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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

∂^{2}t/∂x^{2}+∂^{2}t/∂y^{2}*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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# Nonlinear heat conduction

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