Featuring the significance of Soret and Dufour effects for the thermally radiated viscous fluid inside a porous square cavity

In this article, we investigates the computational analysis of viscous fluid within a porous square cavity, presenting a novel analytical approach that incorporates Soret and Dufour effects alongside thermal radiation influences. The heat and mass transport processes are significantly influenced by the Soret and Dufour effects, especially in fluid dynamics involving thermal radiation, porous media, and viscous flows. There are several significant uses for investigating these phenomena in a thermally radiated viscous fluid inside a porous square cavity in a variety of scientific and technical fields including chemical processing, hyperthermia treatment, energy sector, material processing, crystal growth, microgravity experiments, Jet engine cooling, atmospheric flows, petroleum and natural gas industries. The fluid flow through the porous medium is modeled by using the Darcy law, which assumes the linear relationship between flow velocity and pressure gradient. The analysis is based on the assumption of incompressible flow and incorporates the Boussenisq approximation to account for buoyancy effects. The cavity features distinct boundary conditions, with its left and right walls oscillating sinusoidally, introducing a periodic thermal and velocity perturbation, while the upper and lower walls are adiabatic. Through similarity transformations, non-dimensional partial differential equations are transformed into dimensionless forms. The numerical computations are obtained by using the Peaceman-Rachford alternating direction implicit method. The results of several key parameters are obtained graphically. Each parameter encapsulates specific physical mechanisms, allowing a detailed exploration of their individual and combined impacts. Key trends, such as the influence of oscillatory boundary conditions on convective patterns and the role of dimensionless parameters in modulating heat and mass transfer, are explored. The visual representations offer a clear understanding of the system's sensitivity to various parameters, enabling the identification of the optimal conditions for enhanced performance. It is observed that increasing the Rayleigh number enlarges the inner vortex, tilts it toward the upper wall, and enhances the fluid flow pattern with tighter cell spacing. Streamlines are typically more consistent and streamlined in flows where inertial forces are dominant due to increase of Bouyancy ratio parameter. In isotherms, the radiation impact strengthens the fluid's thermal resistance along the top left and lower right walls. When the Dufour number rises, isotherms are dense near the bottom surface and diagonally stratified, indicating heat transmission from the bottom surface to the upper surface in the cavity. The isotherms, streamlines, 3 dimensional and 2 dimensional graphs for velocity profiles are displayed.