Constant Thermal Conductivity and Steady-state Heat Transfer – Poisson’s equation
Poisson’s equation – Steady-state Heat Transfer
Additional simplifications of the general form of the heat equation are often possible. For example, under steady-state conditions, there can be no change in the amount of energy storage (∂T/∂t = 0).
One-dimensional Heat Equation
One of most powerful assumptions is that the special case of one-dimensional heat transfer in the x-direction. In this case the derivatives with respect to y and z drop out and the equations above reduce to (Cartesian coordinates):