| Nano-technology has applications in a wide variety of ?elds like automotive industry,transportation, electronics such as supercomputers, cooling systems, power plants,arti?cial organs and many more. The research on nano?uids are mainly categorized into two categories; basic research and applied research including buildup and experiments. Basic researchers contribute by explaining the anomalous behavior of nano?uids whereas applied researchers make their worthy contributions by designing e?cient nano?uids. Due to highly interdisciplinary nature of nano?uids a uni?ed approach is proposed in this dissertation to further enhance the basic research in nano?uids through di?erent aspects. The main idea of this basic research is to formulate and investigate new problems, which are broadly categorized as one-, twoand three-dimensional ?ows, respectively. The homotopy analysis method(HAM)is found to be reliable and good enough to study one-, two- and three-dimensional?ows of Newtonian and non-Newtonian ?uids with nanoparticles. This dissertation presents the basic research in muliti-layer ?ows of Newtonian and non-Newtonian(third-grade) ?uids, Falkner-Skan ?ows of Newtonian and non-Newtonian(Maxwell and Oldroyd-B) ?uids, non-similarity boundary layer ?ow of stretching surfaces and free convection ?ow in the stagnation point region of a three-dimensional body, with nanoparticles, respectively.It is well-known from a technological point of view that multi-layer ?uid models play a very important role to understand the interactions between di?erent layers consisting of di?erent types of ?uids and their e?ects on ?ow and heat transfer characteristics. Some important and physically more reasonable non-dimensional quantities are used to model one-dimensional multi-layer phenomenon, a uni?ed approach is adopted to obtain the convergent series solutions in these situations also heat and mass transfer analyses have been incorporated in Chapter 2, 3 and 4.In ?uid mechanics, the Falkner-Skan boundary layer ?ow is signi?cant and fundamental in both theory and practice. Such kind of ?ows are particularly more frequent in enhanced oil recovery, packed bed reactor geothermal industries, etc. The successful applications of BVPh 2.0( which is combination of HAM and computer software algebra M athematica) for the two-dimensional Falkner-Skan ?ows of Newtonian ?uid,Maxwell ?uid and Oldroyd-B ?uid, with nanoparticles in the presence of magnetohydrodynamics(MHD) are included in Chapter 5, 6 and 7. These Chapters provide detailed analyses of the ?ow, temperature, concentration, the local skin friction coe?cient, the local Nusselt number and the local Sherwood number for various values of governing physical parameters.Boundary-layer ?ows under similarity transformations exhibits same velocity pro-?les at di?erent x. However, such kind of similarity is lost for non-similarity ?ows.Obviously, the non-similarity boundary-layer ?ows are more general in nature and more important not only in the theory but in applications as well. The HAM is successfully applied to obtain the convergent series solutions for the two-dimensional non-similar boundary layer ?ow of viscous ?uid with nanoparticles. Fundamental equations employed in the mathematical modelling include the novel aspects of Brownian motion and thermophoresis. Non-similar ?ow is induced by a stretching sheet with arbitrary velocity. Two di?erent forms of stretching velocity are analyzed. Appropriate non-similar transformations are utilized to non-dimensionalize the governing equations of momentum, energy and concentration. For this purpose, the velocity,temperature and concentration of nano?uids are assumed to vary with distance. It is hoped that this research work serves as a stimulus in future for further developments on non-similar ?ows in the regime of viscous and non-Newtonian ?uids with nanoparticles.Finally the series solutions are presented for a steady three-dimensional free convection ?ow in the stagnation point region over a general curved isothermal surface placed in a nano?uid by using HAM. The momentum equations in x- and y-directions,energy balance equation and nanoparticle concentration equation are reduced to a set of four fully coupled nonlinear di?erential equations under appropriate similarity transformations. Flow, heat and mass transfer analyses are presented for various values of physical parameters in detail.This dissertation shows the validity and generality of the HAM in the study of boundary layer ?ows of Newtonian and non-Newtonian ?uids with nanoparticles.The heat and mass transfer analyses are incorporated. We have strived to include the rigorous and systematic methodology to obtain series solutions for multi-layer ?ows.It is attempted to provide series solutions of non-similarity boundary layer ?ows that will serve for further developments to study nano?uids in di?erent aspects. |
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