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Effect of the induced magnetic field on peristaltic flow of a couple stress fluid. (English) Zbl 1221.76231
Summary: We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter $\gamma$, the Hartmann number $M$, the magnetic Reynolds number ${R}_{m}$ and the time averaged mean flow rate $\theta$. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.
##### MSC:
 76W05 Magnetohydrodynamics and electrohydrodynamics 78A25 General electromagnetic theory 76A10 Viscoelastic fluids
##### Keywords:
couple stress fluid; induced magnetic field; MHD