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The Modeling of Pulsatile Blood Flow as Cross-Williamson and Carreau Fluids in an Artery with a Partial Occlusion | IEEE Conference Publication | IEEE Xplore

The Modeling of Pulsatile Blood Flow as Cross-Williamson and Carreau Fluids in an Artery with a Partial Occlusion


Abstract:

In the present article behavior of pulsatile blood flow through stenoses is studied using the incompressible non-Newtonian models. The non-Newtonian models chosen are cha...Show More

Abstract:

In the present article behavior of pulsatile blood flow through stenoses is studied using the incompressible non-Newtonian models. The non-Newtonian models chosen are characterized by the Carreau and Cross-Williamson models incorporating the effect of tapering due to the pulsatile nature of blood flow. The flow mechanism in the stenosed artery subject to a pulsatile pressure gradient arising from the normal functioning of the heart has been considered. An improved shape of the time-variant stenoses present in the tapered arterial lumen is given mathematically in order to update resemblance to the in vivo situation. Results were compared with powerlaw model and the differential approximation for the heat flux is invoked in the energy equation. The effect of heat transfer on the velocity is computed and discussed.
Date of Conference: 08-10 September 2008
Date Added to IEEE Xplore: 16 September 2008
CD:978-0-7695-3325-4
Conference Location: Liverpool, UK

1. Introduction

In the arterial systems of humans or animals, it is quite common to find localized narrowings, commonly called stenoses, caused by intravascular plaques. These stenoses disturb the normal pattern of blood flow through the artery. Acknowledge of the flow characteristics in the vicinity of stenosis may help to further the understanding of some major complications which can arise such as, an in growth of tissue in the artery, the development of a coronary thrombosis, the weakening and bulging of the artery downstream from stenosis, etc. [1]. The investigations of blood flow through arteries are of considerable importance in many cardiovascular diseases particularly atherosclerosis. The effect of body acceleration on the flow field in a porous stenotic artery is studied by El-Shaded [2]. Prashanta Kumar Mandal et al [3] also studied the effect of body acceleration on unsteady pulsatile flow of power law fluid through a stenosed artery. They have shown that all the instantaneous flow characteristics are affected by the application of body acceleration. Misra and Chauhan [4] reported the results of a study of pulsatile blood flow in a tube with pulsating walls where blood was modeled as a two-layered fluid. Ogulu and Abbey [5] studied the effect of heat transfer during deep heat muscle treatment in their study on oscillatory blood flow in an indented porous artery. El-shahed[2] reported a study of an analytical expressions of the flow field in a porous stenotic medium subject to periodic body acceleration. J.C.Misra, S.C.Misra and M.K.Patra [6] reported an analytical study on behavior of blood flow through arteries. Prashanta kumar mandal [7] reported the numerical result of a study of pulsatile unsteady flow through tapered arteries. In that, analytical treatment bears the potential to calculate the rate of flow, the resistive impedance and the wall shear stress with minor significance of computational complexity by exploiting the appropriate physically realistic prescribed conditions. Zuhaila ismail, Ilgani abdulah, Norzieha Mustapha and Norsarahaida amin [8] considered a mathematical model of blood flow through a tapered stenotic artery. Prakash and Ogulu [9] reported the results of a study of pulsatile blood flow in a constricted tube where blood was modeled as a power law fluid and they investigated the effect of non-Newtonian parameter (exponential index of power-law model) on the stress and velocity. But this model in small shearing rate shows the unreal value for shear stress. Therefore in this study we propose a mathematical model for pulsatile blood flow which treating blood as Carreau and cross-Williamson fluids that their formulation have been explained in [10]. It is hoped that this study will compliment the study reported in Prakash et al. linear algebraic equation and extend the applicability of this and other studies in this rapidly growing area of physiological fluid dynamics.

References

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