Free Convection of Herschel – Bulkley Fluids WithMHD Effect on a Vertical Moving Plate in Porous Media - Noorkhah, Seyed Ali; Osintsev, Natalja (Mechanical Technology and Engineering Insights, 2025)
In this study, a numerical investigation is carried out to analyze free convection heat transfer of a non-Newtonian Herschel–Bulkley fluid over a vertical moving plate embedded in a porous medium in the presence of a transverse magnetic field. The flow is assumed to be steady, laminar, incompressible, and electrically conducting. The governing continuity, momentum, and energy equations are formulated under the boundary layer approximation and transformed into a set of coupled, nonlinear, dimensionless equations. These equations are solved numerically using a fully implicit finite difference method. The effects of key physical parameters, including the magnetic parameter, porous medium parameter, Prandtl number, Brinkman number, Grashof number, and flow behavior index, on the transient velocity and temperature distributions are examined. In addition, the variation of the local Nusselt number is presented to characterize the heat transfer behavior. The results reveal that the application of a magnetic field significantly suppresses the fluid velocity while enhancing the temperature due to the Lorentz force. An increase in the porous medium parameter reduces the velocity field and raises the temperature distribution. Higher Prandtl numbers lead to thinner thermal boundary layers, resulting in reduced temperature profiles. Moreover, increasing the Brinkman number intensifies viscous dissipation, causing an increase in both velocity and temperature. The local Nusselt number is found to decrease with increasing magnetic and Brinkman parameters, whereas it increases with higher Prandtl and Grashof numbers. The present study provides useful insight into the heat transfer characteristics of Herschel–Bulkley fluids in porous media under magnetic field effects, which are relevant to various industrial and engineering applications.