This paper presents research on a free boundary value problem arising in a nonlinear n-diffiision equation by using a homotopy analysis method(HAM).Approximate analytical solutions are obtained for special nonlinear d...This paper presents research on a free boundary value problem arising in a nonlinear n-diffiision 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.展开更多
基金supported by the National Natural Science Foundation of China(Nos.51276014 and 51476191)supported by Qatar National Research Fund's National Priority Research Project(NPRP)5-674-1-114.
文摘This paper presents research on a free boundary value problem arising in a nonlinear n-diffiision 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.
