An approximate analytical (integral-balance) solution to a nonlinear heat diffusion equation

The communication presents a closed form approximate solution of the nonlinear diffusion equation of a power-law nonlinearity of the diffusivity developed by the heat-balance integral method. The main step in the initial transformation of the governing equation avoiding the Kirchhoff transformation is demonstrated. The consequent application of the integral method is exemplified by a solution of a Dirichlet problem with an approximate parabolic profile. Cases with predetermined positive integer and optimized non-integer exponents have been analyzed.