Numerical Analysis of Radiative Magnetoviscoelastic Micropolar Flow External to a Sphere With a Convective Boundary Surface Condition

Abstract

Increasing attention is being paid to the study of the heat transfer properties of non-Newtonian fluids as a result of their growing use in many industrial and manufacturing processes. Micropolar fluids have garnered a lot of interest for potential industrial uses because of their distinctive microstructures. Both viscoelastic and microstructural characteristics of the non-Newtonian fluid make it mimic several polymers. Motivated by magnetic polymer coating dynamics operations, in this article, thermoconvective nonlinear, steady-state boundary layer flow of an incompressible third-grade viscoelastic micropolar fluid from an isothermal sphere with magnetic field and thermal radiation is investigated theoretically and numerically. The micropolar model incorporates microelement gyratory (rotating) motions and accurately simulates complex polymeric suspensions. An accurate implicit finite-difference Keller-Box method of second order is used to solve numerically the modified nondimensional conservation equations under physically suitable boundary conditions. Verification of the code is conducted using previous special cases of the model from the literature. The impacts of several nondimensional parameters, that is, third-grade viscoelastic parameter (ϕ), third-grade material fluid parameters (ε₁, ε₂), Biot number (γ), thermal radiation parameter (R), Prandtl number (Pr), magnetic parameter (M), micropolar material parameter (V), Eringen vortex viscosity parameter (K), and dimensionless tangential coordinate (ξ) on linear (translational) velocity, angular velocity, and temperature distributions are computed and depicted graphically. Additionally, the impacts of selected parameters on skin friction, wall couple stress (wall angular velocity gradient), and Nusselt number (wall heat transfer rate) are also examined. As the third-grade parameter (ϕ) increases, velocity accelerates farther away from the sphere surface while decelerating close to it. The oscillatory response of microrotation (angular) velocity indicates a reverse spin of the microelements. Increasing the Eringen micropolar coupling parameter K (i.e., the ratio of Newtonian dynamic viscosity to Eringen vortex viscosity) causes the flow to accelerate farther away from the wall while decreasing velocity closer to it. Skin friction and wall couple stress are both increased, while the local Nusselt number is depleted with higher values of the Eringen micropolar coupling parameter. With an elevation in thermal Biot number ($\gamma$), there is a marked increase in Nusselt number and skin friction, whereas the wall couple stress (sphere surface microrotation gradient) is depleted. There is a significant depletion in heat transfer rate (Nusselt number) with increasing first viscoelastic material parameter (ε₁), whereas skin friction and wall couple stress exhibit a considerable elevation. With increasing second viscoelastic material fluid parameter (ε₂), skin friction and heat transfer rate (Nusselt number) are both increased, whereas wall couple stress is reduced. With an elevation in the magnetic interaction parameter, M, linear velocity is significantly damped, whereas angular velocity is enhanced (further from the sphere surface) and temperature is also elevated substantially, as is thermal boundary layer thickness in the magnetic polymer. The current simulations are relevant to the high-temperature coating processing of electromagnetic polymers on curved bodies.