An Integro-Partial Differential Equation

Application ID: 700

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.

This model example illustrates applications of this type that would nominally be built using the following products: