saturs - Latvijas Lauksaimniecības universitāte

U. Iljins, I. Ziemelis The Optimization of Some Parameters of a Flat Plate Solar Collectorπkµ k =L. (13)Thus, the special functions of the problem (1-8) can be expressed in the form:πkxXk(x) = DkcosL. (14)The summarization of the range (9) of the problem (1–8) should be started from k=0, because, as it is seen, thespecial function (14) is not equal to zero, if k=0. In this case, µ=0 is also the particular value. Then it is purposefulto separate the member k=0 of the range (9) and to look for the solution of each layer in the form:∞I I II I IT(x,y) I = T0+ A + By+U (x,y) = T0+ A + By+∑Yk(y)⋅X k(x)k=1, (15)∞II II II II IIIIT II(x,y)= T0+ A + B (y−δ1) + U (x,y) = A + B (y−δ1) + ∑Yk(y−δ1) ⋅X k(x)k=1∞III IIIIIIIII IIIIIITIII(x,y)= T0+ A + B (y−δ1−δ2)+ U (x,y) = T0+ A + B (y−δ1−δ2)+ ∑Yk(y−δ1−δ2)⋅X k(x)k=1whereA I , A II , A III , U I , U II , U III – functions.Further, solutions (15) have to be inserted into boundary conditions (3–8). For example, inserting solution(15) into boundary condition (3) the following coherenceIIB Aλ = α(16)irand condition for the function U I I∂UIλi= αrU∂yy=0(17)y=0are obtained.To continue the insertion procedure into conditions (3–8), we acquire a system of 6 linear equations forobtaining values of coefficients A I , A II , A III , B I , B II , B III:II⎧λiB = αrA⎪IIIIII III⎪−λgB = α(A + B δ3)⎪ I I II⎪A+ B δ1= An⎨ II I 1⎪λB− λiB = ∑ qiL i=1⎪IIII II III⎪λB+ αg( A + B δ2− A ) = Q⎪IIIII II III⎪⎩− λgB = αg( A + B δ2− A )(18) 1and 6 boundary conditions for functions U I , U II , U III :1In order to get equation 4, first of all its both sides should be multiplied by the particular value at m=0 and then integratedfrom zero to L.70 LLU Raksti 12 (308), 2004; 67-75 1-18