Numerical investigation of fractional Maxwell nano-fluids between two coaxial cylinders via the finite difference approach

Abstract

This study deals with numerical solution of momentum and heat transfer of fractional ordered Maxwell fluids within a coaxial cylinder. It is well known that the complex dynamics of flow regime can be well-described by the fractional approach. In this paper, a fractional differentiation operator (Formula presented.) of Caputo was applied for fractional modeling of magneto-hydro-dynamic (MHD) fluid. A set of appropriate transformations was applied to make the governing equations dimensionless. The finite differences were calculated by the discretization of momentum profile (Formula presented.) and heat profile (Formula presented.). The results obtained for (Formula presented.) and (Formula presented.) were plotted against different physical parameters, such as Prandtl number (Formula presented.), the square of Hartmann number (Formula presented.), thermal Grashof number (Formula presented.) thermal radiation parameter (Formula presented.), and heat source/sink parameter (Formula presented.). The results were verified by comparing data from the proposed method with MAPLE built-in command results. Subjecting the system to a strong magnetic field led to increasing (Formula presented.) and decreasing (Formula presented.). It was found that increasing (Formula presented.) increased the velocity and temperature profiles. Addition of (Formula presented.) nanoparticles to a base fluid of (Formula presented.) enhanced its heat transfer capability. Also, increasing the angular frequency of inner cylinder velocity resulted in a high velocity profile of fractional Maxell nano-fluids within a coaxial region (cylinder).