Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet

An analysis is performed for flow and heat transfer of a steady laminar boundary-layer flow of an electrically conducting fluid of second grade subject to suction and to a transverse uniform magnetic field past a semi-infinite stretching sheet. The influence on the skin-friction parameter b   of various non-dimensional parameters like viscoelastic parameter λ1λ1, magnetic parameter M and suction parameter R is discussed and the variations of the dimensionless stream function f and its derivatives with these parameters are graphed and tabulated. Therewith, the effects of viscous dissipation and work due to deformation are considered in the energy equation and the variations of dimensionless surface temperature and dimensionless surface temperature gradient with the above-mentioned non-dimensional parameters and other ones like Prandtl number σ   and Eckert number EckEck are also plotted and tabulated. Two cases are studied, namely, (i) the sheet with constant surface temperature (CST case) and (ii) the sheet with prescribed surface temperature (PST case). A novel result of the analysis is that for a given viscoelastic fluid subjected to a constant suction the work due to deformation's effect increases with increase in the magnetic parameter M.