Lie Group Analysis of Magnetohydrodynamic Flow and Mass Transfer of a Visco-Elastic Fluid Over a Porous Stretching Sheet

An analysis is carried out to study the momentum and mass transfer characteristics in a visco-elastic fluid flow over a porous stretching sheet in the presence of a transverse magnetic field. The flow is generated solely due to the linear stretching of the sheet. The symmetry groups obtained using a special form of Lie group transformations viz. Scaling group of transformations, reduce the momentum equation and the concentration conservation equation into fourth order and second order ordinary differential equations respectively. Closed form analytical solutions have been derived for non-dimensional concentration and mass flux profiles in the form of confluent hyper geometric (Kummer s) functions, for two different cases of the boundary conditions, namely (1) Prescribed Sheet Concentration (PSC) and (2) Prescribed Mass Flux (PMF). The main emphasis of this paper is to derive the final equations using the scaling group of transformations and to study the effects of the visco-elastic parameter, suction/blowing parameter, magnetic parameter, concentration and mass flux parameters and Schmidt number on the mass transfer characteristics. It has been observed that, for the case of suction and for the values of the parameters considered, an ideal combination to obtain a reduced concentration boundary layer thickness would be to choose smaller values of the visco-elastic and magnetic parameters and relatively larger value for the Schmidt number. This is seen to be more significant in the PMF case. An increase in the concentration and mass flux parameters has shown a steep decrease in the concentration boundary layer thickness.