Copyright © 2010 Jun Yu et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We use an approximation method to study the solution to a nonlinear
heat conduction equation in a semi-infinite domain. By expanding an energy density
function (defined as the internal energy per unit volume) as a Taylor polynomial in
a spatial domain, we reduce the partial differential equation to a set of first-order
ordinary differential equations in time. We describe a systematic approach to derive
approximate solutions using Taylor polynomials of a different degree. For a special case,
we derive an analytical solution and compare it with the result of a self-similar analysis.
A comparison with the numerically integrated results demonstrates good accuracy of our
approximate solutions. We also show that our approximation method can be applied
to cases where boundary energy density and the corresponding effective conductivity
are more general than those that are suitable for the self-similar method. Propagation
of nonlinear heat waves is studied for different boundary energy density and the