Mr.G.Purushotham, Dr.Maddileti Pasupula 02 07 An investigation on the non linear problem of the effect of Hall current on the unsteady magnetohydrodynamic free convective Couette flow of incompressible electrically conducting fluid between two permeable plates is carried out when a uniform magnetic field is applied transverse to the plate while the thermal radiation viscous and Joules dissipations are taken into account The fluid is considered to be a gray absorbing emitting but non scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation The dimensionless governing coupled non linear boundary layer partial differential equations are solved by an efficient accurate and extensively validated and unconditionally stable finite element method The effects of thermal radiation and Hall current on primary and secondary velocity skin friction and rate of heat transfer are analyzed in detail for heating and cooling of the plate by convection currents Physical interpretations and justifications are rendered for various results obtained Copyright (c) Journal of Science Engineering Technology and Management Science. All rights reserved 2026