The temperature distribution u(x, t) of the one-dimensional gold rod is governed by the heat equation as follows. a?u 0.25- ди at Given the boundary conditions u(0, t) = 2t², u(1, t) = 5t, for 0

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Chapter2: Second-order Linear Odes
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The temperature distribution u(x,t) of the one-dimensional gold rod is governed by
the heat equation as follows.
(a)
a²u
ди
= 0.25
at
əx?
Given the boundary conditions u(0, t) = 2t², u(1, t) = 5t, for 0 <t < 0.04 s and
the initial condition u(x,0) = x(1 – x) for 0<x< 1.0 mm, analyze the
temperature distribution of the rod with Ax = 0.25 mm and At = 0.02 s in 4 decimal
places.
Transcribed Image Text:The temperature distribution u(x,t) of the one-dimensional gold rod is governed by the heat equation as follows. (a) a²u ди = 0.25 at əx? Given the boundary conditions u(0, t) = 2t², u(1, t) = 5t, for 0 <t < 0.04 s and the initial condition u(x,0) = x(1 – x) for 0<x< 1.0 mm, analyze the temperature distribution of the rod with Ax = 0.25 mm and At = 0.02 s in 4 decimal places.
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