A non-Newtonian fluid flow model for blood flow through a catheterized artery—Steady flow

Sankar, D. S.; Hemalatha, K.

doi:10.1016/j.apm.2006.06.009

Cited by 104 publications

(54 citation statements)

References 20 publications

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“…Thus one can expect more detailed information about the blood flow characteristics. In contrast to the papers of Sankar and Hemalatha [18,22], in the present paper we consider the effect of the elasticity of the tube on the nonNewtonian Herschel-Bulkley fluid. Also, we bring out the salient features of these effects on the physiological organs.…”

Section: Introductionmentioning

confidence: 80%

“…The unsteady case of the harmonic flow simulation in two-dimensional elastic tubes was studied by Hoekstra et al [17]. The effect of catheterization on various physiologically important flow characteristics for blood flow was studied theoretically by Sankar and Hemalatha [18]. Recently, Vajravelu et al [19] studied the peristaltic pumping of a Herschel-Bulkley fluid in an inclined tube.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

et al. 2011

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Abstract:The constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index = 1 and the yield stress τ 0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters ( 1 and 2 ) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

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Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

et al. 2011

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“…At some finite stress which is usually small (of the order 0.05 dyne/sec 2 ), the aggregate is disrupted and blood begins to flow. If the shear rate again becomes zero, these aggregate structures reform very rapidly [8]. The effects of the finite yield stress is that the fluid exhibits solid-like behavior or plug flow in regions where the shear stress is less than the yield stress.…”

Section: Introductionmentioning

confidence: 99%

“…Casson fluid model and Herschel-Bulkley (H-B) fluid model are some of the non-Newtonian fluid models with finite yield stress which are widely used to model blood when it flows through narrow diameter arteries at low shear rates [6][7][8]. Dash et al [20] studied the flow of Casson fluid in a pipe filled with a homogenous porous medium using the Brinkman's model and mentioned that blood flow in arteries is one of the major application areas to their study.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Analysis of Blood Flow in Porous Tubes: A Comparative Study

Sankar

Nagar

2013

Advances in Mechanical Engineering

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The steady flow of Herschel-Bulkley and Casson fluids for blood flow in tubes filled with homogeneous porous medium with (i) constant and (ii) variable permeability is analyzed. The expression for the shear stress is obtained first by general iteration method and then using numerical integration; the solutions for velocity and flow rate are obtained. It is noticed that the shear stress and plug core radius are considerably higher in the case of variable permeability than those of the constant permeability case. The velocity and flow rate of both the fluids increase considerably with the increase in the permeability factor and they decrease with the increase in the yield stress of the fluids. The velocity and flow rate of Herschel-Bulkley fluid are considerably higher than those of Casson fluid. Aforesaid flow quantities are significantly higher for flow in tubes with variable permeability than for flow in tubes with constant permeability.

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“…14) In recent years, the literature has witnessed several publications demonstrating that the non-Newtonian behavior of the blood can dramatically affect its flow through local constrictions. [15][16][17][18][19][20] In the present study, we are going to study constriction flow of a purely-viscous non-Newtonian fluid having a sheardependent viscosity. An objective of the present study is to see how flow irregularities (i.e., separation) downstream of the constriction are affected when the degree of shear-thinning or shear-thickening behavior of the blood is manipulated either deliberately (say, through the use of appropriate injections into the blood) or inadvertently (say, by a typical disease).…”

Section: Introductionmentioning

confidence: 99%

MHD Flow of Power-Law Fluids in Locally-Constricted Channels

Esmaeili

Sadeghy

2009

J. Soc. Rheol., Jpn

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In the present study, the effect of a transverse magnetic field is investigated on the flow separation phenomenon at the lee of a single, two-dimensional symmetric constriction assuming that the fluid of interest is of the power-law type. For steady, two-dimensional, and incompressible flow, the equations of motion will be solved using the finite volume formulation based on a staggered grid. Numerical results obtained for the velocity and pressure fields suggest that flow separation occurring downstream the constriction can be controlled by manipulating the degree of the shear-thinning behavior of the fluid and/or by applying an external magnetic field. That is, the size of the separation bubble formed in flow through constrictions is predicted to decrease by an increase in the power-law exponent and/or the strength of the externally imposed magnetic field. The wall shear stress is also predicted to increase by an increase in the strength of the magnetic field.

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A non-Newtonian fluid flow model for blood flow through a catheterized artery—Steady flow

Cited by 104 publications

References 20 publications

Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

Mathematical Analysis of Blood Flow in Porous Tubes: A Comparative Study

MHD Flow of Power-Law Fluids in Locally-Constricted Channels

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