Heat transfer analysis for a free boundary problem arising in n-diffusion equation

This paper presents research on a free boundary value problem arising in a nonlinear n-diffusion equation by using a homotopy analysis method (HAM). Approximate analytical solutions are obtained for special nonlinear diffusion functional coefficient (variable thermal conduction) k(s)=s^{i} for i=1, 3, 5 and convection functional coefficient h(s)=s^{j} for j=1, 4 and power law parameter of n=0.2, 0.5, 1.0, 2.5. Reliability and efficiency of the approximate solutions are verified by numerical ones showing good agreement. The effects of the power law exponent, the nonlinear diffusion or convection functional coefficients, and the free boundary parameter on the flux transport characteristics are presented graphically and analyzed in detail. The mathematical techniques employed in this paper have the significance in studying some other problems of engineering.