Influence of magnetic field on the periodically oscillating fluid inside a porous medium attached to a thick solid plate

This paper presents a rigorous mathematical analysis of the influence of a magnetic field on a periodically oscillating fluid inside a porous medium. We consider a porous medium coupled with a thick solid plate with a magnetic field perpendicular to the direction of fluid oscillations. The hydrodynamic and thermal interactions of the oscillating fluid with the porous medium and the thick solid plate are modeled analytically as a thermoacoustic system under the influence of a transverse magnetic field. The velocity and temperature expressions of the oscillating fluid are derived using the perturbation technique after simplifying the governing Darcy momentum and energy equations. From the flow and thermal fields' results, Nusselt number, heat flux, and work flux are calculated and presented graphically. Consequently, the entropy generation rate for the overall system is investigated to assess the irreversibility associated with the proposed system enabling one to improve the efficiency of the system. Finally, the efficiency of the proposed thermoacoustic system is determined using the expressions of heat and work fluxes. It is observed that the thermoacoustic irreversibility can be minimized by increasing the applied magnetic force resulting in increased efficiency of the proposed system.