saturs - Latvijas Lauksaimniecības universitāte

λµ/ α −1exp( −2µ/ α + 1III g kϕ k =kδ3). (26)λgµkIn a similar way, inserting functions U I and U II into equation (19.3), the following formula is received:Condition (19.6) gives coherenceIIII IIA k (exp( µ kδ1)+ ϕ k exp( −µ kδ1))= A k + B k . (27)⎛IIIIIII III λgµk ⎞IIIA k exp( µ kδ2) + B k exp( −µ kδ2) − B k ⎜ϕ+ 1−( ϕ −1)⎟ = 0⎜⎟⎝α, (28)g ⎠but condition (19.5) produces the formula⎛ ⎞⎛ ⎞IIA 1kIIIII IIIexp( ) B 1kk ⎜λµk ⎜λµ+ ⎟ µ kδ2+ − ⎟exp(−µ kδ2) − B k ( ϕ + 1) = 0. (29)⎜ ⎟⎜ ⎟⎝αg⎠⎝αg⎠It is more complicated with condition (19.4). After inserting into it formula (15), it is obtained thatnII IIIIλ∑µk ( A k −Bk)cosµkx−λi∑µkAk(exp(µ kδ1)−ϕ k exp( −µ kδ1))cosµkx= ∑qiδ(x−xoi). (30)kki=1Further, both sides of the coherence (30) are multiplied by the particular function cosµ kx and integrated withinthe limits from zero to L.As the intervals areL2∫ cos µ kxdx = L / 2 and δ( x − x0i)cosµkxdx= cosµkx0i0the expression (30) changes into the form ofL∫,0λnII II i II2A k −Bk − A k(exp(µ kδ1)−ϕ k exp( −µ kδ1))= ∑qicosµkx0i. (32)λλµ kLi=1To determine the rest of unknown coefficients A I , A II , B II , B III , let us look at the system of 4 equations madeby formulas (27), (28), (29), and (32). For this purpose, from equations (28) and (29) the coefficient B III has to bekexcluded. Then the following coherence is obtained:AIIkU. Iljins, I. Ziemelis The Optimization of Some Parameters of a Flat Plate Solar Collector⎛⎛⎞⎛g kexp( ) ⎜ 1kλ µ⎜ λµ ⎜kδ2+ ⎟ 1−⎜⎜⎟⎜⎝⎝αg⎠⎝αg( ϕ−1)⎞ ⎞⎟−1⎟+ B+ 1) ⎟ ⎟⎠ ⎠⎛⎛⎞⎛gexp( ) ⎜ 1kλ µ⎜ λµ−µ ⎜kδ2− ⎟ 1−⎜⎜⎟⎜⎝⎝αg⎠⎝αg( ϕ−1)⎞ ⎞⎟−1⎟= 0+ 1) ⎟ ⎟⎠ ⎠IIIIII( ϕIIk ( ϕµIIIkIII. (33)(31)Introducing designationsandab⎛⎛⎞⎛λ µ III ⎞ ⎞⎜⎜λµ⎟⎜( ϕ −1)⎟ − ⎟= exp( µ δ ) 1+k g kk 21−1⎜⎜⎟⎜⎟ ⎟⎝⎝α⎠⎝α IIIg g ( ϕ + 1) ⎠ ⎠k (34)⎛⎛⎜⎜λµ) 1−⎜⎜⎝⎝α⎞⎛λ µ⎟⎜g1−⎟⎜⎠⎝αg−1)⎞⎟ −+ 1)⎟⎠III( ϕ= exp( −µ δkkk k 21III(35)g( ϕ⎞⎟⎟⎠72 LLU Raksti 12 (308), 2004; 67-75 1-18