saturs - Latvijas Lauksaimniecības universitāte

U. Iljins, I. Ziemelis The Optimization of Some Parameters of a Flat Plate Solar CollectorThe Optimization of Some Parameters of a Flat Plate Solar CollectorPlakana saules kolektora dažu parametru optimizācijaUldis IljinsDepartment of Physics, Faculty of Information Technologies, LLU, e–mail: fkuldis@cs.llu.lvLLU Informācijas tehnoloģiju fakultātes Fizikas katedra, e–pasts: fkuldis@cs.llu.lvImants ZiemelisInstitute of Mechanics, Faculty of Engineering, LLU, e–mail: imantsz@cs.llu.lvLLU Tehniskās fakultātes Mehānikas institūts, e–pasts: imantsz@cs.llu.lvAbstract. In order to investigate the possibility to increase the efficiency of a flat-plate solar collector, a mathematicalmodel of the collector has been worked out. By solving the Laplace heat transfer equation at theboundary conditions accordingly to the construction of the collector, the obtained solution gives possibility tosimulate the construction of the collector on a computer in dependence on physical, thermal and economicvalues of materials used for the construction. The results computed by theoretical formulas were compared toexperimentally obtained data, which demonstrated a good concurrence.Key words: solar collector, absorber, temperature, equations, calculations.IntroductionSolar water heating systems are widely used in many countries all over the world (Харченко, 1991;Твайделл, Уэйр, 1990; Renewable Energy World, 2003). Latvia is situated around the 57th latitude. In Latvia, inspite of its northern location, solar heating has been successfully used for drying of hay, straw and grain formany years. Latvia’s cold and rainy climate with short summers and annual solar irradiation far below half of thesolar irradiation around the equator requires much of a solar heating system. Therefore, in order to create a solarheating system working with the highest possible efficiency, it is necessary to know all relationships among theconstructive, thermal and economical parameters influencing the work of the system.Materials and MethodsAs the intensity of solar radiation is relatively low in Latvia, an important part of the solar heating system isa solar collector. In literature, a large number of examples and recommendations about its construction usuallylack the necessary theoretical foundation (Renewable Energy World, 2003). In order to investigate the influenceof different physical and thermal parameters and to work out for Latvia’s meteorological conditions an economicallymaximum reliable construction of the flat plate solar collector, we have developed the mathematical model ofthe collector. The model allows simulating the different kinds of the collector’s construction and optimizing itselements. The scheme of the mathematical model is given in Figure 1.When the heat flow is stationary, the distribution of the temperature in the solar collector can be determinedby the following heat transfer equation (Riekstiņš, 1969):2 2∂ T ∂ T+2 2∂x∂y= 0 ,(1)where T – temperature in the point with co-ordinates x and y, o C.For solving the equation (1), boundary conditions of the solution have to be formulated. The thickness of thecollector compared to its width and length is considerably smaller. Therefore it is possible to assume that throughthe side surfaces at x=0 and x=L, the heat flow is equal to zero. Besides, in a real construction, the side surfacesof the collector are covered with a layer of thermal insulation, which restricts the heat flow through thesesurfaces. Considering that, the following boundary conditions can be written:∂T∂xx = o∂T=∂xx = L= 0 .(2)LLU Raksti 12 (307), 2004; 67-75 1-1867