Electro-osmotic peristaltic flow of non-Newtonian nanofluid Al2 O3 inside a microchannel with modified Darcy's law and activation energy.

Document Type : Original Article


1 Department of Mathematics Faculty of Education Ain Shams University. Cairo, Roxy, Egypt

2 b) Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt

3 Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, 11757, Cairo, Egypt.

4 Mathematics Department, Faculty of Education, Ain Shams University, Cairo, Egypt


The main objective of this study was to investigate the peristaltic flow of an unsteady non-Newtonian nanofluid through a uniformly symmetric vertical duct. The investigation was conducted considering the presence of external electric and magnetic fields, which led to the occurrence of both electroosmosis and induced magnetic field phenomena. The non-Newtonian fluid obeys the third-order model. Furthermore, the flow is through a porous medium which follows the modified form of Darcy's law. The study also considered the influences of mixed convection, Dufour and Soret, chemical reaction, activation energy, viscous dissipation, and heat generation in the system. To simplify the governing equations that describe velocity, temperature, and nanoparticle concentration, wave transformation techniques were employed. The resulting simplified equations were then analytically solved using the homotopy perturbation method (HPM). Furthermore, a set of figures were utilized to visually illustrate and discuss the influence of the various physical parameters involved in the problem on the solutions obtained. The investigation provided a clearer understanding of the relationships and effects of the parameters on the system's behavior. It is found that the modified Darcy term significantly extends the impact of permeability in the porous medium (near the walls) to the core flow (middle of the tube). As a result, the axial velocity is enhanced in the flow direction. Moreover, the investigation reveals a clear correlation between the permeability parameter and the electro-osmotic parameter. This relationship exists due to the inverse proportionality between the electro-osmotic parameter and the length of the electric double layer (EDL) that is formed adjacent to the walls of the tube (high porous region). Furthermore, it is found that as the activation energy increases the rate of the chemical reaction is reduced which in turn reduces the concentration of nanoparticles. Additionally, it is found that as the external magnetic field strength increases the nanoparticles are more concentrated which helps in many biological applications such as drug delivery. Conversely, as induced electric field strength increases the nanoparticles disperse through the fluid.

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