A numerical study is conducted to analyze steady natural convection of a micropolar fluid along a vertical surface embedded in a Darcy–Forchheimer porous medium, accounting for viscous dissipation effects. The governing boundary-layer equations for mass, linear momentum, angular momentum, and energy conservation are formulated under the Boussinesq approximation and reduced to a coupled system of nonlinear ordinary differential equations using a local similarity transformation. The resulting boundary-value problem is solved numerically using MATLAB’s bvp5c solver based on a Lobatto IIIa collocation scheme. Numerical accuracy is ensured through mesh refinement, domain truncation tests, and consistency checks, and benchmark results are reported for future reference. The influences of key physical parameters, including micropolar coupling, porosity, Darcy resistance, Forchheimer inertia, Prandtl number, and viscous dissipation, on velocity, microrotation, and temperature distributions are systematically examined. The results reveal that micropolar effects and non-Darcy porous resistance significantly modify the boundary-layer structure, suppress fluid motion, and alter heat transfer characteristics. Viscous dissipation increases fluid temperature and reduces wall heat transfer, while microrotation parameters primarily govern angular momentum transport near the surface. Quantitatively, increasing the micropolar parameter from K=0 to K=1 increases the wall shear f′′(0) by approximately 30%, while higher porous resistance significantly suppresses the velocity field and steepens the near-wall temperature gradient. The influence of viscous dissipation remains moderate for Ec≤0.1, primarily affecting the thermal distribution. In the limiting cases of vanishing micropolar and Forchheimer effects, the classical similarity solutions for Newtonian free convection in porous media are recovered, confirming the validity of the present formulation.
Maaitah et al. (Sun,) studied this question.