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GF for Solid Cylinder, Steady 3D

The steady Green's function represents the response at point $(r,\phi,z)$ caused by a point source of heat located at $(r^{\prime },\phi^{\prime },z^{\prime})$. The GF associated with equation (1) satisfies the following equations:

$\displaystyle \frac{\partial ^{2}G}{\partial r^{2}}+\frac{1}{r}\frac{\partial G...
...\frac{\partial ^{2}G}{\partial \phi^{2}}
+\frac{\partial ^{2}G}{\partial z^{2}}$ $\textstyle =$ $\displaystyle -\frac{1}{r}\delta (r-r^{\prime })\delta (\phi-\phi^{\prime })
\delta (z-z^{\prime })$ (3)
    $\displaystyle 0<r<a; \; 0<\phi<2\pi ; \; 0<z<L$  
$\displaystyle k_{i}\frac{\partial G}{\partial n_{i}}+h_{i}G$ $\textstyle =$ $\displaystyle 0\mbox{ \ for faces }%
i=1, \; 2, \;3$  

Note that the boundary conditions are homogeneous and of the same type as the temperature problem, Eq. (1). The volume energy generation is replaced by point heat source described by a Dirac delta function, $\delta $. Most of the quantities in this discussion have units: $k=[W/m/K]$; $h=[W/m^{2}/K]$; and, $G=[meters]$ for steady heat conduction in the cylinder.

Frank Pribyl 2005-06-07