HYBRID PERTURBATION-GALERKIN TECHNIQUE FOR NONLINEAR HEAT CONDUCTION PROBLEMS II: PARTIAL DIFFERENTIAL EQUATIONS

Abstract

A two-step hybrid perturbation-Galerkin analysis technique described in Part I is applied to a variety of nonsteady, nonlinear heat conduction problems involving a parameter. The technique is applied to model problems representing four classes of nonsteady, nonlinear heat conduction problems: (1) conduction in a rod with a temperature-dependent conductivity; (2) a nonsteady problem with fourth-power radiation loss; (3) phase-change moving boundary; and )4) conduction in a cube. In each case, the hybrid solution is compared with the perturbation solution on which it is based, as well as with other approximate solutions and the exact (analytical) solution, when it exists.