Numerical investigation of natural convection flow in a porous cavity considering activation energy, Soret–Dufour effects and variable viscosity

The natural convection flow and heat-mass transport characteristics in porous cavities are critical in thermal insulation, energy storage, geothermal systems, catalytic reactors, chemical processing, and other heat and mass transfer applications where chemical reactions, variable fluid properties, and cross-diffusion all have a significant impact on transport properties. Motivated by these applications, the current study provides a numerical analysis of the convective behavior of a Casson fluid confined within a two-dimensional porous square cavity, highlighting the intricate coupling between fluid motion, temperature distribution, and species transport. The Darcy-Boussinesq framework is used to create the mathematical model, which includes an Arrhenius-type reaction mechanism in the concentration equation and temperature-dependent viscosity in the momentum transfer. A significant bidirectional connection between the temperature and concentration fields is established by the Soret and Dufour mechanisms. Such combined mechanisms significantly enrich the transport characteristics within the enclosure. The system is subjected to periodic thermal excitation imposed along the vertical boundaries, while the horizontal surfaces remain thermally insulated. The resulting dimensionless governing equations describing momentum, temperature, and concentration are solved numerically using a finite difference framework. To enhance computational stability and efficiency, an advanced solution strategy is employed by coupling the alternating direction implicit (ADI) scheme with Gauss-Jordan elimination. The findings show that while raising the heat-generation parameter increases the temperature level and changes the convection-cell structure. The flow resistance is significantly modified by the variable-viscosity parameter, which also causes the thermal field to be redistributed. The Dufour effect alters the thermal field through concentration-gradient-driven energy flux, whereas the Soret effect enhances species movement caused by temperature distribution. The higher chemical reaction results in more noticeable species decrease in the reactive region; an increase in activation energy slows the reaction rate and so modifies the concentration distribution.