Ex. The temperature u(x.t) in a strip of metal of width L is govemed by the heat equation au =u, for 05XSL and t>0. Use separation of variables method to find the unsteady state temperature distribution in the strip given that the initial condition is u(x,0) =x and the boundary conditions u, (0.1) =u(Lt)=0 for t>0. The condition u, (0,1)=0 expresses mathematically the constraint that no heat flows through the left boundary (insulated end condition).
Ex. The temperature u(x.t) in a strip of metal of width L is govemed by the heat equation au =u, for 05XSL and t>0. Use separation of variables method to find the unsteady state temperature distribution in the strip given that the initial condition is u(x,0) =x and the boundary conditions u, (0.1) =u(Lt)=0 for t>0. The condition u, (0,1)=0 expresses mathematically the constraint that no heat flows through the left boundary (insulated end condition).
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:Ex. The temperature u(x,t) in a strip of metal of width L is govemed by the heat
equation au =u, for 05XSL and t>0. Use separation of variables method to
find the unsteady state temperature distribution in the strip given that the initial
condition
is
u(x,0) =x
and
the
boundary
conditions
u, (0.1) =u (Lt)=0 for t>0.
The condition u, (0,t)=0 expresses
mathematically the constraint that no heat flows through the left boundary (insulated
end condition).
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