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A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation %3| a?u a?u 0. + ax2 ' ay² Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (AeP* + Be-Dx)(C cos py + D sin py).

A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation %3| a?u a?u 0. + ax2 ' ay² Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (AeP* + Be-Dx)(C cos py + D sin py).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using half range Fourier series

A rectangular steel sheet is bounded by the axis x = 0,y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation a?u a?u 0. dx² ' ðy² Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (AeP* +Be-p*)(C cos py + D sin py). ха-
Transcribed Image Text:A rectangular steel sheet is bounded by the axis x = 0,y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation a?u a?u 0. dx² ' ðy² Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (AeP* +Be-p*)(C cos py + D sin py). ха-
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