Rotation and initial stress effect on MHD peristaltic flow of reacting radiating fourth-grade nanofluid with viscous dissipation and Joule heating

Abstract

In the present paper, the authors discuss a numerical study of the peristaltic flow of the Newtonian fourth-grade nanofluid under the Joule heating effect in the presence of rotation and initial pressure in addition to the influence of the induced magnetic field and heat transfer. On the other hand, the governing basic partial differential equations are the differential equations of the fourth-grade fluid model, which consists of the momentum equations, the energy equation, and, finally, the nanoparticle concentration equation, bearing in mind that the wave is very long with low Reynolds number. It is worth mentioning that the final form of the basic equations was solved numerically by the fourth-order Runge–Kutta method with the shooting technique and trapping is addressed graphically. Furthermore, the effects of all physical parameters on the distributions of velocity, temperature, and concentration of nanoparticles inside the fluid, in addition to the distribution of pressure gradients and the distribution of magnetic force are retained. Some results of the current study show that the behavior of the velocity distribution is reversed from decreasing to increasing under the influence of rotation, Deborah number , and the concentration of nanoparticles distribution increases with the increase in the heat Grashof number and the nonlinear thermal radiation parameter . Comparison of current similarity solutions with available previous results indicates the accuracy and guarantee of the present numerical results and the used method.