How can I solve non-linear heat conduction with a variable thermal conductivity?

AI Thread Summary
The discussion focuses on solving non-linear heat conduction with temperature-dependent thermal conductivity using the finite difference method. The equation presented involves a quadratic form where temperature is a root, with variables a and b representing coefficients. The user seeks alternative methods or insights for addressing the problem, particularly in relation to the variable thermal conductivity. The conversation highlights the challenges faced in finding solutions and encourages sharing of new findings or approaches. Overall, the thread emphasizes the need for collaborative problem-solving in complex thermal conduction scenarios.
annie.1991
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Hi everyone

I am trying to solve non linear heat conduction where thermal conductivity is function of temperature, I am solving it by finite difference method. this is my equation
∂2t/∂x2+∂2t/∂y2 *k(t)= -q (x,y)

i have solved the equation taking k(t)= a-b*t,and when i further solved the equation it gave an quadratic equation. where temparature is the root of the equation. a and b are variables, where a>>b . i just taught i can see the variations of temperature depending on the values of a and b.I just wanted to write down in the equation where tempearture is changing with some other variables.

If anybody is having any other idea to solve the " thermal conductivity is function of temperature " in different manner please do share with me kindly.
 
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annie.1991 said:
Hi everyone

I am trying to solve non linear heat conduction where thermal conductivity is function of temperature, I am solving it by finite difference method. this is my equation
∂2t/∂x2+∂2t/∂y2 *k(t)= -q (x,y)
i am running out of ideas can anybody help me out in solving this .
 

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