Peristaltic Flow of a Bingham Fluid in Contact with a Jeffrey Fluid
The article concerns the peristaltic transport of two-layered fluid, consisting of a Bingham fluid in the core region and a Jeffrey fluid in the peripheral region through a channel. The flow is analyzed in the wave of reference under the assumptions of lo
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Abstract The article concerns the peristaltic transport of two-layered fluid, consisting of a Bingham fluid in the core region and a Jeffrey fluid in the peripheral region through a channel. The flow is analyzed in the wave of reference under the assumptions of long wavelength and low Reynolds number. The analytical expressions for stream function, pressure rise, and the frictional force per wavelength in both the regions are obtained. The effect of physical parameters namely yield stress, Jeffrey parameter associated with the flow are presented graphically. This model helps to understand the behavior of two immiscible physiological fluids in living structures and in modeling the biomechanical instruments.
1 Introduction The mechanism of peristalsis takes place in the food bolus transport through esophagus, chyme movement in the gastrointestinal tract, lymph transport in the lymphatic vessels, urine transport from kidney to bladder through the ureter, and in the vasomotion of small blood vessels. In mechanical aspects, the peristaltic pumps are modeled to transport the corrosive liquids in nuclear industries and to filter blood in dialysis machine. A few investigations on the peristaltic flow of physiological R. Saravana (&) Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle 517325, Andhra Pradesh, India e-mail: [email protected] P. Hariprabakaran Department of Mathematics, Thiruvalluvar University College of Arts and Science, Gajalnaickanpatti, Tirupattur 635901, Tamil Nadu, India R. Hemadri Reddy Department of Mathematics, School of Advanced Science, VIT University, Vellore 632014, Tamil Nadu, India S. Sreenadh Department of Mathematics, Sri Venkateswara University, Tirupati 517502, Andhra Pradesh, India © Springer Nature Singapore Pte Ltd. 2018 M.K. Singh et al. (eds.), Applications of Fluid Dynamics, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-10-5329-0_37
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fluids have been reported in the literature (Nadeem and Akram 2009; Saravana et al. 2011; Vajravelu et al. 2013). The behavior of blood flow through small vessels represents two-layered flow which includes plasma peripheral layer and suspension of all erythrocytes in core region. Brasseur et al. (1987) reported the influence of Newtonian peripheral layer of different viscosities on the peristaltic pumping. Usha and Ramachandra Rao (1997) investigated the two-layered peristaltic flows with long wavelength and low Reynolds number assumptions. Narahari and Sreenadh (2010) analyzed the peristaltic pumping of a Bingham fluid with Newtonian peripheral region, and Hari Prabakaran et al. (2013) extended this work through an inclined channel. Very recently, Kavitha et al. (2015) addressed the peristaltic pumping of a Jeffrey fluid in contact with a Newtonian fluid in an inclined channel. Keeping all these aspects in mind, we investigated the peristaltic flow of a Bingham fluid in the core region in contact with a Jeffrey fluid in the peripheral region. The analytical
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