Mathematical Analysis of Casson Fluid Model for Blood Rheology in Stenosed Narrow Arteries

The flow of blood through a narrow artery with bell-shaped stenosis is investigated, treating blood as Casson fluid. Present results are compared with the results of the Herschel-Bulkley fluid model obtained by Misra and Shit (2006) for the same geometry. Resistance to flow and skin friction are normalized in two different ways such as (i) with respect to the same non-Newtonian fluid in a normal artery which gives the effect of a stenosis and (ii) with respect to the Newtonian fluid in the stenosed artery which spells out the non-Newtonian effects of the fluid. It is found that the resistance to flow and skin friction increase with the increase of maximum depth of the stenosis, but these flow quantities (when normalized with non-Newtonian fluid in normal artery) decrease with the increase of the yield stress, as obtained by Misra and Shit (2006). It is also noticed that the resistance to flow and skin friction increase (when normalized with Newtonian fluid in stenosed artery) with the increase of the yield stress.

[1]  Two-Fluid Nonlinear Mathematical Model for Pulsatile Blood Flow Through Stenosed Arteries , 2010 .

[2]  D. S. Sankar,et al.  Pulsatile flow of Herschel–Bulkley fluid through stenosed arteries—A mathematical model , 2006 .

[3]  D. S. Sankar.  Perturbation Analysis for Blood Flow in Stenosed Arteries under Body Acceleration , 2010 .

[4]  S. Cavalcanti,et al.  Hemodynamics of an artery with mild stenosis. , 1995, Journal of biomechanics.

[5]  D. Sankar,et al.  Two -fluid nonlinear mathematical model for pulsatile blood flow through catheterized arteries , 2009 .

[6]  M E Clark,et al.  Stenosis severity effects for unbalanced simple-pulsatile bifurcation flow. , 1983, Journal of biomechanics.

[7]  S. U. Siddiqui,et al.  A mathematical model for pulsatile flow of Herschel-Bulkley fluid through stenosed arteries , 2015 .

[8]  J F Gross,et al.  Pulsatile flow in small blood vessels. I. Casson theory. , 1972, Biorheology.

[9]  S. Charm,et al.  Viscometry of Human Blood for Shear Rates of 0-100,000 sec−1 , 1965, Nature.

[10]  P. Chaturani,et al.  A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases. , 1985, Biorheology.

[11]  Mario Ippolito,et al.  Rheology of Disperse Systems — Influence of NaCl on Viscous Properties of Aqueous Bentonite Suspensions , 1980 .

[12]  J. C. Misra,et al.  Blood flow through arteries in a pathological state: A theoretical study , 2006 .

[13]  M. Mathematical,et al.  Pulsatile Flow of Couple Stress Fluid Through a Porous Medium with Periodic Body Acceleration and Magnetic Field , 2009 .

[14]  P. Chaturani,et al.  Pulsatile flow of Casson's fluid through stenosed arteries with applications to blood flow. , 1986, Biorheology.

[15]  G. W. Blair,et al.  An Equation for the Flow of Blood, Plasma and Serum through Glass Capillaries , 1959, Nature.

[16]  Norbert Willenbacher,et al.  Rheology of Disperse Systems , 2013 .

[17]  Giles R Cokelet,et al.  The rheology of human blood , 1963 .

[18]  D Liepsch,et al.  Experimental analysis of the influence of stenotic geometry on steady flow. , 1992, Biorheology.

[19]  E W Salzman,et al.  Pressure-flow relations of human blood in hollow fibers at low flow rates. , 1965, Journal of applied physiology.