| Summary: | In this article, we have presented the exact solutions of the Couette, Poiseuille and generalized Couette flows of an incompressible magnetohydrodynamic Jeffrey fluid between parallel plates through homogeneous porous medium. The effects of slip boundary conditions and heat transfer are considered. Viscous dissipation, radiation and Joule heating are also considered in the energy equation. The governing equations of the Jeffrey fluid flow are modeled in Cartesian coordinate system. Analytical solutions for the velocity and temperature profiles are obtained for all mentioned cases. The influences of the sundry parameters on the velocity and temperature profiles are studied and the results are presented through graphs. It is noted that, with increase of slip parameter and pressure gradient increases the velocity. Temperature behaves as a decreasing function due to the impact of Hartmann number, non-Newtonian parameter and slip parameter in all noted problems. Keywords: Jeffrey fluid, Heat transfer, Joule heating, Radiation, Viscous dissipation, Slip boundary conditions
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