TEAM PROJECT. Piecewise Constant Boundary Temperatures. (a) A basic building block is

Chapter 18, Problem 18.1.38

(choose chapter or problem)

Piecewise Constant Boundary Temperatures.

(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 \(w=a+z^{2}\) 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.

Text Transcription:

w = a + z^2

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