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In this paper, the effects of Dufour and Soret numbers on the peristaltic motion of a non‐Newtonian micropolar fluid are discussed. The motion inside a nonuniform vertical channel under the effect of the uniform magnetic field is considered. The Ohmic and elastic dissipations, as well as heat generation and chemical reaction, are taken into account. The problem is modulated mathematically by using continuity, momentum, angular momentum, and heat and mass transfer equations. The nonlinear partial differential equations describing these equations are written in terms of the physical parameters of the problem. The equations are transformed from the laboratory frame to the wave frame and then written in dimensionless form. The approximations of long wavelength and small Reynolds number are applied, then the equations are solved by using the homotopy perturbation method. The velocities, stream function, temperature, and concentration distributions are obtained as functions of the physical parameters of the problem. The effect of these parameters on the obtained solutions are computed mathematically and illustrated graphically through a set of figures. It is found that the parameters play an important role in controlling the solutions. It is found that the stream function decreases by increasing both non‐Newtonian and micropolar parameters on the left side of the channel and vice versa occurs on the right side.

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The motion of viscoelastic nanofluid flow with heat and mass transfer over a permeable flat plate under the action of uniform magnetic field is discussed. The effects of Brownian motion, thermophoresis and viscous and ohmic dissipations are considered. The system of equations describes the motion is converted to ordinary non-linear differential equations by using suitable transformations, and then solved numerically by using fourth order Runge-Kutta method with shooting technique. The obtained solutions are functions of the physical parameters of the problem. The effects of these parameters on the obtained solutions are discussed numerically and illustrated graphical to show that the parameters controlled the solutions.