Heat Conduction in a Semi-Infinite Plate (2-D)                          

 

In a Nut Shell:  The governing equation for steady-state heat conduction in a thin

semi-infinite plate is:

 

                                 ∂2u/∂x2 + ∂2u/∂y2  =  0   

 

Use the method of separation of variables to solve this equation subject to the boundary

conditions and the notion that the temperature must be bounded as one boundary

approaches infinity.

 

     

Consider a thin, semi-infinite plate of width   a  and of infinite length in the

y-direction as shown below.  The objective is to find the steady state temperature

distribution given specified boundary conditions.

 

                               

 

 

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