What is the solution of heat transfer equation when there is continuous heating ( flux of energy) to one end of a metal rod? what will be the temperature profile before reaching the steady state? when I try the boundary condition where one end (x=0) is kept at T1, I got the general solution of the space dependent component X(x)= C1 sin(ux)+C2cos(ux). substituting x=o leads to C2=T1, then I stopped !! How to retrieve the other constant and the general solution too? will the rod reach steady state given the other end is exposed to room temperature.