Exact analytical solution of a nonlinear reaction–diffusion model in porous catalysts

In two papers published recently in Chemical Engineering Journal, [Y.P. Sun, S.B. Liu, S. Keith, Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by decomposition method, Chem. Eng. J. 102 (2004) 1–10; S. Abbasbandy, Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method, Chem. Eng. J. 136 (2008) 144–150], a nonlinear model of diffusion and reaction in porous catalysts has been investigated by approximate analytical methods (the Adomian decomposition method, [Y.P. Sun, S.B. Liu, S. Keith, Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by decomposition method, Chem. Eng. J. 102 (2004) 1–10] and the homotopy analysis method, [S. Abbasbandy, Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method, Chem. Eng. J. 136 (2008) 144–150], respectively). The present paper shows, however, that the model is exactly solvable in terms of Gauss’ hypergeometric function. The exact solution is illustrated by specific examples. Several new physical features are reported and discussed in detail.