(a) A basic building block is shown in Fig. 407. Find the corresponding temperature and complex potential in the upper half-plane.

(b) Conformal mapping, what temperature in the first quadrant of the z-plane is obtained from (a) by the mapping w = a + z2 and what are the transformed boundary conditions?

(c) Superposition, find the temperature T* and the complex potential F* in the upper half-plane satisfying the boundary condition in Fig. 408.

(d) Semi-infinite strip, applying w = cosh z to(c), obtain the solution of the boundary value problem in Fig.409.

Transcribed Image Text:

D T* = T₂ T = T₁ Fig. 407. Team Project (a) y TO T-0 T* = To T=0 Fig. 408. Team Project (c) T = T₁ V 00 a U T=0 u T=0 Fig. 409. Team Project (d)