Separation of Variables Heat flows along an infinite (in the y-direction) strip of width a (in the x-direction). Find the general solution u(x, y, t) to the two-dimensional heat equation ди - k√² u = 0 Ət subject to the boundary conditions: u(0, y, t) = 0 = u(a, y, t); — u(x, y, t) lim u(x, y, t) = 0. x+h = = 0; and |t=0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Separation of Variables
Heat flows along an infinite (in the y-direction) strip of width a (in the x-direction).
Find the general solution u(x, y, t) to the two-dimensional heat equation
ди
- k√² u = 0
Ət
subject to the boundary conditions: u(0, y, t) = 0 = u(a, y, t); — u(x, y, t)
lim u(x, y, t) = 0.
x+h
=
= 0; and
|t=0
Transcribed Image Text:Separation of Variables Heat flows along an infinite (in the y-direction) strip of width a (in the x-direction). Find the general solution u(x, y, t) to the two-dimensional heat equation ди - k√² u = 0 Ət subject to the boundary conditions: u(0, y, t) = 0 = u(a, y, t); — u(x, y, t) lim u(x, y, t) = 0. x+h = = 0; and |t=0
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