Computational analysis for the modeling of fractional time-dependent Maxwell fluid

Abstract

Through the use of some extended fractional operators, this study models and analyzes time-dependent fractional Maxwell's fluid. The effect of buoyancy is taken into account in the presence of a magnetic field, to make the model as realistic as possible. The nanofluid model is based on the uniform dispersing of nano-size solid particles of silver in an engine taken as base fluid. Atangana Baleanu Caputo (ABC), Caputo Fabrizio (CF), and Caputo (C) fractional derivatives are used in the model formulation (FD). To find the behavior of the modeled problem, a finite difference scheme is suggested. To determine whether the fractional derivative operator was more accurate than the others, a simulation was run. Additionally, graphs are drawn to display the distribution of velocity and temperature as they change the physical parameters. A comparative analysis is also provided to demonstrate that the devised scheme is an effective tool for the topic under consideration and that it may be expanded to address a variety of physical challenges. Qualitative behavior was observed to be almost similar for C, CF and ABC fractional derivatives; however, ABC fractional derivative gives more appropriate and significant results quantitively.