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If the temperature u(x, t) in a one-dimensinal rod 0 < x < L is given by the following initial boundary value problem ди + 1; 0 0, dt u(x,0) = f(x); ди (0, t) = 1; 0 < x < L ди -(L,t) = a, dx t>0 dx Determine an equilibrium temperature distribution if it exists and find the value(s) of a for which this equilibrium is possible.

If the temperature u(x, t) in a one-dimensinal rod 0 < x < L is given by the following initial boundary value problem ди + 1; 0 0, dt u(x,0) = f(x); ди (0, t) = 1; 0 < x < L ди -(L,t) = a, dx t>0 dx Determine an equilibrium temperature distribution if it exists and find the value(s) of a for which this equilibrium is possible.

Advanced Engineering Mathematics
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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If the temperature u(x, t) in a one-dimensinal rod 0 < x < L is given by the following initial boundary value problem u + 1; ди 0 < x < L, t > 0, dx2 u(x, 0) = f(x); 0<x<L ди (0, t) = 1; dt ди -(L,t) = a, t > 0 dx dx Determine an equilibrium temperature distribution if it exists and find the value(s) of a for which this equilibrium is possible.
Transcribed Image Text:If the temperature u(x, t) in a one-dimensinal rod 0 < x < L is given by the following initial boundary value problem u + 1; ди 0 < x < L, t > 0, dx2 u(x, 0) = f(x); 0<x<L ди (0, t) = 1; dt ди -(L,t) = a, t > 0 dx dx Determine an equilibrium temperature distribution if it exists and find the value(s) of a for which this equilibrium is possible.
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