Particle Swarm Optimization for exploring Darcy-Forchheimer flow of Casson fluid between co-axial rotating disks with the Cattaneo-Christov model.

In this paper, we carried out a numerical analysis of the fluid dynamics and heat transfer occurring between two parallel disks. The study accounts for the impact of temperature-dependent fluid viscosity and thermal conductivity. We systematically investigated various parameters, including viscosity, thermal conductivity, rotational behavior (rotation or counter-rotation), and the presence of stretching, aiming to comprehend their effects on fluid velocity, temperature profiles, and pressure distributions. Our research constructs a mathematical model that intricately couples fluid heat transfer and pressure distribution within the rotating system. To solve this model, we employed the 'Particle Swarm Optimization' method in tandem with the finite difference approach. The results are presented through visual representations of fluid flow profiles, temperature, and pressure distributions along the rotational axis. The findings revealed that the change in Casson factor from 2.5 to 1.5 resulted in a reduction of skin friction by up to 65%, while the change in local Nusselt number was minimal. Furthermore, both the viscosity variation parameter and thermal conductivity parameters were found to play significant roles in regulating both skin friction and local Nusselt number. These findings will have practical relevance to scientists and engineers working in fields related to heat management, such as those involved in rotating gas turbines, computer storage devices, medical equipment, space vehicles, and various other applications.