SPECTRAL NUMERICAL SIMULATION OF MAGNETO-PHYSIOLOGICAL LAMINAR DEAN FLOW

• Published in: Journal of mechanics in medicine and biology Vol. 14; no. 4; pp. 1450047 - 1-1450047-18
• Main Authors: BEG, O. ANWAR, HOQUE, MD. MAINUL, WAHIDUZZAMAN, M., ALAM, MD. MAHMUD, FERDOWS, M.
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 01.08.2014; World Scientific Publishing Co. Pte., Ltd
• Subjects: Axial flow; Blood flow; Blood vessels; Boundary conditions; Boundary value problems; Computational fluid dynamics; Computer simulation; Conservation equations; Coordinates; Curvature; Electrical resistivity; Flow characteristics; Flow control; Fluid flow; Laminar; Laminar flow; Magnetic properties; Magnetohydrodynamics; Mathematical analysis; Mathematical models; Navier-Stokes equations; Parameters; Rheological properties; Secondary flow; Spectra; Stream functions (fluids); Viscous flow; Vorticity; pressure gradient; Bio-magnetohydrodynamics; spectral numerics; vortex flow; Dean number; Newtonian viscous flow; Navier–Stokes model; curved vessel; toroidal coordinates; Fourier series; blood flow; Chebyshev polynomials
• ISSN: 0219-5194; 1793-6810
• DOI: 10.1142/S021951941450047X

A computational simulation of magnetohydrodynamic laminar blood flow under pressure gradient through a curved bio-vessel, with circular cross-section is presented. Electrical conductivity and other properties of the biofluid (blood) are assumed to be invariant. A Newtonian viscous flow (Navier–Stokes magnetohydrodynamic) model is employed which is appropriate for large diameter blood vessels, as confirmed in a number of experimental studies. Rheological effects are therefore neglected as these are generally only significant in smaller diameter vessels. Employing a toroidal coordinate system, the steady-state, three-dimensional mass and momentum conservation equations are developed. With appropriate transformations, the transport model is non-dimensionalized and further simplified to a pair of axial and secondary flow momenta equations with the aid of a stream function. The resulting non-linear boundary value problem is solved with an efficient, spectral collocation algorithm, subject to physically appropriate boundary conditions. The influence of magnetic body force parameter, Dean number and vessel curvature on the flow characteristics is examined in detail. For high magnetic parameter and Dean number and low curvature, the axial flow is observed to be displaced toward the center of the vessel with corresponding low fluid particle vorticity strengths. Visualization is achieved with the MAPLE software. The simulations are relevant to cardiovascular biomagnetic flow control.