Leveraging elasticity of blood stenosis to detect the role of a non-Newtonian flow midst an arterial tube: Mazumdar and Keller models.

Blood stenosis is considered one of the most serious risks which face humanity nowadays. In addition, it is also one of the most apparent symptoms of COVID (19) (Corona Virus). Consequently, this research is shedding light on studying the blood flow in case of having blood clots and artery elasticity in the presence of stenosis during studying the flow. Hematopoiesis requires a model of the yield stress fluid, 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). Navier stokes equation is used to simulate this subject in a mathematical way. The elasticity on the stenosis arterial walls is simulated by Rubinow & Keller model [24] and Mazumdar model [25]. The results reveal exciting behaviors that, in turn, require adequate study of non-Newtonian fluid flow phenomena, especially the results showed that the increase in the parameters related to the elasticity of the walls facilitating the flow of blood through the stenosis area. In addition, a comparison between two elasticity models (Rubinow & Keller model and Mazumdar model) is considered. Further, for normal artery without stenosis, our results are the same as those obtained by Vajravelu et.al [22].

Residual time of sinusoidal metachronal ciliary flow of non-Newtonian fluid through ciliated walls: fertilization and implantation.

The monitoring of the ciliated walls in the uterine tube has supreme importance in enhancing the sperm to reach the egg (capacitation processes), and at peristaltic ciliary flow has a more favorable residual time along the canal when compared to the peristaltic flow. Based on the importance of this study, a mathematical simulation of this process has been carried out by studying the behavior of a non-Newtonian magnetized fluid with a Darcy flow model with an oscillating wall having an internal ciliated surface. The governing equation is formed with Eyring-Powell fluid (tubal fallopian fluid) without using any approximations and solved using the Adomian analysis method. Using the vorticity formula, the components of the velocity function, pressure gradient, and stream function are obtained. The influence of relevant parameters is explained through diagramming and discussion. We also analyzed the residue time effects on the flow parameters. The results indicate that peristaltic ciliary flow has a more favorable residual time along the canal when compared to peristaltic flow.

Peristaltic transport of a couple stress fluid in a uniform and non-uniform channels.

The problem of peristaltic transport of a couple stress fluid in uniform and non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation. Blood is represented by a couple stress fluid (a fluid which its particles size are taken into account, a special case of a non-Newtonian fluid). It is found that the pressure rise decreases as the couple stress fluid parameter gamma increases (i.e., small size fluid particle). So the pressure rise for a couple stress fluid (as a blood model) is greater than that for a Newtonian fluid. Also the pressure rise increases as the amplitude ratio phi increases for different values of gamma. Further, the pressure rise in the case of non-uniform geometry is found to be much smaller than the corresponding value in the case of uniform geometry. Finally, the maximum pressure rise when the mean flow rate over one period of the wave, Q = 0, increases as phi increases and gamma decreases.