Two-fluid Casson model for pulsatile blood flow through stenosed arteries: A theoretical model

Sankar, D. S.; Lee, Usik

doi:10.1016/j.cnsns.2009.08.021

Cited by 52 publications

(21 citation statements)

References 29 publications

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“…Keeping this view in mind many successful studies have been carried out by treating blood as a non-Newtonian fluid (cf. Mann and Tarbell, 1990;Usha and Prema, 1999;Pontrelli, 2001;Khanafer et al, 2006;Mandal et al, 2007;Lukacova-Medvidova and Zauskova, 2008;Sarifuddin et al, 2008Sarifuddin et al, , 2009Ikbal et al, 2010;Sankar and Lee, 2010). Thurston (1972) was among the earliest to recognise the viscoelastic nature of blood which is less prominent with increasing shear rate.…”

Section: Introductionmentioning

confidence: 95%

Physiological flow of shear-thinning viscoelastic fluid past an irregular arterial constriction

Sarifuddin

Chakravarty

Mandal

2013

Korea-Aust. Rheol. J.

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The present investigation deals with the effect of the shape of a stenosis on the flow characteristics of blood, having shear-thinning viscoelastic rheological properties by using a suitable mathematical model. Keeping the relevance of the physiological situation, the mathematical model is developed by treating blood as a non-Newtonian shear-thinning viscoelastic fluid characterised by unsteady Oldroyd-3-constant model through an axisymmetric irregular arterial stenosis obtained from casting of a mildly stenosed artery (cf. Back et al., 1984). Comparison with the well-known cosine-shaped stenosis, in order to estimate the effect of surface roughness on the flow characteristics of blood, has however not been ruled out from the present study. Numerical illustrations are presented for a physiological flow, as well as for an equivalent simple pulsatile flow with equal stroke volume to that of the physiological flow, and the differences in their flow behaviour are recorded and discussed. The Marker and Cell method is developed in cylindrical co-ordinate system in order to tackle the highly nonlinear governing equations of motion. The effects of the quantities of significance such as Reynolds number, Deborah number, blood viscoelasticity and flow pulsatility, as well on the velocity components, pressure drop, wall shear stress and patterns of streamlines are quantitatively investigated graphically. Comparison of the results reveals that although the behaviour of two different pulses are similar at the same instant of time, there exist some important deviations in the flow pattern, pressure drop and wall shear stress as well. The present results also predict that the excess pressure drop across the cosine stenosis compared with the irregular one is consistent with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration.

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Section: Introductionmentioning

confidence: 95%

Physiological flow of shear-thinning viscoelastic fluid past an irregular arterial constriction

Sarifuddin

Chakravarty

Mandal

2013

Korea-Aust. Rheol. J.

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“…Keeping this view in mind many successful studies have been carried out by treating blood as a non-Newtonian fluid (cf. [5][6][7][8][9][10][11][12][13][14][15]). …”

Section: Introductionmentioning

confidence: 99%

Heat transfer to micropolar fluid flowing through an irregular arterial constriction

Sarifuddin

Chakravarty

Mandal

2013

International Journal of Heat and Mass Transfer

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“…The problem of biomechanics has attracted the attention of many investigation [6][7][8] . The important contributions of recent years to the topic are referenced in the literature [9][10][11][12][13][14][15][16][17][18] . Theoretical investigations have been carried out to study the effect of multi-stenosis in the presence of a magnetic field [19][20][21][22] .…”

Section: Introductionmentioning

confidence: 99%

Effects of magnetic field, porosity, and wall properties for anisotropically elastic multi-stenosis arteries on blood flow characteristics

Mekheimer

Haroun

Elkot

2011

Appl. Math. Mech.-Engl. Ed.

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A mathematical model for blood flow through an elastic artery with multistenosis under the effect of a magnetic field in a porous medium is presented. The considered arterial segment is simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid representing blood. An artery with mild local narrowing in its lumen forming a stenosis is analyzed. The effects of arterial wall parameters represent viscoelastic stresses along the longitudinal and circumferential directions Tt and T θ , respectively. The degree of anisotropy of the vessel wall γ, total mass of the vessel, and surrounding tissues M and contributions of the viscous and elastic constraints to the total tethering C and K respectively on resistance impedance, wall shear stress distribution, and radial and axial velocities are illustrated. Also, the effects of the stenosis shape m, the constant of permeability κ, the Hartmann number Ha and the maximum height of the stenosis size δ on the fluid flow characteristics are investigated. The results show that the flow is appreciably influenced by surrounding connective tissues of the arterial wall motion, and the degree of anisotropy of the vessel wall plays an important role in determining the material of the artery. Further, the wall shear stress distribution increases with increasing Tt and γ while decreases with increasing T θ , M , C, and K. Transmission of the wall shear stress distribution and resistance impedance at the wall surface through a tethered tube are substantially lower than those through a free tube, while the shearing stress distribution at the stenosis throat has inverse characteristic through totally tethered and free tubes. The trapping bolus increases in size toward the line center of the tube as the permeability constant κ increases and decreases with the Hartmann number Ha increased. Finally, the trapping bolus appears, gradually in the case of non-symmetric stenosis, and disappears in the case of symmetric stenosis. The size of trapped bolus for the stream lines in a free isotropic tube (i.e., a tube initially unstressed) is smaller than those in a tethered tube.

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Two-fluid Casson model for pulsatile blood flow through stenosed arteries: A theoretical model

Cited by 52 publications

References 29 publications

Physiological flow of shear-thinning viscoelastic fluid past an irregular arterial constriction

Physiological flow of shear-thinning viscoelastic fluid past an irregular arterial constriction

Heat transfer to micropolar fluid flowing through an irregular arterial constriction

Effects of magnetic field, porosity, and wall properties for anisotropically elastic multi-stenosis arteries on blood flow characteristics

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