Peristaltic Flows With Heat and Mass Transfer in a Curved Channel

Abstract

Peristaltic pumping is a fluid transport phenomenon which is attained through a progressive dynamic wave of expansion or contraction propagating along the walls of a distensible tube containing fluid. Many researchers, biologists, engineers and physicist studied peristaltic transport in different geometries due to its wide range applications in numerous fields. It is an intrinsic phenomena of several biological/physiological systems such as reproductive system, nervous system, digestive system, cardiovascular system and renal system. Several modern engineering devices also operate on the principle of peristalsis. Examples abound: diabetic pumps, corrosive fluid transport pumps in nuclear industry, roller and finger pumps, pharmacological delivery pumps, infusion pumps etc. In recent times, electro osmosis-modulated peristaltic transport in micro fluids channel is proposed as a model for the design of lab-on-a-chip device. It is evident from above mentioned applications that peristaltic motion is the nature’s as well as humans way of transporting the fluids. Heat transfer is an important phenomenon of nature, which works on the first law of thermodynamics. According to this law the energy added per unit mass to a closed system increases the total energy per unit mass of the system (fluid). The application of this law to flowing fluid yield the well-known energy equation. The study of non-isothermal peristaltic flows required the application of both momentum and energy equations. The motivation to analyze heat transfer in peristaltic flows arises due to applications of such flow in hemodialysis process, blood pumps, dispersion of chemical impurities, heart lung machine and corrosive fluids transport in machines. Moreover, temperature variations inside the fluid may affect the bolus movement. The latest techniques of heat transfer like cryosurgery and laser therapy have also inspired researchers for thermal modeling in tissues. Mass transfer phenomenon is vital in the diffusion process such as the nutrients diffuse out from the blood to the contiguous tissues. A multifarious relationship is observed between driving potentials and fluxes when heat and mass transfer are considered simultaneously. The analysis of peristaltic flow with heat and mass transfer is of valuable importance due to its promising applications in biomedical sciences. Example abound: conduction in tissue, convection due to circulation of blood in porous tissue, food processing and vasodilation. It is important to point out the mass diffusion from boundaries into the fluid is always happening in physiological flows and therefore a complete analysis of such flows must incorporate concentration equation along with momentum and energy equations. The utility of peristaltic flow with heat and mass transfer is further enhanced when curvature effects with non-Newtonian characteristics of the fluid are also integrated in the whole analysis. However, not much literature is available pertaining to peristaltic flows of complex fluids with heat/ mass transfer through a curved channel. Motivated by this fact the main objective of this thesis is to develop and simulate mathematical models of peristaltic flows with heat/ mass transfer in a curved channel. The model development is achieved through the use of fundamental conservation laws of mass, momentum, energy and concentration for fluids. Employing these laws, a system of partial differential equations is developed which is later simplified by using physiologically relevant approximations. The reduced system is simulated by using appropriate numerical technique. The solution obtained through this technique is later used to explain physical structure of flow and heat/ mass transfer features. This thesis is composed on following nine chapters. Chapter 1 starts with brief explanation of the topics such as peristaltic flow, non Newtonian fluids and heat/ mass transfer. The fundamental equations and dimensionless number related to the topic of research are provided in the main body. A comprehensive review of the available literature on peristaltic flows is also presented at the end. Chapter 2 investigates the hydromagnetic peristaltic flow in a porous-saturated heated channel by utilizing Darcy-Forchiemmer law. The equations for velocity, temperature and mass concentration are developed by using the delta approximation. A finite difference scheme is employed to solve these equations. The effects of pertinent rheological parameters are thoroughly investigated. It is observed that presence of porous media obstructs the flow velocity and reduces circulations of streamlines. The results of this chapter are published in Thermal Science; TSCI170825006A. Chapter 3 explores the heat and mass transfer to mixed convective hydromagnetic peristaltic flow in a curved channel in the presence of joule heating. Boussinesq approximation is used to couple the momentum and energy equations. Numerical solution of these equations is developed by neglecting the inertial and streamline curvature effects. The results of simulations are displayed graphically. It is noted that thermal Grashof number enhances the temperature while it has an opposite effect on mass concentration. The results of this chapter are submitted for publication in Theoretical and Computational Fluid Dynamics. Chapter 4 presents the analysis of heat/ mass transfer to peristaltic flow of Sisko fluid in a curved channel. The fundamental equations are derived by employing an orthogonal coordinate system for delta approximation. The effect of relevant parameter are observed on velocity, pressure rise, temperature and concentration fields and streamlines. It is observed that circulating bolus shift from upper half to the lower half of the channel as we switch from shear-thinning to shear-thickening fluid. The results of this chapter are published in Thermal Science; TSCI161018115A. Chapter 5 provides modeling and simulations for peristaltic flow of Carreau fluid model with heat/ mass transfer in a curved channel. The calculations for axial velocity, pressure rise per wavelength, temperature and concentration fields and stream function are carried out under delta approximation in the wave frame by employing suitable numerical implicit finite difference technique. It is noticed that rapid changes occur in flow velocity and streamlines for shear-thinning fluids due to which a boundary layer develop in the vicinity of channel walls for increasing values of Hartmann number. Furthermore, the amplitude of heat transfer coefficient is suppressed for larger values of channel curvature, power-law index and Hartmann number. The results of this chapter are submitted for publication in Communications in Theoretical Physics. Chapter 6 investigates the analysis of peristaltic flow of Rabinowitsch fluid in a curved channel with heat transfer. The reduced set of equations is solved via a semi-analytic procedure while energy equation is simulated numerically using Mathematica routine “NDSolve”. The effects of important parameters on flow velocity, temperature field and streamlines are shown in detail. It is observed that with increasing coefficient of pseudoplasiticity flow velocity achieve symmetric profile. Moreover, flow velocity becomes symmetric with increasing dimensionless radius of curvature. The fluid temperature inside the channel rises with increasing the coefficient of pseudoplasiticity. The results of this chapter are published in Zeitschrift für Naturforschung A 2016; 72(3): 245–251. Chapter 7 investigates the effects on heat and mass transfer in peristaltic flow of magnetically influenced incompressible micropolar fluid model through a curved channel. The set of fundamental equations is derived by utilizing delta approximation. The effects of coupling number, micropolar parameter, Hartmann number and curvature parameter on velocity, pressure rise and temperature and concentration fields are thoroughly examined. It is observed that the axial velocity rises with increasing micropolar parameter in vicinity of the lower wall while it shows opposite behavior near the upper wall. The fluid bolus concentrated in vicinity of upper part of the channel for lower values of micropolar parameter splits into two parts with increasing micropolar parameter. The results of this chapter are submitted for publication in Journal of fluid mechanics. Chapter 8 reveals the features of heat and mass transfer in peristaltic flow of bi-viscosity fluid through a porous-saturated curved channel in the presence of magnetic field and Joule heating effect. The governing equations are reduced by using delta approximation and then integrated numerically using FDM. It is noted that bi-viscosity fluid parameter, permeability parameter and Hartmann number have similar effects on the axial velocity. The results of this chapter are submitted for publication in Results in physics.