Turkish J. Eng. Env. Sci. 32 (2008) , 117 – 123. c  T ¨ UB ˙ ITAK Interaction of Couple Stresses and Slip Flow on Peristaltic Transport in Uniform and Nonuniform Channels Ayman Mahmoud SOBH Mathematics Department, Faculty of Applied Science, Al Aqsa University, Gaza-PALESTINE e-mail: aymansobh@yahoo.com Received 06.02.2008 Abstract The effect of slip velocity on peristaltic flow of a couple stress fluid in uniform and nonuniform symmetric channels is studied. This problem has numerous applications. It serves as a model for the blood flow in living creatures. Using long wavelength approximation and neglecting inertial forces, a closed form solution for the axial velocity and the pressure gradient was obtained. Numerical computations were carried out to investigate the effect of couple stress parameter α and Knudsen number Kn on pressure rise, maximum pressure rise, and friction force for uniform and nonuniform channels. It is noted that the pressure rise decreases with increasing α and increasing Kn. The friction force has an opposite behavior compared with pressure rise. Key words: Peristalsis, Couple stresses, Slip flow Introduction The study of fluid transport by means of peristaltic waves in both mechanical and physiological situa- tions has been a subject of scientific research since the first investigation by Latham (1966). By peri- staltic pumping, we mean a device for pumping flu- ids, generally from a region of lower pressure to one of higher pressure, by means of a contraction wave traveling along the tube. This mechanism is found in many physiological situations like urine transport from the kidney to the bladder through the ureter, movement of chyme in the gastrointestinal tract, the movements of spermatozoa in the ductus efferentes in the male reproductive tract, and ova in the female fallopian tube. Moreover, a peristaltic mechanism is involved in transporting the lump in lymphatic ves- sels, movement of bile in the bile duct, and the circu- lation of blood in small blood vessels such as arteri- oles, venules, and capillaries. In addition, peristaltic pumping occurs in many practical applications in- volving biomechanical systems. Furthermore, finger and roller pumps are frequently used for pumping corrosive or very pure materials so as to prevent di- rect contact of the fluid with the pump’s internal surfaces. The initial mathematical models of peristalsis obtained by a train of sinusoidal waves in an in- finitely long symmetric channel or tube were intro- duced by Fung and Yih (1968), and Shapiro et al. (1969). After these studies, several analytical, nu- merical, and experimental attempts have been made to understand peristaltic action in different situa- tions for Newtonian and non-Newtonian fluids. Some of these studies have been done by Brown and Hung (1977), Takabatake and Ayukawa (1982, 1988), Sri- vastava and Srivastava (1983, 1984, 1988), Siddiqui and Schwarz (1994), Ramachandra and Usha (1995), Elshehawey et al. (2000), Elshehawey and Sobh (2001), Sobh (2003), Abd El Naby et al. (2004), Hayat et al. (2006, 2007), and Sobh and Mady (2008). The study of a couple stress fluid is very use- ful in understanding various physical problems be- cause it possesses the mechanism to describe rhe- ological complex fluids such as liquid crystals and human blood. By couple stress fluid, we mean a 117