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 D-t(alpha) 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 u (r ,t) and heat profile T(r ,t) . The results obtained for u (r ,t) and T (r ,t) were plotted against different physical parameters, such as Prandtl number Pr , the square of Hartmann number H-a , thermal Grashof number Gr , thermal radiation parameter N-r , and heat source/sink parameter Q(0) . 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 T(r ,t) and decreasing u(r ,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).