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Schmoozer
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Homework Statement
The one dimensional steady-state heat conduction equation in a medium with constant conductivity (k) with a constant volumetric heat generation in three different coordinate systems (fuel rods in a nuclear power plant) is given as:
[tex]\frac{d^2 T}{dx^2}=-\frac{\dot{q}}{k}[/tex] T(x=0)=1 T(x=1)=2 Cartisian
[tex]\frac{1}{r}\frac{d}{dr}(r\frac{dT}{dr})=-\frac{\dot{q}}{k}[/tex] T(r=R)=1 Cylindrical
[tex]\frac{1}{r^2}\frac{d}{dr}(r^2\frac{dT}{dr})=-\frac{\dot{q}}{k}[/tex] T(r=R)=1 Sperical
a. Find an expression for the temperature distribution in a solid for each case
b. What is a temperature distribution if the heat generation is zero?
Homework Equations
The Attempt at a Solution
[tex]T(x)=\sum_{n=0}^{\infty}b_n x^n[/tex]
[tex]T'(x)=\sum_{n=0}^{\infty}nb_n x^n^-^1[/tex]
[tex]T''(x)=\sum_{n=0}^{\infty}n(n-1)b_n x^n^-^2 [/tex] so n=0, n=1
[tex]b_{0}=0[/tex]
[tex]b_{1}=0[/tex]
[tex]b_{2}=2x[/tex]
[tex]b_{3}=3x^2[/tex]
Am I at least on the right track?