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
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-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26f5e1bf-14c5-4636-9b76-187c82ce1442%2F8e20e7b6-b863-4e41-b0af-a4d8a59fc5ea%2Fbc04dnq_processed.png&w=3840&q=75)
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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