Matrices of Green's type of steady-state heat conduction in multiply connected piecewise homogeneous regions
The author's modification of the method of functional equations is used for accurate evaluation of steady-state thermal fields generated by a point concentrated source in two-dimensional multiply connected regions that are occupied with piecewise homogeneous materials. Resolving potentials are built with the aid of matrices of Green's type, which are constructed for simply connected piecewise homogeneous regions. Importance of operating with readily computable representations of such matrices is emphasized. Since the sets of field (observation) and source points in the resolving potentials never coincide, the boundary value problems to consider reduce to some functional (integral type) equations with relatively smooth kernels. It is shown that not only the heat distribution but also the flux components caused by a point source are accurately computable within the approach.
multiply connected regions green's (influence) functions potential fields nonhomogeneous media