Peristaltic motion with heat and mass transfer of nano‐Williamson fluids in two layers

Abstract

AbstractIn this paper, we have investigated the peristaltic motion with heat and mass transfer through a vertical channel divided into two equal regions, the right region filled with a clear non‐Newtonian fluid obeying the Williamson model and the left region with a nano‐Williamson fluid. The system is stressed by a gravity force with a uniform external magnetic field. The problem is modulated mathematically with a system of coupled nonlinear partial differential equations that describe the velocities, temperatures, and concentration of the fluids. The system of nondimensional, nonlinear, and partial differential equations is solved analytically with the homotopy perturbation method after using the approximations of low Reynolds number and long wavelength. The obtained solutions are functions of the physical parameters of the problem. Then, the effects of these parameters on velocities, temperatures, and concentration are discussed numerically and illustrated graphically through a set of figures. It is found that the parameters play an important role in controlling the solutions. It is shown that the stream function decreases on the left side and increases on the right side with an increase in the Wissenberger parameter and thermal conductivity ratio. Also, the temperature in the two regions increases with an increase in the thermophoretic parameter, whereas it decreases with an increase in the Brownian motion parameter. Furthermore, the concentration increases with an increase in the Brownian motion parameter and decreases with an increase in the thermophoretic parameter.