Magneto hydro dynamic Non-Similar solutions of a Visco-elastic fluid with slip flow and heat transfer over a non – linearly stretching porous sheet

The study of boundary layer flow and heat transfer of an electrically conducting visco-elastic second grade fluid in a porous medium past a stretching sheet is conducting with power law surface temperature or power law surface heat flux. The flow in boundary layer is considered to be generated solely by the linear stretching of the boundary sheet adjacent to porous medium in a magnetic field with boundary wall slip condition. The governing partial differential equations are converted into non linear ordinary differential equations by similarity transformations. The solutions of dimensionless surface temperature as well as non-similar flow and heat transfer characteristics with the governing dimensionless parameters of the problem which include a non-linear stretching sheet , viscous dissipation , internal heat generation /absorption and temperature gradient dependent heat sink, power-law index of wall temperature parameters are obtained in terms of Confluent Hypergeometric Functions (CHF) and tabulated. The skin friction at the wall is also derived. It is observed that the suction (S), Slip parameter (L), the permeability of the medium (k2) and the magnetic parameter (M), visco-elastic parameter (k1) depress the longitudinal velocity magnitudes but influences positively the transverse velocity while the suction, wall temperature parameter, temperature gradient dependent heat sink (Q), lowers temperature and heat transfer distribution aiding in controlling momentum and heat transfer during material processing.