Non-linear heat transfer of solids in orthogonal coordinate systems

Solutions to the non-linear partial differential equation of heat conduction, (Poisson type), are obtained in which the conductivity is temperature dependent, by solving a linear partial differential equation and transforming it to the non-linear form using the Kirchhoff transformation. The method applies to any orthogonal coordinate system.

Transformations for handling boundary conditions of the Dirichlet, Neumann, convection and non-zero type are developed. The method is extended to solve a special class of non-linear unsteady-state conduction problems.

Two non-linear examples are solved to illustrate the method.