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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

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