On Models and Analysis of Curvature in Peristalsis of Rheological Materials

Abstract

Fluid flow by peristaltic mechanism is quite popular area due to its applications in physiology, mechanical and industrial engineering and nuclear industry. Mechanism of peristalsis is used in various physiological processes for example chyme movement in the gastrointestinal tract, ovum transportation in the female fallopian tube, spermatozoa delivery in the ductus afferents of the male reproductive tract, passage of lymph via lymphatic vessels, vasomotion of small blood vessels, urine passage from kidney to bladder etc. In nuclear industry peristalsis is useful during sanitary and corrosive materials transportation. Peristaltic action is also valid in biomedical engineering to design finger and roller pumps, dialysis and blood pump machines. The literature on the peristaltic flow at present is quite rich. However most of the studies involving viscous and non-Newtonian fluids are configured through planner/straight channel. In nature such configurations are not realistic when flows of physiological materials through glandular ducts and industrial liquids through pipes are considered. Therefore peristalsis through curved configurations seems more realistic. Further the simultaneous aspects of heat and mass transfer give very complicated expression between the fluxes and the driving potentials. In situations like this the energy flux can be induced not only by the temperature gradient but by composition gradient as well. In view of the above mentioned applications this thesis is prepared by considering features of radial magnetic field, porosity, mixed convection, thermal radiation and Soret and Dufour effects. Boundary conditions for channel walls are through physical constraints. This thesis has eleven chapters. Chapter wise detail here is given below. Chapter one is based upon literature survey on the peristaltic transport and some basic equations. Chapter two addresses the aspects of convective heat transfer and radial magnetic field for peristalsis of an incompressible Carreau fluid through curved channel. Joule heating is also present. Mathematical analysis is carried out under long wavelength and low Reynolds number considerations. Solutions of resulting non-linear system for small values of Weissenberg number are constructed. The salient features of flow quantities are pointed out with particular focus to pumping, velocity, temperature and trapping. It is observed that pressure gradient enhances for larger values of power law index parameter. This analysis is published in AIP Advances 6 (2016) 045302. Chapter three consists of the analysis of peristaltic mechanism of Carreau nanoliquid in a curved channel. Features of radial MHD and mixed convection are retained. Heat and mass transfer phenomena is discussed in view of Brownian motion and thermophoresis impacts. Zero mass flux at the channel walls is taken. The relevant equations are first modelled and then simplified through lubrication technique. The system of non-linear equations is solved numerically. Plots for velocity, temperature and concentration are studied. Heat and mass transfer rates at the upper wall of the curved channel is also discussed. The results of this study are published in Results in Physics 7 (2017) 451-458. Chapter four contains Hall and MHD effects on peristaltic transport of Carreau-Yasuda fluid through convectively heated curved configuration. Thermal radiation and Soret and Dufour effects are also accounted. The channel walls comprised the no slip and compliant properties. Constitutive equations for mass, momentum, energy and concentration are first modelled in view of considered assumptions and then simplified under long wavelength and low Reynolds number approximation. Solution of the resulting system of equations is carried out by regular perturbation technique. Physical behaviors of velocity, temperature, concentration and streamlines are discussed with the help of graphical representation. The contents of this chapter are published in Journal of Magnetism and Magnetic Materials 412 (2016) 207-216. Chapter five examines peristalsis of non-Newtonian liquid in curved channel. Soret and Dufour and radial magnetic field effects are present. Channel walls are of compliant properties. Problem formulations for constitutive equations of Jeffrey fluid are made. Lubrication approach is implemented for the simplification of mathematical analysis. Dimensionless problems of stream function, temperature and concentration are computed numerically. Characteristics of distinct variables on the velocity, temperature, coefficient of heat transfer and concentration are examined. Besides this graphical results indicates that velocity profile enhances significantly for compliant wall parameters. However due to the resistive characteristics of Lorentz force the velocity profile decays. Furthermore it is noted that temperature profile enhances for larger Dufour number whereas reverse behavior is noticed to concentration profile when Soret and Schmidt numbers are increased. Such observations are accepted for publication in Scientia