NONLINEAR HEAT TRANSFER BY THE ITERATIVE VARIATIONAL METHOD
For most nonlinear heat transfer problems, the iterative solutions of the governing equation exist. The iterative equations are linear in terms of the highest order derivative involved. Instead of solving these linear equations by direct integration, a variational functional with the Euler equation identical to the iterative equation can be formulated. This variational formulation permits the use of approximate methods of solution in place of direct integration of the iterative equation. This iterative variational approach makes it possible to solve nonlinear heat transfer problems as if they were linear and to use many of the approximate methods of solution available in variational calculus.
In this paper, the application of the iterative variational method to nonlinear heat transfer problems is presented. The approximate methods of solution used include the finite element method, the finite difference method, and the method of orthogonal sequences. Methods for improvements of the rate of convergence during the iteration are also described.