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Model ID: 700

An Integro-Partial Differential Equation

The heat distribution in a hollow pipe, whose ends are held at two different temperatures, is studied. The outside surface is assumed to be thermally isolated and the inner surfaces have radiation boundary conditions. The role of convection in the heat transfer is taken to be negligible.

The temperature is assumed to be constant along the thickness of the pipe and rotational symmetry is also assumed, allowing the pipe to be modeled in 1D. A comparison is made with a purely conductive model in order to visualize the effect of the heat radiation.

A 3D model is also shown as a comparison.

This model comes courtesy of Daniel Smith and Ali Shajii of MKS Instruments, Wilmington, Massachusetts, USA.

A surface plot showing the temperature distribution on the outside surface of a 3D pipe and with internally radiating surfaces.

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