Mathematical modeling of unsteady flow and heat transfer in a porous square cavity along with thermal radiation and temperature dependent viscosity

This study examines the two-dimensional natural convection flow and variable viscosity of viscous fluid within a porous square cavity, focusing on the effects of thermal radiation and chemical reactions. The features of the square cavity include the vertical walls moving sinusoidally while the upper and lower walls are assumed adiabatic, creating a dynamic environment for heat and mass transfer. The fluid flow is modeled using the Darcy model and analyzed under the Boussinesq approximation, capturing buoyancy-driven convection. Variable viscosity introduces significant nonlinearity, influencing velocity and temperature distributions, while radiation enhances thermal gradients, altering convection patterns. Chemical reactions further complicate the system by affecting species concentration and interacting with thermal and flow fields. A hybrid numerical approach, combining the Gauss-Jordan elimination method and the Peaceman-Rachford alternating direction implicit technique, is employed to solve the governing equations with high accuracy and computational efficiency. The results demonstrate that parameters like viscosity variations and radiation intensity critically impact flow behavior and heat transfer efficiency. Higher radiation increases thermal transport, while magnifying the viscosity variations creates localized resistance and flow stratification. This study provides valuable insights into optimizing processes in porous media, with applications in energy systems, chemical reactors, and environmental engineering.