Help with Heat Transfer Equation: Second-Order Partial Differential Equation

michel.rahman

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Mar 17, 2020
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I have solved the equation that follows the format

1584502686348.png

with BC1: T(0,t)=77.15K, BC2: ∂T(L,t)/∂x=0 (isolated), IC: T(x,0)=293.15K

Answer is quite long with a transient portion:

1584502657636.png

I am now trying to solve the equation of the following form where the conductivity changes with the function of temperature and follows a quadratic relationship with the same BCs and IC.

1584502748928.png

Any direction on how to solve the question is appreciated.
 
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