Abstract

In this article, peristaltically induced motion of couple stress fluid under the suspension of small particles have been studied. A peristaltic wave with non-uniform motion is traveling with a constant wave celerity. An extrinsic magnetic field is applied to an electrically conducting incompressible fluid with irrotational motion. Lubrication theory is applied for the mathematical formulation of both fluid- and particle-phase equations. Analytically and numerically, the formulated equations are solved using computational software Mathematica. The exact solutions are determined against the velocity profile for both fluid- and particulate-phases. The volumetric flow rate is also presented and calculated numerically to examine the pumping characteristics. Trapping mechanisms via streamlines are plotted and discussed against all the leading parameters. The present results are also beneficial to observe the Newtonian behavior and single phase fluid model. It is also observed that magnetic field opposes the fluid movement in the middle of the channel, while the presence of small particles tends to resist the fluid motion along the whole channel. A significant reduction in the pumping rate was observed due to the rise in the couple stress fluid parameter, the fraction of the particle volume, and the average volume flow rate, but a dual behavior is observed against the magnetic parameter. The fluid bolus diminishes in magnitude and reduces in quantity against the higher values of Hartmann number.

摘要

本文研究了小颗粒悬浮下耦合应力流体的蠕动诱导运动。具有非均匀运动的蠕动波以恒定的波速传播。将外在磁场施加到具有无旋转运动的导电不可压缩流体。润滑理论适用于流体和粒子相方程的数学公式。在分析和数值上，公式化的方程使用计算软件 Mathematica 求解。精确解是根据流体相和颗粒相的速度分布确定的。还给出了体积流量并进行了数值计算，以检查泵送特性。针对所有主要参数绘制并讨论了通过流线的捕获机制。目前的结果也有利于观察牛顿行为和单相流体模型。还观察到，磁场阻碍通道中间的流体运动，而小颗粒的存在往往会阻碍整个通道的流体运动。由于耦合应力流体参数、颗粒体积分数和平均体积流量的增加，观察到泵送速率显着降低，但观察到对磁参数的双重行为。相对于 Hartmann 数的较高值，流体推注的量级减小并且数量减少。而小颗粒的存在往往会阻碍沿整个通道的流体运动。由于耦合应力流体参数、颗粒体积分数和平均体积流量的增加，观察到泵送速率显着降低，但观察到对磁参数的双重行为。相对于 Hartmann 数的较高值，流体推注的量级减小并且数量减少。而小颗粒的存在往往会阻碍沿整个通道的流体运动。由于耦合应力流体参数、颗粒体积分数和平均体积流量的增加，观察到泵送速率显着降低，但观察到对磁参数的双重行为。相对于 Hartmann 数的较高值，流体推注的量级减小并且数量减少。