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Two-Dimensional, Steady-State Conduction Excel Spread Sheet Calculator

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Engineering and Physics Excel Calculators

Two-Dimensional, Steady-State Conduction. Evaluate 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 new, second worksheet 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 discontinuity at two of the corners and the animation shows the Gibbs phenomenon clearly. 

Download  Two-Dimensional, Steady-State Conduction Spreadsheet

The Gibbs phenomenon, is the Fourier series of a piecewise continuously differentiable periodic function behaves at a jump discontinuity. The nth partial sum of the Fourier series has large oscillations near the jump, which might increase the maximum of the partial sum above that of the function itself. The overshoot does not die out as n increases, but approaches a finite limit. This sort of behavior was also observed by experimental physicists, but was believed to be due to imperfections in the measuring apparatus.

Credit:

Professor Robert J. Ribando, University of Virginia

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