Numerical Investigation of Skin Friction and Heat Transfer in Micropolar Free Convection Through a Porous Medium

ABSTRACT

A comprehensive numerical investigation is presented for steady free convection of a micropolar fluid along an isothermal vertical plate embedded in a saturated porous medium, incorporating Darcy–Forchheimer resistance and viscous dissipation effects. The governing equations for continuity, linear momentum, microrotation, and energy are formulated within the framework of micropolar fluid theory and reduced to a coupled system of nonlinear ordinary differential equations using a local similarity transformation. Despite extensive studies on micropolar convection and porous‐media transport, the combined influence of Darcy–Forchheimer resistance and viscous dissipation on micropolar free convection remains insufficiently understood. The primary objective of this study is to investigate the coupled effects of Darcy–Forchheimer resistance and viscous dissipation on momentum and heat transfer in micropolar free convection within porous media. The novelty of the present work lies in the simultaneous incorporation of micropolar fluid microstructure, nonlinear porous resistance, and viscous dissipation within a unified similarity‐based framework. Therefore, the resulting boundary‐value problem is solved numerically using the MATLAB Boundary Value Problem Solver (bvp5c) collocation‐based solver. A systematic parametric study is conducted to elucidate the individual and coupled influences of porous‐medium resistance, inertial drag, micropolar viscosity ratio, microrotation boundary condition, microrotation coupling and diffusion parameters, effective Prandtl number, porosity, and viscous dissipation on the skin‐friction coefficient and local Nusselt number. The findings reveal that both the Darcy and Forchheimer resistance forces strongly influence heat‐ and momentum‐transfer processes due to the restriction of fluid flow in the porous medium. In comparison, both micropolar viscosity and wall micromotion significantly enhance near‐wall momentum and convective heat transfer, underscoring the importance of microstructure effects. The influence of viscous dissipation on the thermal fluid dynamics is found to increase temperatures and reduce wall temperature gradients, thereby decreasing heat transfer without substantially affecting the skin friction characteristics. Furthermore, there is a clear distinction between the parameters affecting momentum transfer and those influencing heat transfer. In summary, this investigation presents important physical understanding of the influence of micropolar microstructure, porous resistance, and viscous dissipation on the free‐convection heat‐transfer process.