A study of fractional Oldroyd-B fluid between two coaxial cylinders containing gold nanoparticles

Abstract

In this study, momentum and heat transport of fractionally ordered Oldroyd-B bio nanofluid within a coaxial cylinder are solved numerically. It is common knowledge that fractional approaches can successfully deal with the intricate dynamics of flow regimes. Modern basic science sectors like medicine, the use of fluid in brake systems, cooling system in the industry, lowering pollutants and food industry, etc., all have a wide range of applications for the study. In this study, the magneto-hydrodynamic (MHD) Oldroyd-B bio nanofluid is fractionally modeled using the Caputo fractional differentiation operator Dtα. To make the governing equations dimensionless, a set of suitable transformations is used. The finite differences are used to discretize the momentum u(r,t) profile and heat T(r,t) profile. The obtained results are plotted graphically against different physical parameters such as Hartmann number Ha, thermal Grashof number Gr, thermal radiation parameter Nr, volume fraction parameter of nanoparticles φ, fractional parameter α, angular velocity ωr, time retardation parameter λr, and heat source-sink parameter Q0. By contrasting the findings with those from built-in MAPLE commands, the validation of the results is confirmed. When the system is exposed to a strong magnetic field, temperature profile T(r,t) increases and velocity profile u(r,t) decreases. It is discovered that raising Gr and Nr raises the temperature and velocity profile. The heat capacity of the base fluid (blood) is improved by the addition of nanoparticles (Gold). The velocity profile of fractional Oldroyd-B nano-fluid increases with the angular frequency of inner cylinder velocity and becomes high in a coaxial region (Cylinder).