Numerical simulations of heat and mass transfer in Sutterby fluid within porous media using Caputo fractional derivative

Abstract

This study enhances fluid modeling by integrating Caputo’s fractional derivative to improve accuracy in representing integer and non-integer order dynamics. Addressing the complexities of viscoelastic fluid behavior, it extends our understanding of fluid dynamics across diverse applications. A two-dimensional fractional Sutterby fluid model is analyzed under time-dependent conditions, incorporating convection, porous media, diffusion, thermal radiation, and chemical reaction. The model highlights the memory and inheritance effects of viscoelastic fluids. The governing equations are transformed using non-dimensional parameters and discretized via the explicit finite difference method. Quantities of physical interest, including the skin friction coefficient, Nusselt number, and Sherwood number, are computed to ensure model reliability, with stability analysis confirming convergence. A MATLAB algorithm is developed to visualize fractional and dimensionless parameter effects, with graphical results demonstrating model robustness. This study uniquely integrates fractional derivatives with porous media analysis in viscoelastic fluid contexts. The findings have implications for catalytic converters, gas turbines, and condensers, showing the potential of fractional derivatives to improve efficiency and reduce energy consumption.