Three dimensional nonlinear flow problems in the presence of nanoparticles

Abstract

Nanofluids are engineered colloids made of base fluid and nanoparticles (1-100 nm). The nanoparticles colloids have certain physical characteristics that enhance their importance in industrial applications like ceramics, paints, coatings, food industries and drug delivery systems. These colloids are made of ultrafine nanoparticles. The ultra-high performance cooling is one of the major requirements of present industrial technologies. Metals (Cu, Fe, Al and Au), oxide ceramics (CuO and Al₂O₃), carbide ceramics (TiC and SiC), single, double or multiple wall nanotubes (SWCNT, DWCNT and MWCNT), semiconductors (SiO and TiO₂) and various composite materials are implemented in the production of nanoparticles and are submerged in a working fluid to make them nanofluids. The nanofluids are usually used to overcome the poor thermal performance of ordinary fluids like propylene glycol, water, oil and ethylene glycol. Nanotechnology is very useful in the development of better lubricants and oils. Such consideration is successfully implemented now in field of biomedical engineering like cancer therapy and safer surgery. The boundary-layer flows due to stretching surface are prominent in plastic and metal industries like annealing and thinning of copper wires, drawing of stretching sheets through quiescent fluids, polymer filament or sheet extruded from a dye, manufacturing of plastic and rubber sheets, continuous cooling of fiber spinning, boundary layer along a liquid film condensation process and aerodynamic extrusion of plastic films. There is no doubt that nanofluids have vital role in the heat transfer enhancement. Thus we intend to study the boundary-layer flows in the presence of nanoparticles. It is further noted that two-dimensional flow problems in literature are much studied when compared with the three-dimensional flow problems. Keeping such facts in mind the prime objective of present thesis is to analyze three-dimensional flow problems of nanofluids due to stretching surface. The present thesis is structured as follows. Chapter one contains literature survey of relevant previous published works and laws of conservation of mass, momentum, energy and concentration transport. Mathematical formulation and boundary-layer expressions of Maxwell, Oldroyd-B, Jeffrey and Sisko fluids are provided. Basic concept of optimal homotopy analysis method is also included. Chapter two addresses three-dimensional flow of viscous nanofluid in the presence of Cattaneo-Christov double diffusion. Thermal and concentration diffusions are considered by introducing Cattaneo-Christov fluxes. Novel features of Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system is done through suitable transformations. The obtained nonlinear systems are solved. Graphs are plotted in order to analyze that how the temperature and concentration profiles are affected by distinct physical parameters. Skin friction coefficients and rates of heat and mass transfer are numerically computed and addressed. The contents of this chapter are published in Results in Physics 6 (2016) 897-903. Chapter three explores three-dimensional flow of viscous nanofluid characterizing porous space by Darcy-Forchheimer relation. Both thermal convective and zero nanoparticles mass flux conditions are utilized. The modeled systems are reduced into dimensionless expressions. The governing mathematical system is solved by optimal homotopy analysis method (OHAM). Importance of physical parameters is described through the plots. Numerical computations are presented to study skin-friction coefficients and Nusselt number. The outcomes of this chapter are published in Results in Physics 7 (2017) 2791-2797. Chapter four examines three-dimensional flow of Maxwell nanofluid. Flow is generated due to a bidirectional stretching surface. Mathematical formulation is performed subject to boundary layer approach. Heat source/sink, Brownian motion and thermophoresis effects are considered. Newly developed boundary condition requiring zero nanoparticle mass flux at boundary is employed. The governing nonlinear boundary layer expressions are reduced to nonlinear ordinary differential system through appropriate transformations. The resulting nonlinear system has been solved. Graphs are plotted to examine the contributions of various physical parameters on velocities, temperature and concentration fields. Local Nusselt number is computed and examined numerically. The results of this chapter are published in Applied Mathematics and Mechanics-English Edition 36 (2015) 747-762. Chapter five describes magnetohydrodynamic (MHD) three-dimensional flow of Maxwell nanofluid subject to convective boundary condition. Flow induced is by a bidirectional stretching surface. Effects of