saturs - Latvijas Lauksaimniecības universitāte

U. Iljins, I. Ziemelis The Optimization of Some Parameters of a Flat Plate Solar CollectorTI= Ty= δ II1 y=δ (5)1andn∂T∂λII T− λIi = ∑qiδ(x− xoi) ,∂yy=δ∂y(6)1y=δ1i=1whereλ – the heat transfer coefficient of the metal sheet, W ⋅ (m ⋅ K) -1 ;q I– intensity of the heat absorbed by the circulating liquid, W⋅m -1 ;n – number of twines of the heat absorbing tube;x oi– co-ordinates of the twines, m;δ(x-x oi) – delta function for the point-shape absorber, m -1 .On the boundary at y=δ 1+δ 2, the heat flows are equal:∂Tλ∂yIIy=δ1+δ2+ αabs( T − T ) = QIIIIIy=δ1+δ2whereα abs– the contact heat transfer coefficient between the absorber and the air, W⋅ (m 2 ⋅K) -1 ;Q – the specific power of absorbed solar energy, W⋅ m -2 ,andαabs( TII y− TIII∂T) = −λgy= δ1+ δ 2 y=δ1+ δ 2∂III1,y=δ + δ2(7). (8)The developed problem of mathematical physics (1–8) can be solved by using the method of separating thevariables at the stated boundary conditions (2)–(8). For that the problem can be solved like the sum of aninfinitely long range in the following form:T (x, y) = T0 + A + By + ∑ Yk(y) ⋅ Xk(x), (9)kwhereA and B – constants, which will be determined later;X k(x) and Y k(y) – functions, depending only on x and y.Inserting expression (9) into equation (1) and after performing the common procedure, the problem (1–8) isdivided into two ordinary differential equations:22k′k Xk(x)= 0 and Yk(y)′′− µ k Yk(y) = 0 , (10a and 10b)X (x)′+ µwhereµ k– the constants of separation of variables (particular values).General solution of the equation (10a) is known in the form:X(x)Csin µx + Dk = k k k µ k . (11)Inserting expression (9) into the boundary condition (2) the following condition is obtained:cosx∂Xk (x)∂xx = o=∂Xk (x)∂xx = L= 0 . (12)The equality (12) is satisfied, if C k=0 andLLU Raksti 12 (307), 2004; 67-75 1-1869