On the Mathematical Modeling of Two and Three Dimensional Flows of Nanofluid

Abstract

Nanofluids are relatively new class of heat transfer fluids which exhibit much higher thermal conductivity in comparison to the conventional coolants even at low particle concentrations. This enhanced thermal behavior has been vital in several technological and biomedical applications such as solar water heating, cooling of transformer oil, delivery of drugs and radiation in cancer patients, space cooling, power generation and many others. On the other hand, the flow over deformable surfaces has potential engineering applications such as metal and polymer extrusion, die forging, crystal growth processes and many others. Moreover flows in rotating frame are prominent in sand milling, mixing, viscometery, centrifugal filtration process, rotating machinery, chemical and food processing and many other. In the dissertation, we employ the two famous models namely the Buongiorno’s model and the Tiwari and Das model to analyze some interesting two and three dimensional boundary layer flow problems involving nanofluids. Several new results pertaining to the considered problems have been established. Chapter 1 is introductory in nature and contains some basic preliminaries and detailed review related to the problems considered in subsequent chapters. The boundary layer equations through both nanofluid models have also been presented. In Chapter 2, we discuss the three-dimensional flow of nanofluid developed by a bi-directional stretching surface. Aspects of Brownian motion and thermophoresis are considered in the mathematical model. Numerical simulations for interesting flow parameters are performed by shooting method. The numerical solutions are compared with the existing literature in limiting sense and found in very good agreement. Plots for velocity, temperature and nanoparticle volume fraction are presented and explained. The key points of this chapter have been published in Journal of Molecular Liquids 194 (2014) 41- 47 (Impact Factor: 2.515) Chapter 3 deals with the axisymmetric flow of nanofluid driven by a non-linearly stretching surface. Here the general power-law surface velocity and temperature distributions are assumed. Different from Chapter 2, the passively controlled wall nanoparticle volume fraction is employed here. Numerical computations with high precision are presented by Keller-Box method. Graphical results for skin friction coefficient and local Nusselt number are presented. The main frame work of this Chapter has been published in International Journal of Non-Linear Mechanics 71 (2015) 22–29 (Impact Factor: 1.977). viii Bödewadt flow is the three-dimensional motion of viscous fluid due to its rotation at sufficiently larger distance from stationary disk. Chapter 4 explores the Bödewadt flow of nanofluid when the disk is subjected to uniform stretch in the radial direction. Tiwari and Das model has been employed for the problem formulation. Three different nanoparticles namely Copper-Cu, Copper-oxide –CuO and Silver-Ag are considered with water as the base fluid. The arising non-linear system is tackled by Keller-Box method. The results of this work have appeared in Journal of Molecular Liquids 211 (2015) 119–125 (Impact Factor: 2.515). Chapter 5 analyzes the Bödewadt flow of nanofluid by considering the novel aspects of Brownian motion and thermophoresis. Numerical results for velocity, temperature and concentration are obtained by Keller-box method. A comparison of the results with available study of Turkyilmazoglu (Int. J. Mech. Sci. 90 (2015) 246-250) is shown in a limiting case, which is very good. The main contents of this chapter have been submitted for publication. Chapter 6 describes the three-dimensional flow of nanofluid induced by a bi-direction exponentially stretching surface. Here the temperature and nanoparticle volume fractions at the surface are also exponentially distributed. Buongiorno’s model accounting for combined influence of Brownian motion and thermophoresis is employed for the problem formulation. Keller-box method is utilized for computing numerical results. The findings of this Chapter have been published in PloS ONE 10 (2015) e0116603 (Impact Factor: 3.234). Chapter 7 extends the contents of Chapter 6 by considering more realistic convective surface boundary conditions. Here the passively controlled model for nanoparticle volume fraction is also employed. The contents of the Chapter have appeared in Canadian Journal of Physics http://dx.doi.org/10.1139/cjp-2014-0433 (Impact Factor: 0.964). Chapter 8 investigates the two-dimensional flow of viscoelastic nanofluid caused by an exponentially stretching sheet. Upper-convected Maxwell model is utilized for the formulation of momentum equation whereas energy and nanoparticle concentration equations are formulated in view of Buongiorno’s model. Numerical results are derived by shooting method and validated by the MATLAB built-in routine bvp4c. The main results of this Chapter have been published in AIP Advances 5 (2015) 037133 (Impact Factor: 1.524). Chapters 9 and 10 report the numerical solutions for two- and three- dimensional flows of nanofluid induced by a power-law stretching surface. Numerical results are presented and analyzed through shooting method. The results of Chapters 9 and 10 have been appeared in ix IEEE transactions on nanotechnology 14 (2015) 159-168 (Impact Factor: 1.825) and International Journal of Heat and Mass transfer 86 (2015) 158-164 (Impact Factor: 2.383) respectively.