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