Abstract:The constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid 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 flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index = 1 and the yield stress τ 0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters ( 1 and 2 ) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.
This paper is concerned with the peristaltic transport of an incompressible non-Newtonian fluid in an elastic tube. Here the flow is due to three different peristaltic waves and two different types of elastic tube. The constitution of blood suggests a non-Newtonian fluid model and it demands the applicability of yield stress fluid model. Among the available yield stress fluid models for blood, the non-Newtonian Casson fluid is preferred. The Casson fluid model describes the flow characteristics of blood accurately at low shear rates and when it flows through small blood vessels. Long wavelength approximation is used to linearize the governing equations. The effect of peristalsis and non-Newtonian nature of blood on velocity, plug flow velocity, wall shear stress and the flux flow rate are derived. The flux is determined as a function of inlet, outlet, external pressures, yield stress, amplitude ratio, and the elastic properties of the tube. Furthermore, it is observed that, the yield stress, peristaltic wave, and the elastic parameters have strong effects on the flux of the non-Newtonian fluid, namely, blood. One of the important observation is that the flux is more when the tension relation is an exponential curve rather than that of a fifth degree polynomial. Further, in the absence of peristalsis and when the yield stress tends to zero our results agree with the results of Rubinow and Keller (1972). This study has significance in understanding peristaltic transport of blood in small blood vessels of living organisms.
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).
MHD peristaltic transport of copper-water nanofluid in an artery with mild stenosis for different shapes of nanoparticles is studied in this paper. The exact solution is obtained for velocity, temperature and pressure gradient. The influence of all the parameters on velocity, temperature and pressure gradient is observed. The effect of stenosis plays a vital role in this paper, as it finds its application in the field of medicine. It is observed that the nanofluid flows rapidly in the presence of stenosis, which helps in destroying of the stencils soon. The shape of the nanoparticle is another important point to be concentrated due to based on the shape of the nanoparticle the fluid flow depends. The shape of the nanoparticle should be considered as bricks to increase the velocity, temperature and the pressure gradient. But a reversed behavior is observed if the shape of the nanoparticle is chosen as platelets. Streamlines are also concentrated and it is observed that there are more number of boluses if the shape of the nanoparticle is chosen as bricks. The effect of volume of the solid nanoparticle and stenosis warrants further study of the flow of nanofluids in tube and channel.
In this paper, the peristaltic wave propagation of a Non-Newtonian Casson liquid in a non-uniform (flexible)channel with wall properties and heat transfer is analyzed. Long wavelength and low Reynolds number approximations are considered. Analytical solution for velocity, stream function and temperature in terms of various physical parameters is obtained. The impact of yield stress, elasticity, slip and non-uniformity parameters on the peristaltic flow of Casson liquidare observed through graphs and discussed. The important outcome is that an increase in rigidity, stiffness and viscous damping force of the wall results in the enhancement of the size and number of bolus formed in the flow pattern.
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