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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 is included as an example in the following products:

COMSOL Multiphysics®

The combination of COMSOL® products required to model your application depends on several factors and may include boundary conditions, material properties, physics interfaces, and part libraries. Particular functionality may be common to several products. To determine the right combination of products for your modeling needs, review the Specification Chart and make use of a free evaluation license. The COMSOL Sales and Support teams are available for answering any questions you may have regarding this.