Abstract: Numerical and analytical investigations of the thermosolutal instability in a viscoelastic Rivlin-Ericksen fluid are carried out in the presence of a uniform vertical magnetic field to include the Hall current with a uniform angular velocity in a porous medium. For stationary convection, the stable solute gradient parameter and the rotation have stabilizing effects on the system, whereas the magnetic field and the medium permeability have stabilizing or destabilizing effects on the system under certain conditions. The Hall current in the presence of rotation has stabilizing effects for sufficiently large Taylor numbers, whereas in the absence of rotation, the Hall current always has destabilizing effects. These effects have also been shown graphically. The viscoelastic effects disappear for stationary convection. The stable solute parameter, the rotation, the medium permeability, the magnetic field parameter, the Hall current, and the viscoelasticity introduce oscillatory modes into the system, which are non-existent in their
absence. The sufficient conditions for the non-existence of overstability are also obtained.

Key words: boundary-layer; heat transfer;stagnation point;stretching sheet;homotopy analysis method, magnetic field, thermosolutal instability, porous medium, Rivlin-Ericksen rotating fluid, Hall current