The temperature ne-dimensional distribution u(t) along a wire of length L is governed by th heat equation: a a² [u(x, t)]=- [u(x, t)] əx² where ß is a positive constant. olve this equation using the ssumption that the form of the solution is: .)-f(x) u(x, t) = f(x) g(t) wil.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2. The temperature distribution u(t) along a wire of length L is governed by the
one-dimensional heat equation :
a
2²
[u(x, t)]
-Bax² [u(x, t)]
where is a positive constant.
Solve this equation using the
assumption that the form of the solution is:
0,1)=0
sir.0)=f(x)
Onitial temps, distribution)
u(x, t) = f(x) · g(t)
(1.1)
Transcribed Image Text:2. The temperature distribution u(t) along a wire of length L is governed by the one-dimensional heat equation : a 2² [u(x, t)] -Bax² [u(x, t)] where is a positive constant. Solve this equation using the assumption that the form of the solution is: 0,1)=0 sir.0)=f(x) Onitial temps, distribution) u(x, t) = f(x) · g(t) (1.1)
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