entropy analysis of a radiating magnetic liquid film along a slippery inclined heated surface with convective cooling

The hydromagnetic flow of a newtonian incompressible and electrically conducting variable-viscosity liquid film along an inclined isothermal or isoflux hydrophobic surface is investigated numerically. it is assumed that the fluid is subjected to a convective cooling at the free surface in the presence of a transversely imposed magnetic field. we incorporated in the energy equation, the viscous dissipation, joule heating due to the magnetic field and the local radiative heat flux term for optically thick gray fluid reported by roseland approximation. the governing non-linear differential equations are obtained and solved numerically using the shooting method coupled with a fourth-order runge-kutta method. the effects of some parameters on velocity and temperature profiles, skin friction, nusselt number entropy generation rate, and the bejan number profiles are analyzed graphically and discussed.