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

Abstract

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.

Numerical Investigation of Pulsatile Blood Flow in Stenosed Artery

“…The time variant parameter a 1 (t) is given by a 1 (t) = 1 + k r cos(ωt − φ) [13,25], where k r represents the amplitude parameter and φ the phase angle.…”

“…The dimensionless pressure gradient [4,13,25]. Where A 0 is the constant amplitude of the pressure gradient, A 1 is the amplitude of the pulsatile component giving rise to the systolic and diastolic pressures, ω = 2π f p , f p is the pulse frequency.…”

“…Several theories have been expressed about the existence of stenosis and the occurrence of cardiovascular disease at vascular stenosis, but the exact theory about the initiation of this phenomenon is not clearly known [16,29]. Many researchers emphasized that the initiation and development of atherosclerosis, is strongly related to the blood flow characteristics [5,10,25,28]. So, this matter shows the importance of the study of blood flow characteristics in stenosed regions.…”

“…Erythrocytes in terms of the number in ratio of other blood suspended cells are in the majority, and their properties are predominant for other cells [22]. In most literatures, blood flow has been considered as single layered Newtonian [4,6,15] or non-Newtonian fluid [14,16,25,29,30]. Chakravarty and Mandal presented a mathematical model of non-linear two-dimensional blood flow in tapered arteries in the presence of the stenosis.…”

“…Blood behaves like a Newtonian fluid when it flows through larger arteries at high shear rates, whereas, it exhibits a non-linear shear stress vs shear rate characteristics when it flows through narrow arteries at low shear rates [14,16,19,25,32]. Also in some diseased conditions, blood exhibits remarkable non-Newtonian characteristics [11,13] and many researchers pointed out that for the blood flow through narrow arteries existence of a peripheral layer of plasma and a core region of suspension of all the erythrocytes was observed.…”