thermophoresis and Brownian motion are present. Unlike the previous cases even in the absence of nanoparticles, the correct formulation for the flow of MHD Maxwell fluid is established. Newly suggested boundary condition having zero nanoparticles mass flux is utilized. The resulting nonlinear ordinary differential systems are solved for the velocities, temperature and concentration distributions. Effects of physical parameters on temperature and concentration are plotted and examined. Numerical values of local Nusselt number are computed and analyzed. The contents of this chapter are published in Journal of Magnetism and Magnetic Materials 389 (2015) 48-55. Chapter six presents three-dimensional flow of Maxwell nanofluid subject to rotating frame. Flow is induced by uniform stretching of boundary surface in one direction. Novel aspects of Brownian diffusion and thermophoresis are accounted. Boundary layer approach is invoked to simplify the governing system of partial differential equations. Suitable variables are introduced to non-dimensionalize the relevant boundary layer expressions. Newly proposed boundary condition associated with zero nanoparticles mass flux is imposed. Uniformly valid convergent solution expressions are developed through optimal homotopy analysis method (OHAM). Graphs have been sketched in order to explore the role of embedded flow parameters. Heat transfer rate has been computed and analyzed. The outcomes of this chapter are published in Journal of Molecular Liquids 229 (2017) 541-547. Chapter seven examines three-dimensional rotating flow of Maxwell fluid in the presence of nanoparticles. Flow is induced due to an exponentially stretching sheet. Optimal homotopic approach is employed for the solution of governing system. The optimal values of auxiliary parameters are computed. The optimal solution expressions of temperature and concentration are elaborated via plots by employing various values of involved parameters. Moreover the local Nusselt and Sherwood numbers are characterized by numerical data. The results of this chapter are published in Journal of Molecular Liquids 229 (2017) 495-500. Chapter eight addresses three-dimensional flow of MHD Oldroyd-B nanofluid. Flow is induced by a bidirectional stretching surface. Novel attributes of Brownian motion and thermophoresis are considered. Newly developed boundary condition requiring zero nanoparticles mass flux is employed. The governing nonlinear boundary layer equations through appropriate transformations are reduced into the nonlinear ordinary differential systems. The obtained nonlinear system has been solved for the velocities, temperature and concentration profiles. The contributions of various physical parameters are studied graphically. The local Nusselt number is tabulated and discussed. The contents of this chapter are published in Journal of Molecular Liquids 212 (2015) 272-282. Chapter nine explores magnetohydrodynamic (MHD) three-dimensional stretching flow of an Oldroyd-B nanofluid in the presence of heat generation/absorption and convective boundary condition. A condition associated with nanoparticles mass flux at the surface is utilized. The strong nonlinear differential equations are solved through optimal homotopy analysis method (OHAM). Effects of various physical parameters on temperature and concentration are studied. The local Nusselt number is also computed and analyzed. The outcomes of this chapter are published in International Journal of Thermal Sciences 111 (2017) 274-288. Chapter ten extends the analysis of chapter eight for Jeffrey nanofluid. The results of this chapter are published in Zeitschrift für Naturforschung A 70 (2015) 225-233. Chapter eleven presents bidirectional stretched flow of Jeffrey nanofluid subject to convective boundary condition. Modeling and computations are prepared subject to thermophoresis, Brownian motion and zero nanoparticles mass flux. Computational results for the velocities, temperature, concentration and Nusselt number are presented. The contents of this chapter are published in Journal of Aerospace Engineering 29 (2016) 04015054. Chapter twelve examines combined effects of magnetic field and nanoparticles in three-dimensional flow of Sisko fluid. Nanofluid for Brownian motion, thermophoresis and zero nanoparticles mass flux at surface is adopted. Nonlinear differential systems are solved first for the convergent solutions and then analyzed. The outcomes of this chapter are published in Advanced Powder Technology 27 (2016) 504-512. Chapter thirteen is prepared to extend the flow analysis of previous chapter in presence of convective condition. The results of this chapter are published in Journal of Magnetism and Magnetic Materials 413 (2016) 1-8. Chapter fourteen presents the major findings and some possible extensions of presented research work.