The mathematics of pulsatile flow in small vessels I. Casson theory

Aroesty, Jerry; Gross, Joseph F.

doi:10.1016/0026-2862(72)90012-x

Cited by 67 publications

(26 citation statements)

References 3 publications

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“…The quantitative results of the α, β, n, δ, N t , andN b for diverging tapering, converging tapering, and non-tapered arteries are observed physically in Figures 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22 that with an increase in the thermophoresis parameter N t and stenosis shape n, the velocity profile decreases, while velocity profile increases with an increase in the maximum height of the stenosis δ, Brownian motion parameter N b , and Prandtl parameters α and β. It is also seen that for the case of converging tapering, it has a larger value as compared with the case of diverging tapering and non-tapered arteries.…”

Section: Resultsmentioning

confidence: 99%

“…Arteries which are basically considered as living tissues need a supply of metabolites including oxygen and removal of waste products. Aroesty and Gross [3] have discussed the pulsatile flow of blood in the small blood vessels. Chaturani and Ponnalagar Samy [4] reported the theory of Aroesty and Gross [3] and studied the pulsatile flow of blood in stenosed arteries modeling blood as Casson fluid.…”

Section: Introductionmentioning

confidence: 99%

“…Aroesty and Gross [3] have discussed the pulsatile flow of blood in the small blood vessels. Chaturani and Ponnalagar Samy [4] reported the theory of Aroesty and Gross [3] and studied the pulsatile flow of blood in stenosed arteries modeling blood as Casson fluid. Scott Blair and Spanner [5] discussed that blood as Casson fluid is valid for moderate shear rate, and the validity of Casson and Herschel-Bulkley theory for blood flow is the same.…”

Section: Introductionmentioning

confidence: 99%

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Nanoparticle analysis for blood flow of Prandtl fluid model with stenosis

2013

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In this article, we have discussed blood flow in the nano-Prandtl fluid flow analysis in tapered stenosed arteries. The occurrence of nanoparticle fraction and heat transfer was found. Gravitational effects were also considered because the tube was taken vertically upward. Homotopy perturbation method was used to find the analytical solution of coupled nonlinear differential equations. Physical features have been discussed through graphs of concentration profile σ , velocity profile w, resistance impedance λ, temperature profile θ , wall shear stress S rz , wall shear stress at the stenosis throat τ s , and the stream lines.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nanoparticle analysis for blood flow of Prandtl fluid model with stenosis

2013

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“…They have pointed out that away from the flow divider, the flow rate becomes higher due to the forward flow and gets reversed near the flow divider. While blood being a suspension of cells which behaves as a nonNewtonian fluid at low shear rates and during its flow through small blood vessels, and especially in diseased states when clotting effects in small arteries are presents [11][12][13]. Many experiments [12][13][14][15][16][17][18] were conducted on blood with varying heamatocrit, anticoagulant, temperature, etc.…”

Section: Introductionmentioning

confidence: 99%

“…suggested that at low shear rates, blood behaves as Casson fluid. Aroesty and Gross [12] have analyzed the pulsatile flow of blood vessels with application to microcirculation. Dash and Mehta [16] have investigated the Casson fluid flow through a pipe filled with porous medium.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Body Acceleration on Two Dimensional Flow of Casson Fluid through an Artery with Asymmetric Stenosis~!2009-07-01~!2009-10-30~!2010-05-17~!

Shaw¹,

Murthy²,

Pradhan³

2010

TOTPJ

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Abstract:Two dimensional flow of a non-Newtonian fluid through an asymmetric stenosed artery is analysed under the influence of body acceleration with an external magnetic field on the flow field. The Casson fluid model is considered to characterize the non-Newtonian behaviour of the blood. The flow is assumed to be unsteady, laminar, two-dimensional, asymmetric and of pulsatile nature. The artery wall has been treated as an elastic (moving wall) cylindrical tube. The unsteady flow mechanics is influenced by externally imposed periodic body acceleration. An explicit finite difference scheme is applied to obtain the flow field. The effect of body acceleration, magnetic field on the flowing blood is analyzed and these results are presented through graphs for the axial and radial velocities, flow rate and wall shear stress.

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Peristaltic Transport of a Herschel–Bulkley Fluid in an Elastic Tube

Vajravelu

Sreenadh

Devaki³

et al. 2014

Heat Trans. Asian Res.

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In this paper, we investigate the peristaltic transport of a non-Newtonian viscous fluid in an elastic tube. The governing equations are solved using the assumptions of long wavelength and low Reynolds number approximations. The constitution of blood has a non-Newtonian fluid model and it demands the yield stress fluid model: The blood transport in small blood vessels is done under peristalsis. Among the available yield stress fluid models for blood flow, the non-Newtonian Herschel-Bulkley fluid is preferred (because Bingham, power-law and Newtonian models can be obtained as its special cases). The Herschel-Bulkley 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 flow rate are derived. The flux is determined as a function of inlet, outlet, external pressures, yield stress, amplitude ratio, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress 0 → 0 and in the absence of peristalsis, our results agree with Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress, peristaltic wave, and the elastic parameters (t 1 or t 2 ) have strong effects on the flux of the non-Newtonian fluid flow. Effects of various wave forms (namely, sinusoidal, trapezoidal and square) on the flow are discussed. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid phenomena, especially the shearthinning phenomena. Shear thinning reduces the wall shear stress. C⃝ 2014 Wiley Periodicals, Inc. Heat Trans Asian Res, 44 (7): 585-598, 2015; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj).

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The mathematics of pulsatile flow in small vessels I. Casson theory

Cited by 67 publications

References 3 publications

Nanoparticle analysis for blood flow of Prandtl fluid model with stenosis

Nanoparticle analysis for blood flow of Prandtl fluid model with stenosis

The Effect of Body Acceleration on Two Dimensional Flow of Casson Fluid through an Artery with Asymmetric Stenosis~!2009-07-01~!2009-10-30~!2010-05-17~!

Peristaltic Transport of a Herschel–Bulkley Fluid in an Elastic Tube

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