UNSTEADY MAGNETOHYDRODYNAMIC CHANNEL FLOW WITH HALL AND ION-SLIP EFFECTS: THE INTEGRAL TRANSFORM SOLUTION PROCEDURE

This paper deals with the generalized integral transform solution procedure to the unsteady magneto-convection problem of an electrically conducting Newtonian fluid within a parallel-plate channel, in which Hall and ion-slip effects are taken into account. It is considered that the magnetic Reynolds number is small, i.e., the flow-induced magnetic fields are not strong enough to modify the applied transversal magnetic field. To cover a broader range of problems, temperature-dependent transport properties, time-dependent pressure gradient, inflow perpendicular to the plates (porous plates), and Couette flow are also considered in the mathematical formulation. Results are illustrated and compared to the main numerical results from the literature for the related velocity and temperature potentials as function of the main governing parameters, namely, Hartmann, suction/injection, transport properties, and electron and ion-slip parameters. In order to illustrate the consistency of the Generalized Integral Transform Technique (GITT) and its use for benchmarking purposes in the magneto fluid dynamics area, convergence analyses are carried out for the main potentials.