Mathematical modelling of unsteady biomagnetic fluid flow and heat transfer with gravitational acceleration

Abstract

Numerical computation and simulation have been carried out on the two-dimensional Navier Stokes equations with a coupling of biomagnetic fluid dynamics and heat transfer. Biomagnetic fluid refers to a fluid that exists in living creature with its flow influenced by the presence of magnetic field. Studies have shown that the flow of biomagnetic fluid under spatially varying magnetic field could be adequately modelled based on the principle of ferrohydrodynamics. The main objective of this research is to employ the model of biomagnetic fluid using the principle of ferrohydrodynamics to investigate the effect of gravitational acceleration on unsteady fluid flow. This study is important because most existing studies on two-dimensional biomagnetic fluids only analyze flows in the steady state conditions and the effect of gravitational acceleration have not been addressed. The governing equations consist of a set of nonlinear partial differential equations which are first non-dimensionalized and then discretized using a finite difference technique on a staggered grid system. The discretized equations are solved using the pressure correction method based on the Semi-Implicit Method for Pressure Linked Equations ( SIMPLE) algorithm. The numerical results show that the gravitational acceleration has a profound effect on both velocity and temperature profiles. The streamlines plotted show that vortices appear near the lower plate where the magnetic source is located and the distraction becomes greater with the increase of magnetic field strength.