Heat transfer inside a cylinder with flowing water

[peet_dk]

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?

 

[Q_Goest]

Hi peet,
If I understand you right, you're saying the pipe is infinitely thin, so it has no thermal mass. If that's the case, then the heat flux going into the water is the same at all points along the pipe starting at time t=0. And if that's the case, then to answer your question:

T2 will rise slowly and reach a max. over some time. How long time will it take?

T2 will come to equilibrium as soon as the water coming in at the inlet of the pipe reaches the outlet. That assumes negligable mixing of water in the axial direction of flow, which I think is a reasonable assumption.

If I were to try and calculate the temperature rise from the information you gave, I'd create a program and do a numerical analysis on it since there are a lot of variables that have to change as the water flows down the pipe.