Electro-osmosis modulated peristaltic flow of oldroyd 4-constant fluid in a non-uniform channel

In this study, we investigate the physical mechanism of the electro-osmosis fluid flow within a non-uniform channel. Fluid model is characterized by the constitutive relation of the Oldroyd 4-constant fluid. We retrieved the Poisson equations by utilizing the mass and momentum conservation models in order to obtain the mathematical formulation of the given problem. The methodology used in obtaining the solution is classified into three different steps. Firstly, we linearized the given differential equations to ascertain the potential Debye-Huckel function. Secondly, we implemented the widely-used assumptions like low Reynolds number and long wavelength to reduce the momentum (partial differential) equations into a system of ordinary differential equations. Thirdly, we solved the simplified differential equations numerically by using the shooting method. Subsequently, we have calculated the graphical results to evaluate the influence of various emerging parameters such as the electroosmotic parameter, viscoelastic fluid parameters and non-uniform parameter on the fluid flow within a non-uniform channel. We have also computed several features of peristaltic pumping for the case of Helmholtz-Smoluchowski velocity. Our results reveal that the behavior of velocity magnitude shows an increasing trend by enhancing the values of the electroosmotic parameter, whereas it also manifests a decreasing trend if the value of the non-uniform parameter is raised.