1D solid, 0<x<L, with the following boundary conditions: The whole solid is at T = T1 at t=0. x = 0 is held constant at initial temperature T1 for all t. There is a constant flow of heat, dQ/dt out of the solid at x = L. T(0,t) = T1, T(L,0) = T1, How do we go about solving the heat equation for such a problem? Does the system reach steady state so that the temperature gradient across the solid is constant in time? Ultimately, what I really need to be able to work out is the time taken for the system to reach steady state. Any help would be greatly appreciated.