Find the solution for the following one-dimensional heat equation: U = k*uz + au, 00, %3D
Find the solution for the following one-dimensional heat equation: U = k*uz + au, 00, %3D
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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Transcribed Image Text:3.Find the solution for the following one-dimensional heat equation:
U = k*uzz + u,
0 <r< L,t> 0,
%3D
u(0, t) = 0,
t> 0,
%3D
uz(L, t) = 0,
t> 0,
u(r, 0) = f(r),
0<r< L.
%3D
where a is a constant. Does the solution converge to 0 as t 00?
Expert Solution
Step 1
In this question, we solve the heat equation with a constant source.
we use the method of separation of the variable
U(x,t)=X(x)T(t).
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