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

[annie.1991]

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.

 

[Greg Bernhardt]

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

 

[annie.1991]

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 .