Exact solutions for the incompressible viscous magnetohydrodynamic fluid of a porous rotating disk flow with Hall current

The purpose of the present work is to obtain explicit analytical solutions for the flow of a viscous hydromagnetic fluid due to the rotation of an infinite disk in the presence of an axial uniform steady magnetic field with the inclusion of Hall current effects and porosity. A treatment of three-dimensional equations of motion results in exact formulas for the angular velocity components, current density field as well as the wall shear stresses. The critical peripheral locations at which extrema of the local skin friction occur are also determined. It is proved from the analytical results that for the specific flow the properly defined thicknesses decay as the magnetic field strength increases in magnitude, approaching their hydrodynamic value in the limit of large Hall numbers. Moreover, the injection-like impact of the Hall current is clarified.Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. The temperature field is shown to accord with the convection, dissipation function and Joule heating. According to Fourier's heat law, a constant heat transfer from the disk to the fluid occurs, though it increases by the presence of magnetic field, the increase is slowed down by the Hall effect eventually reaching its hydrodynamic limit.

► An exact solution is obtained.
► The analytic form of the solution explains the well-known physical effects.
► The Hall current in general acts like mass injection through the disk.
► Displacement thicknesses and thermal layer thickness are evaluated.
► Heat transfer expressions are obtained for both suction and injection cases.