Regression analysis of magnetized fluid flow in a discretely heated square enclosure in the partially filled with porous medium using RSM-CCD.

This computational study looks at the dynamics of free convection in a differentially heated square chamber occupied by ionized propane and saturated permeable partition. The modified Navier–Stokes equations and temperature equations are used to describe fluid and porous domain flow and heat transport phenomena. To solve these equations, the Galerkin finite element technique is used. Parametric adjustments are made for various heat source and sink lengths, Rayleigh number, Hartman number, and Darcy number. The results are quantitatively described in terms of the mean Nusselt number along the heated wall as the Rayleigh number increases (104 ≤ Ra ≤ 106). Streamlines and isotherms are used to visualize qualitative insights on these parametric changes. A comparative study is also performed without the porous media. Conclusive data demonstrate that using a permeable partition over a solid partition improves the mean Nusselt value by 26.28% at Ra = 104 and to a highest value of 56.5% at Ra = 106. Notably, this work presents a sensitivity analysis based on response surface methodology, demonstrating subtle connections between magnetohydrodynamics, Rayleigh number, and porous material effects. These findings provide important perspectives for improving thermal control and energy efficiency in advanced magnetohydrodynamic systems. [ABSTRACT FROM AUTHOR]