An effective modification of finite element method for heat and mass transfer of chemically reactive unsteady flow

A modified technique of Galerkin finite element method is applied to investigate the boundary layer flow of mixed convection with effects of exothermic/endothermic constructive/destructive chemical reaction and heat source. Model of the present flow problem is constructed with the use of partial differential equations and the transformed nonlinear boundary value problems are worked out numerically by the modified technique of FEM. In order to overcome the deficiency of accuracy in standard finite element method with polynomial interpolation for computing derivative numerically, finite difference formulas are coupled with FEM for computing derivatives accurately. Feature of the modified technique is tabulated for findings of the errors in derivatives and numerical values of skin friction coefficient, Nusselt number, and Sherwood number. Present coupling of finite element method with finite difference formulas can be implemented to find continuous derivatives more accurately than the standard FEM with polynomial interpolation which can also balance one of the extra advantages in applying FEM with B-splines. Comparison is made for the obtained results from present coupled technique of FEM with Matlab built in solver "bvp4c." It is also shown that the temperature profile behaved reversely and the concentration profile did not affect exothermic/endothermic reactions but has opposite behavior for constructive and destructive chemical reactions. It can also be deducted that the velocity profile decreases for the cooled plate (for positive Grashof number) and behaves reversely for the heated plate (for negative Grashof number).