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Coordinate Transformation

Coordinate Transformation. Case A. Case B. y. y. T=f(x). T=0. y=b. T=0. T=0. T=0. T=0. x. x. T=0. x=a. T=f(x).

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Coordinate Transformation

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  1. Coordinate Transformation Case A Case B y y T=f(x) T=0 y=b T=0 T=0 T=0 T=0 x x T=0 x=a T=f(x) For the obvious reason, the solution of case A will be different from that of case B. However, the question is whether do we need to derive the solution B from scratch if solution A is available

  2. y T=f(x) y=b y’=0 T=0 T=0 y=0 y’=b x T=0 x=a y’

  3. 2-D Steady Heat Equation y’ y’=b x=a x y=0 x=0 T(x,b)=f(x)

  4. New Example

  5. New variable

  6. Temperature Distribution in x at different y stations f(x)=100(3-x)sin(x) y’=6-y

  7. Constant temperature contour plot has shifted so that the maximum temperature occurs at the bottom as it should be in case B.

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