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 COMSOL elog Not logged in  Sat Jun 28 21:59:11 2014, Sam Moore, Optics, General, Difficulty with the COMSOL stationary module; Test Cases  Sun Jun 29 15:37:18 2014, Sam Moore, Optics, General, Difficulty with the COMSOL stationary module; Test Cases  Sun Jun 29 20:25:44 2014, Koji, Optics, General, Difficulty with the COMSOL stationary module; Test Cases
Message ID: 90     Entry time: Sun Jun 29 20:25:44 2014     In reply to: 88
 Author: Koji Type: Optics Category: General Subject: Difficulty with the COMSOL stationary module; Test Cases

Consider a bar with the length of L.

Let's say there is no body heat applied, but the temperature of the bar at x=L is kept at T=0
and at x=0 is kept at T=T0 Exp[I w t].

The equation for the bar is ...(1)

Consider the solution with the form of T(x, t) = T(x) T0 Exp(I w t), where T(x) is the position dependent transfer function.
T(x) is a complex function.

Eq.1 is modified with T(x) as With the boundary condition of This can be analytically solved in the following form where alpha is defined by So kappa/Cp is the characteristic (angular) frequency of the system.
Here is the example plot for L=1 and alpha = 1 (red), 10 (yellow green), 100 (turquoise), 1000 (blue)  If the oscillation is slow enough, the temperature decay length is longer than the bar length and thus the temperature is linear to the position.
If the oscillation is fast, the decay length is significantly shorter  than the bar length and the temperature dependence on the position is exponential.

Now what we need is to solve this in COMSOL

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