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 Dtα 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 ur,t and heat profile Tr,t. The results obtained for ur,t and Tr,t were plotted against different physical parameters, such as Prandtl number Pr, the square of Hartmann number Ha, thermal Grashof number Gr, thermal radiation parameter Nr, and heat source/sink parameter Q0. 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 Tr,t and decreasing ur,t. It was found that increasing Gr and Pr increased the velocity and temperature profiles. Addition of Cu nanoparticles to a base fluid of H2O 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).