Electro-osmotic Effect on the Peristaltic Flow of Williamson Nanofluid Through a Porous Medium in the Presence of Activation Energy and Modified Darcy's Law

Non-Newtonian nanofluids are widely utilized in medical and engineering fields, such as in cooling of microchips, lubrications, cancer therapy, drug delivery etc. In the present article, we focused on the electro-osmotic effect on the peristaltic transport of a non-Newtonian nanofluid inside a horizontal micro-channel. The fluid obeys Williamson model, flowing through a porous medium with modified Darcy's law. In addition, the effects of a chemical reaction with the contribution of activation energy are taken in consideration. Furthermore, in the case of modified Darcy's law, the apparent viscosity of the fluid is used in the governing equations. Furthermore, when temperature of the hot wall tube is less than three times that of the cold wall, the term of the activation energy is simplified by using Taylor expansion.The governing equations that illustrate the velocity, temperature, and concentration of nanoparticles distributions are considered and simplified under the assumptions of a long wavelength and low Reynolds number. The homotopy perturbation method is used as semi-analytical solution for the governing equations. Moreover, some figures are used to illustrate and discuss the role of physical parameters entering the problem on the obtained solutions. Since, most of non-Newtonian fluids are viscoelastic materials, it is important to discuss the effect of Weissenberg number that represents product of strain rate and relaxation time. It is found that Weissenberg number has dual effects on the axial velocity as well as the temperature and the concentration distributions. In addition, according to Fick's law of diffusion; the temperature and concentration distributionsshould have opposite effects, however, it is found that the increases in the thermophoresis parameter increases both temperature and concentration distributions. This means the nanoparticles are more concentrated when migrates from one side of the tube to the other side. Furthermore, the graphs illustrate the dissimilar effect of the activation energy and the rate of the chemical reaction on the concentration of nanoparticles.