Numerical simulation of fractional order double diffusive convective nanofluid flow in a wavy porous enclosure

Abstract

Fractional order models are becoming a promising tool for modeling complex physical phenomena due to their non-local and memory-dependent properties. In this study, a novel fractional order double-diffusion model is proposed to analyze the transient nature of fluid flow, convective heat, and the solute transfer phenomena within a wavy porous cavity. The fractional time derivative is defined in the Caputo sense for an order of $0<\alpha <1$ and is incorporated into the governing equations formulated using the Darcy-Brinkman-Forchheimer model, along with energy and mass transfer equations. The resulting coupled nonlinear fractional partial differential equations (FPDEs) are subjected to numerical simulation using a fully discrete scheme comprising an L1 finite difference scheme for temporal discretization and a penalty finite element scheme for spatial discretization. The double-diffusion process undergoes varying evolution phases for each $\alpha \in (0,1)$. It is observed that a higher value of the fractional order parameter $\left(\alpha \right)$ accelerates the evolution rate, leading to faster convergence towards steady-state conditions. Additionally, this study also explores the impacts of various parameters such as the Rayleigh number, buoyancy ratio, Darcy number, porosity, and Lewis number on thermal and solute transport processes.