp{0.0475(1-a/60)2}] [H(64550 T/I - 30159)] - 1.74 T/I + 0.82 -0=7 x 10-15 (e/D)°.156 (W/H)-°.°53 (Re)2.535 [exp f-0.993 (1-a/70)2}]/1 H3 rleff for both of the above conditions are subjected to the constraints, 0.018 < e/D < 0.052 6.8 < W/H < 11.5 3000 < Re <18000 40 < a < 90 0.013 < H < 0.022 5 < T < 25 620 < I < 1050 iv This being a highly non-linear optimizing problem poses great difficulty in obtaining-the solution. It is found that the "Controlled Random Search Technique (RST)[33,36] works very wellyielding accurate results for the test problems as well as for the problem for which graphical and -experimental--solution is available [17]. Comparison of the solution by RST method with those of [17] shows good matching. The RST method works very well without difficulty for the present problem of seven variables for which no solution is available. The results of this of seven variable problem show that the optimum value of objective function i.e. the effective efficiency falls between 70 and 75% for both transitionally rough and fully rough flow. The corre-spon-ding values of the parameters giving the optimum efficiency are given in the results -given below : For e+<35, (Tier ) * = 0.7357 -at e/D = Q.0486, W/H = 8.32, Re = 16889, a = 40°. H = 0.021 m, (T.- Ti) = 5.15°C, I = 1045 W/m2, For e+>35, effj= 0.7404 at e/D = 0.018, W/H = 10.95, Re = 14606, a =46°, H = 0.021 m , (T0-Ti) = 5.45° C, I = 1034 W/m2 The optimal angle of attack (a) is found to be 40° to 46° for -transitionally rough (e+<35) and fully rough (e+>35) regions respectively. The optimal value of Reynolds number is close to Its upper range when it-op- erates in transitionally rough regions. The aspect ratio in this regions is close to its-lower-range whereas it is close to upper, range in the case of fully rough regions. The optimal solutions thus obtained are useful to a designer of an efficient solar air heater as well as to a practical engineer for selecting the optimal conditions for varying operating and environmental parameters.