saturs - Latvijas Lauksaimniecības universitāte

U. Iljins, I. Ziemelis The Optimization of Some Parameters of a Flat Plate Solar Collectorthe coherence (33) can be written asAIIkIIk⋅ a + B ⋅ b = 0 . (36)kkSubtracting equation (32) from equation (27) results in:I ⎛ ⎛λ⎛λ⎞ nII A k⎜i ⎞ Ii ⎞ 1−B k − exp( µ kδ1)⎜ −1⎟−ϕk exp( −µ kδ1)⎜ + 1⎟⎟ = ∑qicosµkx0i. (37)2 ⎝ ⎝ λ ⎠⎝ λ ⎠⎠λµ kLi=1Introducing designations1 ⎛ ⎛λ⎞⎜i ⎞ I ⎛λi⎞ck = exp( µ kδ1)⎜ −1⎟−ϕk exp( −µ kδ1)⎜ + 1⎟⎟(38)2⎝⎝ λ ⎠⎝ λ ⎠⎠andn1e k = ∑qicosµkx0i, (39)λµ kLi=1equation (40) is obtainedII I− B k − A k ⋅ ck= ek. (40)Further, from equation (40) the quantity B II is expressed and put into equation (36). Then the followingkconnectedness is produced:b I=k(ek+ A k ⋅ ck), (41)aIIA kkinto which the magnitude A II is expressed by means of coefficient k AI . Analogous from the coherence (40), bykmeans of A I the magnitude k BII is acquired. Inserting quantities k AII and k BII into expression (27), an equation forkIA kcoefficient A I is received: kek(a k − b )=kI. (42)ck(bk− a k ) − a k (exp( µ kδ1)+ ϕ k exp( −µ kδ1))Further, it is possible to express coefficient B III from formula (29):k⎟1 ⎛ ⎛ ⎞⎛ ⎞⎟ ⎞⎜ II ⎜λµ⎜λµ= A 1+k ⎟IIexp( µ δ ) + B 1−kkk⎟exp(−µ δ )IIIϕ + ⎜ ⎜ ⎟ k 21⎜ ⎟ k⎝ ⎝αg⎠⎝αg⎠⎠IIIB k2. (43)ResultsThe final solution of the problem (1–8) can be written in a form:IITI (x, y) = T0+ A + B y+ = ∑ A k (exp( µ k y) + ϕ k exp( −µ k y))cosµk x ; (44)kIII IIIIIITII (x,y) = T0+ A + B (y − δ1)+ ∑ A k(exp(µ k(y− δ1))+ B k exp( −µ k(y− δ1)))cosµkx; (45)kIII IIIIII IIITIII (x,y) = T0+ A + B (y−δ1−δ2)+ ∑ B k(ϕ kexp(µ k(y−δ1−δ2))+ exp( −µ k(y−δ1−δ2)))cosµkx, (46)kILLU Raksti 12 (307), 2004; 67-75 1-1873