Impact of micro-rotation on a double-diffusive radiative flow within a lid-driven enclosure fearuring Joule heating, porosity and Lorentz forces

•The present paper explores the fluid dynamics, heat and mass transmission characteristics within hexagonal enclosure with square object.•The phenomenon encompasses the interplay of various physical mechanism, including micro-rotation of fluid particles, Joule heating, thermal radiation, porous materials, and magnetic field.•The governing nonlinear partial differential equations are transformed into non-dimensional form and then investigated numerically using continuous Galerkin finite element method. The pressure component of the momentum equation is removed by employing the Penalty parameter.•The validation of findings is ensured by establishing a consensus with previous studies. Flow, heat and mass distributions are depicted using streamlines, isotherms and isoconcnetrations.•Graphical representation of average Nusslet number and Sherwood number are also provided. It is anticipated to offer novel concept for enhancing the performance of cooling systems and optimizing the energy efficiency in diverse engineering applications. The present paper explores the fluid dynamics, heat and mass transmission characteristics within hexagonal enclosure with square object. The phenomenon encompasses the interplay of various physical mechanism, including micro-rotation of fluid particles, Joule heating, thermal radiation, porous materials, and magnetic field. The governing nonlinear partial differential equations are transformed into non-dimensional form and then investigated numerically using continuous Galerkin finite element method. The pressure component of the momentum equation is removed by employing the Penalty parameter. In order to achieve the consistent solution the value of Penalty parameter is set to 107. The analysis includes several physical parameters, such as Buoyancy ratio (−1–1), micropolar parameter (2–6), Joule heating parameter (0–5), Richardson number (0.5–5), thermal radiation parameter (0.1 – 0.5), Lewis number (0.1–5), Darcy number (0.001–0.1) and Hartmann number (0–50). Results reveal notable trends regarding the impact of key parameters on flow behavior and thermal-solutal transfer within cavity. Increasing Darcy numbers intensify fluid motion and subsequently augments thermal and solutal transfer. The flow regime shifts from shear fricition-dominated at low Richardson number to buoyancy-induced at high Richardson numbers. For concentration-dominant counter flow, a uniform distribution pattern emerges, while aiding flow leads to increased fl