A metal bar of length 1 = 1 and thermal diffusivity y = 1 is fully insulated, including its ends. Suppose the initial temperature distribution is u(0,r) = I {{ 0≤x≤1/2 - 1 1/2 ≤ 1 ≤ 1. (a) Use Fourier series to write down the temperature distribution at time t > 0. (b) What is the equilibrium temperature distribution in the bar, i.e., the limit of u(t, x) as t→∞o?

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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A metal bar of length 1 = 1 and thermal diffusivity y = 1 is fully insulated, including its
ends. Suppose the initial temperature distribution is
u(0, x) =
I
{{
0≤x≤1/2
-1 1/2 ≤ 1≤1.
(a) Use Fourier series to write down the temperature distribution at time t > 0.
(b) What is the equilibrium temperature distribution in the bar, i.e., the limit of u(t, x)
as t→∞o?
Transcribed Image Text:A metal bar of length 1 = 1 and thermal diffusivity y = 1 is fully insulated, including its ends. Suppose the initial temperature distribution is u(0, x) = I {{ 0≤x≤1/2 -1 1/2 ≤ 1≤1. (a) Use Fourier series to write down the temperature distribution at time t > 0. (b) What is the equilibrium temperature distribution in the bar, i.e., the limit of u(t, x) as t→∞o?
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