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.