Consider steady heat transfer in any orthogonal coordinate system:

where 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.

2004-01-31