Low Reynolds number flow in slowly varying axisymmetric tubes

Manton, M. J.

doi:10.1017/s0022112071002192

Cited by 105 publications

(53 citation statements)

References 5 publications

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“…Hence the concept of flow in a varying cross-section forms the prime basis of a large class of problems in understanding blood flow. Manton [34], Hall [35] and Porenta et al [36] pointed out that most of the vessels could be considered as long and narrow, slowly tapering cones. Thus the effects of vessel tapering together with the non-Newtonian behaviour of the streaming blood seem to be equally important and hence certainly deserve special attention.…”

Section: Introductionmentioning

confidence: 99%

An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis

Mandal¹

2005

International Journal of Non-Linear Mechanics

273

104

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Section: Introductionmentioning

confidence: 99%

An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis

Mandal¹

2005

International Journal of Non-Linear Mechanics

273

104

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“…Asymptotic solutions for flow in axially symmetric pipes have been derived in several papers [11][12][13]. The derivation we present here follows the line of the paper by Kotorynski [13].…”

Section: Methods Of Slow Variationsmentioning

confidence: 87%

Efficient Estimation of the Friction Factor for Forced Laminar Flow in Axially Symmetric Corrugated Pipes

Esquivel

Boonkkamp

Dam

et al. 2010

ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C

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In this paper we present an efficient method for calculating the friction factor for forced laminar flow in arbitrary axially symmetric pipes. The approach is based on an analytic expression for the friction factor, obtained after integrating the Navier-Stokes equations over a segment of the pipe. The friction factor is expressed in terms of surface integrals over the pipe wall, these integrals are then estimated by means of approximate velocity and pressure profiles computed via the method of slow variations. Our method for computing the friction factor is validated by comparing the results, to those obtained using CFD techniques for a set of examples featuring pipes with sinusoidal walls. The amplitude and wavelength parameters are used for describing their influence on the flow, as well as for characterizing the cases in which the method is applicable. Since the approach requires only numerical integration in one dimension, the method proves to be much faster than general CFD simulations, while predicting the friction factor with adequate accuracy.

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“…obtain a solution for flow through a channel with an exponentialshaped constriction. Manton (8) obtained an asymptotic series solution for the low Reynolds number flow through an axisymmetric tube whose radius varies slowly in the axial direction. Forrester and Young (9) derived a solution for a cosineshaped constriction from the Navier-Stokes equations.…”

Section: Flow Through a Tapered Channelmentioning

confidence: 99%