Viscoelastic MHD flow and heat transfer over a stretching sheet with viscous and ohmic dissipations

A mathematical analysis has been carried out on momentum and heat transfer characteristics in an incompressible electrically conducting viscoelastic boundary layer fluid flow over a linear stretching sheet. Momentum boundary layer equation takes into account the effect of transverse magnetic field and electric field. Thermal boundary layer equation takes into account the viscous dissipation and Ohmic dissipation due to transverse magnetic field and electric field. Highly non-linear momentum boundary layer equation and thermal boundary layer equation are converted into similarity equations and then solved numerically by employing fifth order Runge–Kutta–Fehlberg method with shooting. The results are analysed for the situation when stretching boundary is prescribed by non-isothermal temperature, namely, prescribed surface temperature (PST) which varies quadratically with the flow directional coordinate x  . The effects of various physical parameters like viscoelastic parameter, Prandtl number, local Reynolds number, Eckert number Hartmann number and electric parameter on various momentum and heat transfers characteristics are analysed. Some of the important findings of this paper are (i) The combined effect of increasing the values of local Reynolds number RexRex and local electric parameter (E1) is to decrease skin-friction coefficient Cf largely. (ii) In presence of magnetic field the effect of electric field is to decrease temperature near the stretching boundary and increase the same significantly away from the stretching sheet. (iii) If electric field is present and the Prandtl number is lower then there would be a significant decrease of temperature near the boundary sheet in case of viscoelastic fluid. (iv) The presence of electric field reverses the direction of heat transfer on the boundary stretching sheet more significantly in case of viscoelastic fluid.