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Asked Oct 9, 2019
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Find the steady-state solution of the heat conduction equation aux = u, that satisfies the given set of boundary conditions.
u (L, 1) = 0
u(0,)= T,
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Find the steady-state solution of the heat conduction equation aux = u, that satisfies the given set of boundary conditions. u (L, 1) = 0 u(0,)= T,

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A
Cn e nx2 cos(Pi n t)
B
Ce nt 2 cos( Pi n x
T
D
None of the above
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A Cn e nx2 cos(Pi n t) B Ce nt 2 cos( Pi n x T D None of the above

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Expert Answer

Step 1

Given heat conduction equation and the boundary conditions as:

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...1) a'и, — и, хх и (0,) -Т and и, (L,t) -0

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Step 2

By separation method, consider

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u(x,t) f(x).8(t) ..2)

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Step 3

Then equation (1)...

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af"(x)g() (x).8' (f) f(x) g() g'(t) Let = 1, where A is a constant. f(x) a'g(t)

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