Approximate Solutions of Canonical Heat Conduction Equations

Abstract

We consider three analytical methods for finding the approximate solutions of one-dimensional, transient, and nonlinear heat conduction problems based upon the canonical equations of heat transfer. The first method can be considered as a generalization or refinement of the integral method. The second is an iterative method similar to that of Targ utilized in boundary layer theory. The third method is a variational procedure introduced in the spirit of Gauss’ variational principle of least constraint.