Time for heating to equilibrium with constant heat flux

[Komakech]

I have the following scenario and hope one of you can help me. I need to find an equation describing a heating process. A cylindrical metal of known dimensions and properties is heated from one side while the temperature of the other side is kept constant. I need to find the equation describing the temperature rise of the side being heated until it reaches equilibrium, so that from it, one can obtain a temperature time graph and know how long it takes to reach equilibrium.

Or rather does anyone know of an equation that can be used to describe how long a piece of metal being heated with constant heat flux takes to reach equilibrium temperature?

 

[chaoseverlasting]

Ok. If a constant amount of heat is supplied, then H=kA dt/dx=constant. Hdx=kA dt. Integrating from 0 to x and 0 to t. kA (t)=H(x). This would make it seem like the temperature varies linearly... with distance? Dunno... sorry can't be of much help...