Analytical Study of MHD Mixed Convection in a Heated Vertical Porous Channel

Abstract

An analytical analysis is made to examine the influence of MHD flow in a laminar mixed convection flow through a vertical channel embedded with a porous medium. The momentum equations are modeled using the non-Darcy Brinkman extended formulation. The flow is assumed to be steady, laminar and fully developed of an electrically conducting fluid with internal heat generation or absorption. The governing systems of equations are solved analytically to derive expressions for velocity and temperature distributions. Moreover, parametric analysis is conducted to investigate the effects of the Magnetic field strength (M), heat source parameter (Q), mixed convection parameter ($Gr_1=\frac{Gr}{Re}$), and Darcy number (Da) on the velocity and temperature distribution. The analysis show that increasing M progressively smooths the inflection point in the velocity profile, leading to a more flattened flow structure. Higher values of Q induce the formation of an inflection point along with backflow in the velocity field. Furthermore, an increase in thermal buoyancy forces (Gr/Re) promotes the development of inflection points and flow separation near the channel walls.