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Numerical Analysis of Peristaltic Transport of Casson Fluid for non-zero Reynolds Number in Presence of the Magnetic Field

Abstract In this study, the peristaltic flow of a Casson fluid in a channel is considered in the presence of an applied magnetic field. Flow is considered in the moving frame of reference with constant velocity along the wave. The developed mathematical model is presented by a set of partial differential equations. A numerical algorithm based on finite element method is implemented to evaluate the numerical solution of the governing partial differential equations in the stream-vorticity formulation. The obtained results are independent of low Reynolds number and long wavelength assumptions, so the effects of non-zero moderate Reynolds number are presented. The expression for the pressure is also calculated implicitly and discussed through graphs. Computed solutions are presented in the form of contours of streamlines and vorticity. Velocity profile and pressure distribution for variation of different involved parameters are also presented through graphs. The investigation shows that the strength of circulation for stream function increases by increasing the Reynolds and Hartmann numbers. Enhancement in longitudinal velocity is noted by increasing the Reynolds number and Casson parameter while increasing Hartmann number reduces the longitudinal velocity. Comparison of the present results with the available results in literature is also included and found in good agreement.