Beginning with the separation-of-variables solutions for 2 = 0 and 2 < 0 [Equations (3-9) and (3-10)],

Question:

Beginning with the separation-of-variables solutions for λ2 = 0 and λ2 < 0 [Equations (3-9) and (3-10)], show that it is not possible to satisfy the boundary conditions for the constant temperature at y = H with either of these two forms of solution. That is, show that, in order to satisfy the boundary conditions
T = T1 at y = 0
T = T1 at x = 0
T = T1 at x = W
T = T2 at y = H
either a trivial or physically unreasonable solution results when either Equation (3-9) or (3-10) is used.