Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference Approach

Abstract

Fractional-order mathematical modelling of physical phenomena is a hot topic among various researchers due to its many advantages over positive integer mathematical modelling. In this context, the appropriate solutions of such fractional-order physical modelling become a challenging task among scientists. This paper presents a study of unsteady free convection fluid flow and heat transfer of Maxwell fluids with the presence of Clay nanoparticle modelling using fractional calculus. The obtained model was transformed into a set of linear nondimensional, partial differential equations (PDEs). The finite difference scheme is proposed to discretize the obtained set of nondimensional PDEs. The Maple code was developed and executed against the physical parameters and fractional-order parameter to explain the behavior of the velocity and temperature profiles. Some limiting solutions were obtained and compared with the latest existing ones in literature. The comparative study witnesses that the proposed scheme is a very efficient tool to handle such a physical model and can be extended to other diversified problems of a complex nature.

Space-fractional heat transfer analysis of hybrid nanofluid along a permeable plate considering inclined magnetic field

“…The most widely used fractional derivatives are the Caputo 27 – 29 and Riemann–Liouville (R–L) 30 derivatives. Recently, Asjad et al used time-fractional derivatives for convection flow of nanofluid between parallel plate 31 and heat transfer of maxwell fluid over a vertical surface 32 – 34 . Since the terms of space derivatives are nonlinear in the transport equations, such as momentum and energy, the boundary conditions dominate the results more than the initial conditions.…”