Numerical Computations of Biomagnetic Fluid Flow in a Lid Driven Cavity

Abstract

The study on the effects of biological fluids in the presence of magnetic field is known as biomagnetic fluid dynamics (BFD) and the most common biological fluid that exhibit such magnetic properties is blood. An extensive research work has been done in this area due to its applications in medical and bioengineering. Basically, it is essential for a study to be justified according to certain benchmark before progressing. Hence, biomagnetic fluid flow in a lid driven cavity is numerically investigated by utilizing two numerical schemes: finite difference and finite element methods. The formulation adopted is consistent with the principles of ferrohydrodynamics. The mathematical model describes Newtonian blood flow under the influence of a spatially varying magnetic field. The model considers the biofluid as non-conducting. The flow is assumed to be two-dimensional, steady, laminar and isothermal. The implementation of finite element method shows stability issue due to extremely steep magnetic field gradient while finite difference method shows no issue. Due to this, a solution is proposed to alleviate the problem and the result for various magnetic field intensity presented.

A Stabilized Finite Element Formulation of Non-Newtonian Fluid Model of Blood Flow in A Bifurcated Channel with Overlapping Stenosis

“…Heinrich et al, [4] reviewed the penalty finite element method which is applied to Stokes and Navier-Stokes equations that can deal with incompressibility constraint and reducing number of the degrees of freedom by implicitly eliminating pressure as an unknown. Abdullah et al, [6] with the helps of stabilization parameter which is added to the magnetic source term of the momentum equations are able to solve the numerical instability which arised in their solutions in a form of chaotic velocity vector. On the other hand, Skála et al, [7], Machado et al, [5] and Zinani et al, [8], all employed Galerkin least-squares approach that was good deals with two major sources of problems in classical Galerkin formulation.…”

Finite Element Analysis of Biomagnetic Fluid Flow in a Channel with an Overlapping Stenosis

“…The model is validate using previous literature from [24] and the results shows a good agreement for both the numerical method used. Figure 3 shows the streamline pattern of lid driven cavity for ferrohydrodynamics case as compared between finite difference method by Tzirtzilakis and Xenos [24] and Galerkin finite element method from the current study, Abdullah et al [25].…”