Non-linear mathematical analysis of carreau fluid for blood rheology in constricted arteries under external body acceleration

초록

This non-linear mathematical model analyses the pulsatile blood flow in a tapered narrow artery with mild multiple stenoses in the presence of body acceleration, considering blood as non-Newtonian Carreau fluid. Double perturbation method is applied to solve the resulting non-linear boundary value problem and the asymptotic solutions to the flow rate, pressure gradient, velocity profile, wall shear stress and longitudinal impedance to flow are obtained. It is noted that the blood velocity rises when the angle of tapering of artery, body acceleration and power law index increase, whereas this rheological behavior is reversed for longitudinal impedance to flow and wall shear stress when each of the aforesaid parameters increases. It is also found that the wall shear stress in blood flow increases considerably when the maximum depth of the stenosis increases and it decreases considerably when the pulsatile Reynolds number increases. The estimates of the percentage of increase in the longitudinal impedance to flow increase significantly with the increase of the maximum depth of the stenosis and Weissenberg number. It is also observed that the mean velocity of blood increases noticeably with the increase of angle of tapering of the artery and body acceleration parameter. © 2018 Pushpa Publishing House, Allahabad, India.

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