Group analysis of nonlinear heat-conduction problem for a semi-infinite body

Abstract

The transformation group theoretic approach is applied to present an analysis of the nonlinear unsteady heat conduction problem in a semi–infinite body. The application of one–parameter group reduces the number of independent variables by one, and consequently the governing partial differential equation with the boundary and initial conditions to an ordinary differential equation with the appropriate corresponding boundary conditions. The ordinary differential equation is solved analytically for some special forms of the thermal parameters. The general analysis developed in this study corresponds to thermal parameters that has different forms with coordinates and time. © 1995 by Mathematical Ukraina Publisher.