THE STUDY OF COMPLIANT WALL EFFECTS ON PERISTALTIC TRANSPORT OF VISCOUS FLUID UNDER VARIOUS CONDITIONS

Abstract

Peristaltic flow is a transport mechanism characterized by the contraction and relaxation of flexible tubes. Peristalsis is primarily used in the human body to transport fluids. Peristalsis is a fundamental process that moves food automatically through the digestive tract, urine from the kidneys to the bladder through the ureters, food mixing, chime movement in the intestine, movement of spermatozoa in the ducts efferent of the male reproductive organ, movement of egg in the female fallopian tube, and transport of bile in bile duct. It has been suggested that peristalsis may be associated with the vasomotion of small blood vessels. Also, in many practical mechanisms pertaining to biomechanical systems pumping occurs through peristalsis. The peristaltic process has several applications as seen in the roller and finger pumps and in several bio-mechanical instruments (e.g., heart-lung machine, blood pump machine and dialysis machine). In nuclear industry the transportation of a toxic liquid uses peristalsis so that the valuable environment is not contaminated. The diameters of the tree trunks are found to change with time hence some investigators have studied peristalsis with reference to water transport in trees. The actual mechanism of motion of water to upper branches of tall trees from the ground is not well understood however it is speculated that free convection and peristalsis both contribute to this mechanism. Flow through porous matrix of the tree contributes to the translocation of water. Many researchers have contributed to explain peristaltic pumping in physiological systems through their experimental as well as theoretical research work. Thus, peristaltic flow has become the core interest of many recent studies of researchers/scientists owing to the wide applications. Several attempts have been made to analyze the peristaltic transport of physiological fluids, which are non-Newtonian in behavior. In non-Newtonian fluids, the shear stress and the shear rate may be correlated where both shear stress and shear rate may be time dependent and the fluid exhibits viscous as well as elastic characteristics. Therefore it is difficult to describe the non-Newtonian fluids by a single constitutive relationship between stress and strain rate. Moreover these constitutive equations lead to complicated mathematical problems. The non- ii Newtonian fluid study has gained interest due of its applications in several industrial and engineering processes. Many materials such as ketchup, blood, drilling mud, tooth-paste, certain polymer melts, oils and greases are treated as non-Newtonian fluids. It is known that blood, being a complex and electrically conducting fluid acts like a non-Newtonian fluid at low shear rates. Hence, numerous constitutive models have been projected to analyze the non-Newtonian characters of the fluid flow. Flow through porous medium has captivated significant attention in recent years due to its prospective applications in nearly all fields of engineering, biomechanics and Geo-fluid dynamics. Analysis of flow past a porous medium is used immensely in biomedical problems to understand the transport process in lungs, gall bladder and kidneys, to investigate inter vertebral disc tissues, cartilage and bones etc. Some of the physiological systems such as blood vessel consist of porous layers. Since peristalsis is also important in blood vessels, it will be interesting to know the effects of permeability on the peristaltic pumping. Porous medium models are applied to identify the various medical conditions and treatments (as in tumor growth and injections). As the fluid displays a loss of adhesion at the wetted wall, the fluid is made to slide along the wall resulting into slip flow, as seen in several applications: flow through pipes wherein chemical reactions occur at the walls, two-phase flows in porous slider bearings. Slippage is claimed to occur in non-Newtonian fluids, molten polymer and concentrated polymer solution as well. The class of non-Newtonian fluids that considers the couple stress and Jeffrey fluids has distinct characters. The couple stress model displays a generalization of the classical viscous Newtonian model that permits the polar effects for instance the existence of couple stresses and body couples in the fluid medium. The vital feature of this fluid is that, the stress tensor is asymmetric. The equations managing the couple stress fluid transport are of higher order in consideration with the standard Navier-Stokes equations. The couple stress fluid flow analysis is very helpful to make out the insight of the diverse physical problems as it possesses the mechanism to explain the rheological complex fluids such as liquid crystals, lubricants that include small quantity of iii polymer additive, human and animal blood and infected urine from a diseased kidney. Many authors have considered blood as a suspension of spherical rigid particles that give rise to couple stresses in a fluid. The non-Newtonian Jeffrey fluid explains the effect of the ratio of relaxation to retardation time and has captured the interest of numerous researchers in fluid dynamics. The Jeffrey model is one of the simplest linear models that describe the non-Newtonian fluid properties. Study of peristaltic motion of a Jeffrey fluid is quite helpful in physiology and industry because of its large number of applications and in mathematics owing to its solutions of nonlinear equations and complicated geometries. In physiology, many systems in the living body make use of peristalsis to drive or to mix the contents of a tube. Applications of Jeffrey fluid can also be seen in science and engineering: food and slurry transportation, thermal oil recovery, food processing and polymer, etc. In view of these, the study of peristaltic transport of a non-Newtonian fluid in porous medium is carried out in the thesis by considering characteristics such as wall effects, slip effects, Darcy effects, magnetic effects and heat transfer effects. The couple stress and Jeffrey fluid models are considered since these are considered to be better models for physiological fluids such as blood. The results are graphically illustrated with the help of MATHEMATICA software