Iranica. Chapter six discusses entropy generation for peristaltic flow of Jeffrey material in a curved configuration. Velocity and thermal slip conditions are invoked. An incompressible fluid in a channel saturates the porous space. Modelling is based upon modified Darcy's law for Jeffrey fluid. Large wavelength and low Reynolds number approximations are utilized. Exact solutions of the resulting system of differential equations with corresponding boundary conditions are computed. Further analysis is made for the pressure gradient, stream function, velocity, temperature, entropy generation and Bejan number. It is found that entropy generation and Bejan number are more visible in the vicinity of the channel walls when compared at channel center. The results of this chapter are published in International Journal of Heat and Mass Transfer 106 (2017) 244-252. Chapter seven investigates the influences of radial magnetic field on peristalsis of EyringPowell liquid in a curved channel. The channel walls satisfy the convective conditions of heat transfer. Problem formulation is made using conservation laws of mass, linear momentum and energy. Perturbation solutions of the resulting problems for flow and temperature through lubrication approach are developed. Attention is mainly focused to the outcome of involved sundry parameters on the pressure gradient, pressure rise, frictional force, velocity and temperature. Phenomena of pumping and trapping are also analyzed. The obtained results of this chapter are submitted in Journal of the Brazilian Society of Mechanical Science and Engineering. Chapter eight addresses impact of Darcy-Forchheimer relation and radial magnetic field on peristalsis of Eyring-Powell nanomaterial in a curved channel. The channel boundaries satisfy the velocity slip and Newtonian heat and mass conditions. The present analysis involves mixed convection, Brownian motion and thermophoresis. The modelled equations are satisfied subject to long wavelength and low Reynolds number. Numerical solution of dimensionless non-linear system is obtained by employing built-in shooting algorithm in Mathematica. Numerical solutions for velocity, temperature and concentration are discussed. The contents of this chapter are published in International Journal of Heat and Mass Transfer 115 (2017) 694-702. Chapter nine explores peristaltic motion of micropolar fluid in the presence of radial magnetic field. Analysis is arranged when homogeneous-heterogeneous reactions effects are accounted. Heat source/sink and Newtonian heating effects are also considered. Small Reynolds number and large wavelength are employed. Solutions of the resulting coupled equations are constructed. The resulting expressions for pressure gradient, pressure rise, velocity, temperature, concentration and stream function are utilized and discussed graphically. The micropolar and coupling parameters have conflicting impacts on pressure gradient, pressure rise and velocity. Such results are published in Journal of Molecular Liquids 223 (2016) 469-488. Chapter ten examines Soret and Dufour effects on peristaltic transport of an Oldroyd 8- constants fluid in a curved channel. Aspects of mixed convection and radially applied magnetic field are considered. Convective conditions of heat and mass transfer at the channel walls are imposed. Governing problems for velocity, temperature and concentration are reduced for long wavelength and low Reynolds number considerations. Resulting problems are analyzed numerically. Specifically the analysis of velocity, temperature, concentration and heat transfer coefficient are focused for the emerging parameters. It is noticed that axial velocity enhances for larger material parameter of fluid. Impact of mixed convection decays axial velocity. Furthermore temperature and concentration have opposite behavior for Soret and Dufour numbers. The contents of this chapter are published in International Journal of Thermal Sciences 112 (2017) 68-81. Chapter eleven studies the peristalsis of non-Newtonian nanoliquid with gyrotactic microorganism in a curved channel. Channel boundaries comprises the wall properties and second order slip conditions for velocity. Consideration of Newtonian heat, mass and gyrotactic microorganisms aspects characterizes the heat, mass and motile density transfer processes. Flow formulation is established utilizing constitutive relations of Sisko fluid. Lubrication theory is employed for the simplification of governing expressions. Numerical solution is carried out for velocity, temperature, concentration and motile density gyrotactic microorganisms. Graphical discussion determined that velocity has opposite behavior for first and second order velocity slip parameters. Interestingly Sisko fluid parameter has opposite impact on velocity for both shear thinning and shear thickening cases. It is seen that temperature enhances for Newtonian heating whereas concentration and gyrotactic microorganism are reduced for Newtonian mass and Newtonian gyrotactic microorganisms. The contents of this chapter are published in International Journal of Heat and Mass Transfer 112 (2017) 521-532.