Hello Please see the attached illustration, hope it gives a idea of what is going on. If I do not include radiation and the cylinder is infinite thin, how can I calculate this situation: (1) The water flow is constant inlet=outlet and steady state flow. (2) First there is not a heat source in the bottom of the closed cylinder. (3) The heat source (Q3=W, T3=C) begin the heat the cylinder, with a constant heat rate. If it makes it easier it can be calculated like the heat source is on every cylinder surfaces.. T2 will rise slowly and reach a max. over some time. How long time will it take? I looked for a lumped capacity method equation in my heat transfer book, but could not find one.. Hope you can help me.. And what if the flow is through a long pipe with inlet and outlet?