Visco-elastic MHD flow, heat and mass transfer over a porous stretching sheet with dissipation of energy and stress work

Abstract

The present paper deals with the study of momentum, heat and mass transfer characteristics in a viso-elastic fluid flow over a porous sheet, where the flow is generated due to linear stretching of the sheet and influenced by a uniform magnetic field applied vertically and a continuous injection of the fluid through porous boundary. In the flow region, heat balance is maintained with a temperature dependent heat source/sink, viscous dissipation, dissipation due to elastic deformation and stress work produced as the result of magnetic field on the non-Newtonian fluid. In mass transfer analysis we have taken into account the loss of mass of the chemically reactive diffusive species by means of first order chemical conversion rate. Using suitable similarity transformations on the highly non-linear partial differential equations we derive several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles in the form of confluent hyper geometric (Kummer's) functions and some other elementary functions as its special form, for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature (PST) and prescribed second order power law concentration (ii) wall with prescribed second order power law heat flux (PHF) and prescribed second order power law mass flux. The effect of the non-dimensional magnetic parameter on momentum, heat and mass transfer characteristics for non-isothermal boundary condition and different physical situations of the fluid, having various degrees of visco-elasticity, Prandtl number, heat source/sink strength and Schmidt number, are discussed in detail. Some of the several important findings reported in this paper are: (i) The combined effect of magnetic field, visco-elasticity and impermeability of the wall is to increase skin-friction largely at the wall; (ii) maximum enhancement of wall-temperature profile due to the application of transverse magnetic field occurs when the boundary heating is maintained with prescribed heat flux, boundary wall is porous and Prandtl number of the fluid is low; (iii) the effect of transverse uniform magnetic field is to increase concentration in the flow region, however, enhancement of concentration is higher when the stretching wall is porous and subjected to injection and (iv) the reduction of concentration due to chemical conversion is of significant order near the wall in PHF case when the wall is maintained with prescribed power low mass flux, in comparison with the PST case when the wall is maintained with prescribed power law surface concentration.