Peristaltic Motion of Jeffrey Nanofluid in a Channel with Slip Condition

Abstract

Peristaltic activity has great value in many physiological processes and industries. Peristalsis can occur due to contraction and expansion of flexible boundaries. In other words this activity includes passing down, mixing and transporting materials through contraction or expansion of the waves propagating along the channel walls. It has wide applications in medical industry and chemical processes. Typical examples in this direction include in distillation towers and fixedbed reactors, urine transport from kidney to bladder through the ureter, transport of lymph in the lymphatic vessels, swallowing food through the esophagus, the movement of chyme in the gastrointestinal tract, ovum movement in the fallopian tube, transport of corrosive fluids, sanitary fluid transport and blood pumps in heart lung machine etc. The worms utilize peristalsis for locomotion. Latham [1] and Shapiro et al. [2] initiated works on peristalsis of viscous fluids via theoretical and experimental approaches. Later on many researchers put forward their research on this topic by considering different kinds of fluid models, no-slip/ partial slip condition and one or more assumptions of long wavelength, low Reynolds number, small amplitude ratio, small wave number etc. Especially the magnetohydrodynamics (MHD) peristaltic transport of fluid in a channel are quite important with reference to conductive physiological materials for example the blood, blood pump machines and with the need of both experimental and theoretical research for operation of peristaltic MHD compressor. Concept of magnetohydrodynamics is useful in Magnetic Resonance Imaging (MRI) when a patient undergoes in a height static magnetic field. On the other hand the heat transfer in peristalsis is useful in the oxygenation processes. Such concept in further important in the industrial applications like sanitary fluid transport and transport of corrosive materials where the fluid contact with the machinery parts is prohibited. Having all such aspects in mind many authors in past analyzed the peristaltic flows in detail (see [3- 16]). Nadeem and Akbar [17] studied influence of radially varying MHD on the peristaltic flow in an annulus. Ellahi and Hussain [18] analyzed effects of MHD and partial slip on peristaltic flow of Jeffrey fluid in a rectangular duct. Ali et al. [19] presented numerical simulation for peristaltic flow of a biorheological fluid with shear dependent viscosity in a curved channel. Mixed convection occurs in vertical channels for improvement of cooling systems in engineering. Analysis of heat transfer with MHD and mixed convection in vertical channels has great applications in solar energy collection, chemical reactions and cooling systems. Sheikholeslami et al. [20] analyzed simulation of MHD CuO-water nanofluid flow and convective heat transfer using Lorentz force. Abbasi et al. [21] discussed effects of inclined magnetic field and Joule heating in mixed convective flows of non-Newtonian fluids. Mustafa et al. [22] analyzed Soret and Dufour effects in the mixed convective peristaltic flow of fourth grade fluid. Soret and Dufour effects in mixed convective peristalsis of viscous nanofluids are examined by Hayat et al. [23]. Srinivas and Muthuraj [24] addressed mixed convective peristalsis in presence of chemical reaction. Heat and mass transfer analysis in mixed convective peristaltic transport of viscous fluid in an asymmetric channel is studied by Srinivas et al. [25]. Peristaltic transport has not been conducted well in connection with elastic behavior of the walls. Wall properties such as elastic tension and damping are of immense importance in practical situations. Hence this dissertation is designed to explore the slip and Joule heating effects on peristalsis of Jeffrey nanofluid in a channel with compliant walls. The organization of dissertation is as follows: Chapter one describes the fundamental laws and definitions regarding the concepts used in the chapters two and three. Chapter two refers to the study of slip and wall properties simultaneously on peristaltic flow of nanofluid. This chapter concerns the review of article [13] proposed by Hayat et al. Chapter three deals with mixed convective peristaltic flow of Jeffrey nanofluid in a compliant walls channel. Analysis has been carried out with compliant walls and slip conditions. Thermal radiation effect is present. Joule heating is taken into account. Graphical results are plotted numerically to analyze the behavior of sundry parameters on temperature, velocity, nanoparticle concentration and heat transfer coefficient.