Slipping of a Spherical Particle Through Peristaltic Curved Tube Filled with Non-newtonian Nanofluid

The slow motion of a solid spherical particle which is immersed in a non-Newtonian nanofluid and flowing through a curved peristaltic channel is studied. The more important physical application of this type of motion is the motion of clots through blood arteries and the motion gallstones in the bile duct. The biviscosity model is applied to represent the rheological property of the non-Newtonian fluid. Also, the biviscosity model is one of the most important models that can be considers to describe rheological properties of the blood flow and the other biological fluids in the human body. Also, the flow motion in the blood vessels and other vital vessels undergo peristaltic movement. So, this type of motion has many medical and biological applications. In the mathematical treatment, due to the symmetry of the flow channel, the stress tensor components of the biviscosity model are obtained twice. Firstly, in the polar coordinates due to the curvature of the channel. Secondly, due to the spherical coordinates for the spherical motion of the particle to obtain the general form of the stream function which represents the flow motion. The peristaltic motion is studied generally without the ordinary longwave approximation and without assuming the small value of Reynolds number. This gives more generalization to the results. The most important factor in this type of motion is the drag force that effect on the spherical body (clot or stone) motion in the vessel. So, the problem is solved analytically, and the drag force is obtained numerically. Also, the heat and the volume fraction distributions are obtained. The results illustrate that the existence of the nanoparticles reduces the drag force, which contributes to increasing the sliding motion of the spherical particle and contributes on removing the blood clot and stone through the vital vessel. Some other important parameters, which effects on the motion, are considered such as the radius ratio, curvature parameter, the wave speed, the wave amplitude, and the slip parameter. The results illustrated that the increase of the fluid viscosity enhances the friction force. Meanwhile, the Brownian motion of the nanoparticles enhances the flow motion which intern enhances the slipping motion of the particle.