FDM analysis for MHD flow of a non-Newtonian fluid for blood flow in stenosed arteries

• Published in: Journal of mechanical science and technology Vol. 25; no. 10; pp. 2573 - 2581
• Main Authors: Sankar, D. S., Lee, Usik
• Format: Journal Article
• Language: English
• Published: Heidelberg Korean Society of Mechanical Engineers 01.10.2011; Springer Nature B.V; 대한기계학회
• Subjects: Amplitudes; Arteries; Biological and medical sciences; Blood vessels and receptors; Control; Dynamical Systems; Engineering; Exact sciences and technology; Flow rate; Fluid dynamics; Fundamental and applied biological sciences. Psychology; Fundamental areas of phenomenology (including applications); Hemodynamics. Rheology; Impedance; Industrial and Production Engineering; Inelasticity (thermoplasticity, viscoplasticity...); Magnetic fields; Magnetohydrodynamics and electrohydrodynamics; Mathematical analysis; Mathematical models; Mechanical Engineering; Physics; Skin friction; Solid mechanics; Structural and continuum mechanics; Vertebrates: cardiovascular system; Vibration; 기계공학; Pulsatile blood flow; Casson fluid model; Stenosed artery; Magnetic field; Finite difference method; Magnetohydrodynamics; Difference scheme; Associated plasticity; Stenosis; Cardiovascular disease; Arteries; Pressure gradients; MHD flow; Height; Modelling; Stress analysis; Skin friction; Magnetic field effects; Non-Newtonian fluids; Skin effect; Blood flow; Blood circulation; Pulsatile flow; Circulatory system; Man; Non linear effect; Shear layer
• ISSN: 1738-494X; 1976-3824
• DOI: 10.1007/s12206-011-0728-x

A computational model is developed to analyze the effects of magnetic field in a pulsatile flow of blood through narrow arteries with mild stenosis, treating blood as Casson fluid model. Finite difference method is employed to solve the simplified nonlinear partial differential equation and an explicit finite difference scheme is obtained for velocity and subsequently the finite difference formula for the flow rate, skin friction and longitudinal impedance are also derived. The effects of various parameters associated with this flow problem such as stenosis height, yield stress, magnetic field and amplitude of the pressure gradient on the physiologically important flow quantities namely velocity distribution, flow rate, skin friction and longitudinal impedance to flow are analyzed by plotting the graphs for the variation of these flow quantities for different values of the aforesaid parameters. It is found that the velocity and flow rate decrease with the increase of the Hartmann number and the reverse behavior is noticed for the wall shear stress and longitudinal impedance of the flow. It is noted that flow rate increases and skin friction decreases with the increase of the pressure gradient. It is also observed that the skin friction and longitudinal impedance increase with the increase of the amplitude parameter of the artery radius. It is also found that the skin friction and longitudinal impedance increases with the increase of the stenosis depth. It is recorded that the estimates of the increase in the skin friction and longitudinal impedance to flow increase considerably with the increase of the Hartmann number.