Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
1. Suppose we have a cylinder of height H and radius R. We want to find the steady-state temperature profile u = solving Laplace's Equation u(r, 0, z) inside the cylinder by Upp + 1 Ur + 2400 + -Up 466 + uzz = 0 subject to the following boundary data: . . . uz(r,0,0)=0 (bottom of cylinder insulated) u(r, 0, H) = f(r,0) (top of cylinder held at a given temperature pro- file) u(R,0,z) = 0 (side of the cylinder held at 0). Give a general formula for u.
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Transcribed Image Text:1. Suppose we have a cylinder of height H and radius R. We want to find the steady-state temperature profile u = solving Laplace's Equation u(r, 0, z) inside the cylinder by Upp + 1 Ur + 2400 + -Up 466 + uzz = 0 subject to the following boundary data: . . . uz(r,0,0)=0 (bottom of cylinder insulated) u(r, 0, H) = f(r,0) (top of cylinder held at a given temperature pro- file) u(R,0,z) = 0 (side of the cylinder held at 0). Give a general formula for u.
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