An approximate analytical (integral-balance) solution to a non-linear heat diffusion equation
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2015-01-01
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Abstract
The paper presents a closed form approximate solution of the non-linear diffusion equation of a power-law non-linearity 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.