This article addresses the hydrodynamic boundary layer flow of a chemically reactive fluid over an exponentially stretching vertical surface with transverse magnetic field in an unsteady porous medium. The flow problem is modelled as time depended dimensional partial differential equations which are transformed to dimensionless equations and solved by means of approximate analytic method. The results are illustrated graphically and numerically and compared with previously published results which shown a good agreement. Physically increasing Eckert number of a fluid amplifies the kinetic energy of the fluid, and as a novelty, the Eckert number under the influence of chemically reactive magnetic field is effective in controlling the kinematics of hydrodynamic boundary layer flow in porous medium. Interestingly, whilst the Eckert number amplifies the thermal boundary layer thickness and velocity as well as the concentration of the fluid, the presence of the magnetic field and the strength of the chemical reaction have a retarding effect on the flow. Also, the chemical reaction parameter and permeability of porous medium are effective in reducing skin friction in chemically reactive magnetic porous medium and are relevant in practice because reduced skin friction enhances the efficiency of a system. The results of the current study are useful in solar energy collector systems and materials processing.

The time-dependent hydromagnetic boundary layer flow across a vertical surface with internal heat regeneration in porous media is investigated. The flow problem has been modelled mathematically in partial differential equations along with appropriate defined boundary conditions. These equations were expressed in dimensionless form using suitable similarity variables. The resulting dimensionless equations along with the conditions defined at the boundaries are solved by means of the Laplace transform methods. Results of the study are graphically illustrated for various quantities of practical importance. It was concluded that time positively influence the flow as a reduced skin friction coefficient was observed. Furthermore, the magnetic parameter, the radiation parameter, the heat absorption parameter and the permeability of the porous media can be used to influence the characteristics of a flow in porous media.