Peristaltic transport of a couple stress fluid in a uniform and non‐uniform channels

Article type: Research Article

Authors: Mekheimer, Kh.S.

Affiliations: Department of Mathematics, Al‐Azhar University, Cairo, Egypt

Note: [] Address for correspondence: Kh.S. Mekheimer, Department of Mathematics, Faculty of Science, Al‐azhar University, Nasr City 11884, Cairo, Egypt. E‐mail: Kh_Mekheimer@yahoo.com.

Abstract: The problem of peristaltic transport of a couple stress fluid in uniform and non‐uniform two‐dimensional channels has been investigated under zero Reynolds number with long wavelength approximation. Blood is represented by a couple stress fluid (a fluid which its particles size are taken into account, a special case of a non‐Newtonian fluid). It is found that the pressure rise decreases as the couple stress fluid parameter γ increases (i.e., small size fluid particle). So the pressure rise for a couple stress fluid (as a blood model) is greater than that for a Newtonian fluid. Also the pressure rise increases as the amplitude ratio ϕ increases for different values of γ. Further, the pressure rise in the case of non‐uniform geometry is found to be much smaller than the corresponding value in the case of uniform geometry. Finally, the maximum pressure rise when the mean flow rate over one period of the wave, $\bar{Q}$=0, increases as ϕ increases and γ decreases.

Keywords: Peristaltic transport, couple stress fluid, non‐uniform channel

Journal: Biorheology, vol. 39, no. 6, pp. 755-765, 2002