Steady State Temperatures

 

Example 11.17. Find the temperature T(x,y) at each point in the
upper half-plane where the temperature at points on the boundary satisfies
[Graphics:t4.txtgr1.gif]

Solution. Use the mapping [Graphics:t4.txtgr2.gif].

The temperature function is:

[Graphics:t4.txtgr4.gif][Graphics:t4.txtgr3.gif]
[Graphics:t4.txtgr4.gif][Graphics:t4.txtgr5.gif]

A graph for the solution is:

Temperature in a half plane, insulated -1<x<1,y=0.

 

 

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(c) John Mathews, 1998, 2006