论文信息 - Symmetry analysis for the nonlinear model of diffusion and reaction in porous catalysts

Symmetry analysis for the nonlinear model of diffusion and reaction in porous catalysts

Abstract In this paper the nonlinear problem arising due to diffusion and reaction in catalyst is investigated. This problem was studied before using the Adomian decomposition, finite differences and homotopy analysis methods. Mathematical analysis for the case of the n th order reactions is performed and exact analytical solutions are investigated by the Lie symmetry method. Moreover, we look for exact solutions for negative reaction constants and show that the solutions exist for various values of n and the Thiele modulus ϕ . Graphs are plotted for these parameters and discussed.

Tasawar Hayat | M. Y. Malik | Raseelo J. Moitsheki | Fazal M. Mahomed

[1] N. Ibragimov,et al. Elementary Lie Group Analysis and Ordinary Differential Equations , 1999 .

[2] Shibin Liu,et al. Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by the decomposition method , 2004 .

[3] Fazal M. Mahomed,et al. Symmetry group classification of ordinary differential equations: Survey of some results , 2007 .

[4] S. Lie,et al. Classification und Integration von gewhnlichen Differentialgleichungen zwischenxy, die eine Gruppe von Transformationen gestatten: Die nachstehende Arbeit erschien zum ersten Male im Frhling 1883 im norwegischen Archiv , 1888 .

[5] S. Lie. Theorie der Transformationsgruppen I , 1880 .

[6] G. Bluman,et al. Symmetries and differential equations , 1989 .

[7] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[8] S. Abbasbandy. Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method , 2008 .