Magnetic effect on the creeping flow around a slightly deformed semipermeable sphere

This paper presents steady axisymmetric creeping motion of a conducting, incompressible viscous fluid past a weakly permeable slightly deformed sphere in the presence of transverse magnetic field. The Stokes approximation of momentum equation and Darcy's law together with Lorentz force are used for the flow outside and within the semi-permeable particle. The governing equations are changed into dimensionless form, and resulting equations are solved using separation of variables method. We have determined the resistance force exerted on the oblate spheroid in the presence of magnetic field as a particular case of an approximate sphere. The impact of Hartmann numbers, permeability and deformation parameter on the coefficient of drag and the streamline pattern is exhibited graphically. Some special cases are deduced from the current study and compared with some previous results. The outcome clarifies that the Hartmann numbers enhance the drag on the oblate spheroid in comparison with prolate spheroid.

Automated summary

This paper investigates the steady axisymmetric creeping motion of a conducting, incompressible viscous fluid past a weakly permeable slightly deformed sphere in the presence of a transverse magnetic field. The governing equations are transformed into dimensionless form and solved using the separation of variables method. The study shows the impact of Hartmann numbers, permeability, and deformation parameter on the coefficient of drag and the streamline pattern, indicating an enhancement of drag on the oblate spheroid compared to the prolate spheroid.