Numerical investigation of fractional Maxwell nano-fluids between two coaxial cylinders via the finite difference approach - Asjad, Muhammad Imran; Usman, Muhammad; Assiri, Taghreed A.; Ali, Arfan; Tag-ElDin, ElSayed M. (Frontiers in Materials, 2023)
This study deals with numerical solution of momentum and heat transfer of fractional ordered Maxwell fluids within a coaxial cylinder. It is well known fact that fractional approach can well encounter the complex dynamics of flow regime. In this paper, a fractional differentiation operator D_t^α of Caputo is applied for fractional modeling of magneto-hydro-dynamic (MHD) fluid. A set of appropriate transformations is applied to make the governing equations dimensionless. The finite differences are calculated by the discretization of momentum profile u(r,t) and heat profile T(r,t). The obtained results for u(r,t) and T(r,t) are plotted against different physical parameters such as Prandtl number Pr, the square of Hartmann number H_a, thermal Grashof number Gr, thermal radiation parameter Nr and heat source/sink parameter Q_0. The validation of results are verified by comparing with MAPLE built-in command results. Subjecting the system to strong magnetic field leads to increasing T(r,t) and decreasing u(r,t). It is found that increasing Gr and Pr increases the velocity and temperature profile. Addition of nanoparticle Cu to base fluid H_2 O enhances its heat capability. Also increasing the angular frequency of inner cylinder velocity, the velocity profile of fractional Maxell nano-fluids becomes high within a coaxial region (Cylinder).