A mathematical analysis of micropolar thermal convection of Casson fluid from a swirling cone with Hall current and Ohmic heating effects

Abstract An investigation is conducted theoretically on steady‐state, nonlinear thermal convection flows of an incompressible Casson non‐Newtonian micropolar fluid past a spinning cone. The fluid exhibits a magnetic field, power‐law temperature variation, viscous dissipation, Hall current, and Ohmic (Joule) heating to mimic the flow of electromagnetic rheological spin coating. Eringen's micropolar and Casson rheological models are integrated to represent the microstructural and shearing characteristics of polymers. The micropolar model incorporates micro‐element gyratory rotating motions and accurately models various polymeric fluids. A second‐order efficient implicit finite difference scheme “Keller Box technique” is employed for numerically solving the altered conservation equations, subject to physically appropriate boundary constraints. The present code is validated using earlier studies from the literature. An in‐depth analysis is presented on the impacts of several emerging nondimensional parameters on axial, tangential and angular velocities, and temperature within the boundary layer domain. These include Casson rheological fluid parameters ( β ), surface temperature exponent ( m ), Prandtl number ( Pr ), magnetic interaction parameter ( M ), Hall current parameter ( β e ), Eckert number ( Ec ), micropolar fluid material parameters ( V 1 ), Eringen vortex viscosity parameter ( K ) and dimensionless tangential coordinate ( ξ ). Additionally, these factors’ impacts on wall couple stress, axial and tangential skin friction and wall heat transfer rate are also examined. As β increases, axial velocity accelerates close to the cone surface but decelerates farther away, while tangential velocity steadily decreases. When β increases, angular velocity responds oscillatory, increasing close to the cone surface and reversing farther away. As β increases, the temperature is uniformly damped over the boundary layer transverse to the cone surface. An increase in β reduces the axial skin friction and wall couple stress whereas an increase in β enhances the tangential skin friction and Nusselt number. The axial flow is accelerated farther away while the axial velocity is weakly decreased close to the wall when the Eringen micropolar coupling value K is increased. Higher Eringen micropolar coupling parameters cause a strong acceleration of temperature and tangential flow throughout the boundary layer regime, while higher Eringen micropolar coupling parameters suppress reversal of micro‐element spin (angular velocity) near the cone surface, despite a strong deceleration of micro‐rotation further towards the free stream. An increase in K decelerates the axial skin friction, tangential skin friction, wall couple stress, and Nusselt number. While increasing the Hall parameter ( β e ) results in a notable increase in axial velocity and cross flow, it also reduces tangential flow, temperature, and the thickness of the thermal boundary layer. Additionally, it causes a noticeable acceleration in angular velocity away from the cone surface. In addition to significantly raising temperatures, increasing the magnetic interaction parameter ( M ) slows down axial velocity, tangential velocity, and micro‐rotation (close to the wall). A higher Eckert number ( Ec ) raises the temperature, speeds up the axial flow, and reduces the tangential flow and angular velocity (micro‐rotation) close to the wall, but it produces a significant angular acceleration farther beyond the boundary line. The results of this study are highly applicable in the modeling of heat transfer in both engineering processes along with real world engineering cooling applications.