Fractional nanofluid flow dynamics of thermal transport and entropy generation in a wavy porous enclosure containing a hot circular cylinder

A numerical study focuses on the temporal evolution of fractional-order convective nanofluid flow along with entropy generation characteristics within a wavy square porous enclosure containing a circular cylinder. The application of fractional derivatives facilitates a more accurate representation of fluid flow dynamics, thermal transport, and entropy production. The governing equations are formulated as fractional partial differential equations, with momentum transport modeled using the Darcy–Brinkman–Forchheimer approach. The complete mathematical framework is solved using a robust numerical technique that integrates the implicit finite difference scheme (L1-scheme) for temporal discretization and the penalty finite element method for spatial discretization. The numerical investigation is carried out for various emerging parameters, including fractional-order parameters (α), Rayleigh number (Ra), Darcy number (Da), and porosity (ε). The results are displayed through contour plots of streamlines, isotherms, and local entropy generation, along with graphical plots of the mean Nusselt number, Bejan number, and total entropy generation. These findings offer valuable insights into the interplay between fractional-order parameter and flow parameters in influencing flow dynamics, thermal transport, and entropy generation. The study reveals that the fractional-order parameter (α) plays a pivotal role in governing the system's temporal evolution, with higher values of α significantly accelerating the rate of evolution.