Heat Transfer Today

Educational Software for
Heat and Mass Transfer

Excel Workbooks

Two-Dimensional, Steady-State Conduction

UPDATED: 08/23/2022

This workbook evaluates the analytical solution for steady-state conduction in a unit square with one boundary held at a different temperature than the other three and returns a raised contour plot of the results. This particular problem is used frequently to demonstrate separation-of-variables as a solution technique for PDE‘s. The user can change the number of terms to be included in the evaluation of the infinite series. A second worksheet (See below) animates the process of adding terms to the series. Quite a few are needed in this particular problem to get a good solution here – because of the discontinuities at two of the corners.   This animation shows the Gibbs phenomenon clearly.

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