NUMERICAL SIMULATIONS OF PROBLEMS OF FLOW, HEAT AND MASS TRANSFER IN NANOFLUIDS

Abstract

The work in this thesis is concerned with a numerical study of the ow, heat and mass transfer problems of nano uids with both Newtonian and non-Newtonian uids as base uids. Due to several drawbacks of single phase model, we have used two-phase non-homogeneous model, proposed by Buongiorno [40] in 2006, to derive the equation governing the ow, heat and mass transfer in nano uids. It was observed that the Brownian motion, thermophoresis and di usiophoresis are the main mechanisms which are responsible for the enhancement of the convection features of the nano uid. The enhancement of various characteristics of uid ow has also been studied for porous medium. Numerical simulation of the problems is carried out using conventional nite element methods (h-FEM) and higher order nite element methods (p-FEM, hp-FEM). Double mesh principle is used to check the convergence of obtained results. The whole work of the thesis is divided into eight chapters and chapter-wise summary of the thesis is as follows: Chapter 1 focuses on introduction and gives the basics for development on nano uids, current status of the eld, motivation to the investigations carried out in this thesis and a review of the literature mainly related to the thesis. Further, the basic equations governing the boundary layer ow are also given. Chapter 2 investigates the transient magnetohydrodynamic (MHD) natural convective boundary layer ow and heat transfer of a nano uid over an inclined plate, with a transverse magnetic eld applied normal to the plate plane. The iii iv presence of Brownian motion and thermophoresis e ects lead to a coupled nonlinear boundary value problem. Convective boundary conditions have been handled for the thermal boundary layer problem. The e ect of various physical parameters magnetic eld parameter M, angle of inclination , Brownian motion parameter Nb, thermophoresis parameter Nt on velocity, temperature, concentration, local heat and mass transfer is studied. Such problems nd applications in many industrial and engineering applications such as electroplating, chemical processing of heavy metals, solar water heaters. In the Chapter 3, steady double di usive boundary layer ow of nano uid over a power law stretching sheet is studied. In this model, where binary nano uid is used, the Brownian motion, thermophoresis and cross-di usion are classi ed as the main mechanisms which are responsible for the enhancement of the convection features of the nano uid. hp-FEM is used to compute the numerical results. The e ects of the modi ed Dufour number Nd, non-linear stretching parameter m, regular Lewis number Le and Dufour Lewis number Ld on the uid properties as well as on the heat, regular and nano mass transfer coe cients are determined and shown graphically. The present study has many applications in polymer extrusion, drawing of copper wires, continuous stretching of plastic lms, arti cial bers and metal extrusion etc. Chapter 4 focuses on the magnetohydrodynamic boundary layer ow and heat transfer of a non-Newtonian nano uid over a stretching sheet, taking into account the e ects of velocity slip, internal heat source/sink. The boundary condition at the surface is taken as partial slip condition. Numerical results were obtained for the modi ed Nusselt, nanoparticle Sherwood number as well as for the velocity, temperature and nanoparticle concentration pro les for the slip parameter K0, the magnetic parameter M, second grade parameter k1, uniform heat source/sink parameter Q. The rate of heat transfer at the surface is a decreasing function of slip parameter, magnetic parameter and uniform heat source/sink parameter. However, v rate of heat transfer increases with an increase in the second grade parameter i.e., enhancement in heat transfer is observed for non-Newtonian nano uid as comparison to Newtonian nano uid. The study of ows with partial slip is important in the micro-electromechanical systems (MEMS). Chapter 5 concentrates on the numerical study of heat and mass transfer in 2D ow of an incompressible non-Newtonian nano uid over a stretching sheet in the presence of thermodi usion e ects. The results are supplemented with the data for the modi ed Nusselt number and the two modi ed Sherwood numbers, one for the solute and the other for the nanoparticles. It is observed that the modi ed solute Sherwood numbers is signi cantly higher for double-di usion in regular uids and nano uids then for mono-di usion in regular uids and nano uids. A signi cant increment in heat transfer rate with increase of second grade parameter is observed which concludes the wide impact of stretching process on heat transfer rate in some of the engineering and manufacturing processes such as cooling of metallic sheets and drawing of plastic sheets. In Chapter 6, an analysis is carried out to investigate the conjugate e ects of viscous dissipation, non-uniform heat source/sink and work done due to deformation on the double-di usive boundary layer ow of a viscoelastic nano uid over a stretching sheet. The analysis has been carried out for two di erent cases, namely, prescribed surface temperature (PST) and prescribed heat ux (PHF) to see the e ects of governing parameters for various physical conditions. The result indicates that the addition of nanoparticles and the salt in the base uid (viscoelastic uid) increases the heat transfer rates. Heat transfer is increasing function of viscoelastic parameter and decreasing function of Eckert number Ec, Prandtl number Pr and non-uniform heat source/sink A ; B . Thus, di erent types of viscoelastic nano uids can be used as a controlling agent for fast and slow removal of heat from the sheet. The physics of the problem is well explored for the embedded material parameters through tables and graphs. vi Chapter 7 deals with the thermal-di usion and di usion-thermo e ects on the 3d boundary layer ow of a elastico-viscous nano uid over a stretching surface. We have examined the e ects of di erent controlling parameters, namely, stretching ratio c, viscoelastic parameter k1, modi ed Dufour number Nd, regular Lewis number Le and Dufour Lewis number Ld on the ow eld, heat, regular and nano mass transfer characteristics. The physics of the problem is well explored for the embedded material parameters through tables and graphs. It has been noted that the skin friction coe cients, the modi ed Nusselt number, modi ed solutal number and modi ed nanoparticle Sherwood number increase with stretching ratio parameter. In the last Chapter 8, triple di usive natural convection over an inclined plate embedded in a porous medium saturated with a binary base uid containing nanoparticles and two salts is studied. The model used for the nano uid incorporates the e ects of Brownian motion, thermopherosis and di usiophoresis, while the Darcy model is used for the porous medium. In addition the thermal energy equations include regular di usion and cross-di usion terms. The vertical surface has the heat, mass and nanoparticle uxes each prescribed as a power law function of the distance along the wall. A wide range of parameter values are chosen to bring out the e ect of buoyancy ratio, regular Lewis number and modi ed Dufour parameters of both salts and nano uid parameters on the free convection process with varying angle of inclinations making the wall geometry from vertical to horizontal plate. The e ect of parameters on the velocity, temperature, solutal and nanoparticles volume fraction pro les, as well as on the important parameters of heat and mass transfer, i.e., modi ed Nusselt, regular and nanoparticle Sherwood numbers, are discussed. It is found that with the inclusion of nanoparticles and salts in the base uid, there is an enhancement in the heat transfer rate. The thesis, nally, ends with the future scope of the research work, appendices and bibliography.