Érick Marcelino Miranda, Marcos Fabrício de Souza Aleixo Filho, Francisco Ricardo Cunha

Abstract: This work examines the effects of a transversal and uniform magnetic field on an electrically conducting liquid. The bottom wall is porous and therefore penetrable, where the jump of shear stress is given in terms of a suitable relative velocity by a semi-empirical boundary condition. The formulation of the flow problem is based on the incompressible Magnetohydrodynamics (MHD) governing equations in terms of non-dimensional variables. The relevant physical parameter measuring the relative importance between magnetic and viscous forces is identified as the Hartmann number. The solution of the problem shows the existence of a flow deceleration strongly dependent upon the Hartmann number. In addition, another interesting result is a decrease in the magnitude of the longitudinal component of the magnetic flux density as Hartmann number increases. The application of a transverse magnetic field in the flow of an electrically conducting fluid in tiny pores can produce an effective effect like the flow deceleration produced as the porous medium permeability is decreased. Therefore, it seems to be possible to produce such an effect by just monitoring the magnetic field instead of changing the complex microstructure of a porous medium. Exact and asymptotic solutions are obtained for the velocity and pressure fields of the unidirectional channel flow. The asymptotic solution describes very well the physical behavior of the flow for Hartmann less than unit. In addition, using the asymptotic solutions is possible to split the flow solution in two parts: a purely hydrodynamic contribution and a leading order magnetic contribution in terms of the Hartmann number.

Keywords: Channel Flow, Penetrable Boundary, Magnetic Field, Flow Control.

Date Published: September 30, 2024
DOI: 10.11159/jffhmt.2024.030

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