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Consider steady heat transfer in any orthogonal coordinate system:
is located on surface . The boundary
condition is type 3; heat transfer coefficient can vary with
position on surface but is independent of temperature. Boundary
conditions of type 1 and 2 may be obtained from the above boundary condition
can be obtained by setting or , respectively.
The Green's function solution equation for steady temperature
is given by:
See Table 1 (under Heat Equation, General Case) for and for
various geometries in rectangular, cylindrical, and spherical coordinates.