Fractional derivative modeling of heat transfer and fluid flow around a contracting permeable infinite cylinder: Computational study

Understanding the complex interplay between the contracting behavior of the cylinder and the fluid flow dynamics has implications for the design of porous structures for heat exchange and filtration systems. In this study, we investigate the dynamics and thermal behavior of fluid flow past a contracting permeable infinite cylinder. First, we developed a mathematical model based on the Navier–Stokes equations to describe the fluid dynamics around the contracting permeable infinite cylinder. A new simple well-behaved definition of fractional derivative called conformal fractional derivative introduced by authors Khalil et al., (2014) is employed to generalize the PDE's of momentum and energy. The similarity transformation technique is utilized to transform the proposed mathematical problem into a non-linear ODE's. Then, we utilized IPS technique to numerically solve the governing equations and obtain detailed insights into the flow patterns and thermal characteristics. We observed significant changes in the flow velocity and temperature distribution as the cylinder contracted, highlighting the intricate thermal behavior of the system. Additionally, the changes in the fraction order was found to have a notable impact on the overall flow patterns and heat transfer processes.