A finite difference explicit-implicit scheme for fractal heat and mass transportation of Williamson nanofluid flow in quantum calculus

Abstract

This study introduces a novel and versatile fractal finite difference scheme designed to address unsteady flow challenges in quantum calculus over flat and oscillatory sheets. Motivated by the need to advance our understanding of nanofluid dynamics, particularly in heat and mass transportation, this research aims to bridge existing gaps and contribute to improving computational methodologies. Our approach involves a two-stage scheme incorporating explicit and implicit methods, focusing on q-derivatives for spatial terms within the mathematical model. The system encompasses the Navier-Stokes equation, energy equation, and concentration equation, offering a comprehensive framework for analyzing mixed convective Williamson nanofluid flow under the influence of chemical reactions. The convergence condition for the time-dependent partial differential equations system, particularly the scalar convection-diffusion equation, is presented. Stability requirements for our proposed fractal scheme are also delineated. Notably, our study explores the implications of the Weisenberg parameter on the velocity profile, revealing a decline that underscores its influence on nanofluid behavior. Our fractal finite difference scheme demonstrates a substantially faster convergence rate than the fractal Crank-Nicolson scheme. This outcome emphasizes the computational efficiency and efficacy of our proposed technique. In a broader context, our work contributes to the field by leveraging fractal geometry and quantum calculus to enhance our understanding of nanofluid dynamics. These tools present exciting opportunities for groundbreaking applications and technological advancements across various industries. As we delve into these research areas, our work sets the stage for exploration, providing a framework with great potential for transformative progress in nanofluid dynamics.