Interplay of conducting and non-conducting walls on hydromagnetic natural convection flow in a vertical micro-channel with Hall current

Basant K. Jha ^a, Peter B. Malgwi ^b,*

a. Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
         b. Department of Mathematics, Air Force Institute of Technology, Kaduna, Nigeria

Abstract: Theoretical investigation on the interaction between conducting and non-conducting walls on hydromagnetic natural convection flow of viscous incompressible and electrically conducting fluid through a vertical micro-channel taking into account the effects of induced magnetic field in presence of Hall current is presented. Governing coupled equations responsible for the flow are obtained when either the micro-channel walls are electrically conducting or are electrically non-conducting. Using the method of undetermined coefficients, exact solution are obtained and presented in dimensionless form subject to relevant boundary conditions. Expressions for fluid velocity, induced magnetic field, skin friction, volume flow rate and induced current density in both primary and secondary flow directions are also obtained. Effects of some governing parameters like Hall current parameter, rarefaction parameter and Hartmann number on the different flow situations are given using the aid of line graphs and Tables. The main conclusion of the present analysis is that, in the existence of rarefaction parameter, primary fluid velocity could be enhanced with the increase in Hall parameter when the micro-channel walls are either insulated or when the left micro-channel wall is electrically conducting. Results obtained in this work are relevant in many magnetically controlled devices and could also be used as a benchmark in checking the accuracies of result obtained in some empirical experiments.

Keywords: Magnetohydrodynamic (MHD); Hall current; Micro-channel; Velocity slip; Temperature jump