A Note on the Integral-Balance Solutions to Transient Diffusion with a Power-Law Diffusivity: a Test of the H Rule with Dirichlet Boundary Condition


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Abstract


Closed form approximate solutions to nonlinear diffusion equation with nonlinear power-law D=D0 (C/Cref )m diffusivity developed by the integral-balance method and the concept of finite penetration depth δ(t) have been developed with and the assumed profile u = (1-x/δ)n. Numerical tests with exponents defined through the H rule as n = 1/m (or 1/(m+1)) been have been performed. The results have been compared to exact solutions and approximate (integral-balance) ones with exponents defined through optimization.
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Keywords


Integral-Balance Method; Double-Integration Method; Optimal Exponents; H-Rule

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