Numerical investigation of transient free convective fluid over a porous media under external thermal influence

The flow analysis and energy transfer coupled with mass diffusion of a unsteady free convective fluid under external thermal influence are numerically investigated in this paper. The fluid's viscosity, incompressibility, along with specific mass diffusivity are its key properties. The coupled mathematical model is scrupulously handled by employing an unconditionally stable finite difference method (FDM) which is used for small and large deflections of the physical parameters, resulting in a noticeable fluid flow behaviour. The stability analysis is done by Von Neumann analysis. To elucidate the results, numerical setups that offer sharp graphical depictions enabling refined understanding of fluid behaviour are used. The Schmidt number, Prandtl number, External heat source parameter, Permeability parameter, Thermal Grashof number and Mass Grashof numbers are the salient parameters that are carefully examined in this work. A meticulous analysis of mass diffusion, momentum and energy is conducted. The research provides captivating aggregates notably emphasising that the addition of an external heat source not only increases fluid flow but also maintains an exceptionally consistent temperature distribution across the system. Furthermore, an in-depth examination of the Schmidt and Prandtl numbers demonstrates that increasing these parameters reduces fluid flow intensity while progressively slowing down the concentration and temperature distributions. Our simulations demonstrate that external heating boosts fluid flow without compromising temperature consistency, a key requirement for nuclear safety systems. Findings further demonstrate that greater mass diffusivity enhances contaminant removal in groundwater treatment, and that porous material characteristics significantly affect efficiency in thermal energy storage and petroleum extraction systems. These findings provide engineers with practical tools to optimise diverse applications including catalytic reactors for chemical processing, metal foam coolers for electronics and demonstrating how fundamental fluid dynamics research translates into solutions for energy, and healthcare challenges.