Transient Heat Transfer Problem
 

Ok, this problem has been nagging me from a very long time, i took a very simple plate, and put a temperature boundary condition at one of its edges, and the other edge is exposed to convection, and then obtained the temperature time curves, to my surprise they are linear, and not a step function or a even a function of 'e'. How do i solve the problem, i have attached images for your reference.

I have also patched the solid zones with a temperature of 298 K To set the initial temperature, these curves are for any point inside the solid domain, they should be non linear isn't it, instead of that, they are linear, please could anybody help me