Flow and Heat Transfer Analysis of Some Newtonian and Non-Newtonian Fluids

Boundary layer flow in Newtonian and non-Newtonian fluids is encountered in many industrial processes. Particularly boundary layer flow over stretching surface is significant due to their practical applications in processes involving continuous pulling of sheet in textile and paper industries and in the manufacturing of polymer sheets, sheet glass and crystalline materials. Processes like paper production, wire drawing, crystal growth, drawing of plastic films, food processing, metal spinning process, cooling of metallic plate in a cooling bath etc. involves the phenomena of a continuous stretching sheet. In these processes the quality of final product is strongly dependent upon the temperature provided in the process. Therefore to discuss heat transfer characteristics of such boundary layer flows is also important. A literature survey reveals that a large number of research papers are available to discuss flow and heat transfer phenomena due to stretching sheet. This phenomenon is discussed both for two and three-dimensional boundary layer flows. The literature survey indicates that there is room for discussing the three dimensional boundary layer flows over an unsteady stretching surface. Motivated by the practical importance of such boundary layer flows we have discussed three-dimensional flows of viscous, Maxwell and Oldroyd-B fluids due to an unsteady bidirectional stretching sheet in the first half of this thesis. Furthermore, heat transfer analysis for these flows is also considered in the presence of heat source or sink. Some industrial and biological processes involve the flow situations when one fluid is flowing over another fluid having thin layer usually known as a lubrication layer. These have applications in living systems, such as flow pattern of red blood cells in narrow capillaries, liquid flow in the lungs, eye etc. and in the machinery components including fluid bearing and mechanical seals, coating, preparation of thin films and paintings. For the stretching flows with no-slip one has to deal with the nonlinear differential equations with linear boundary conditions. However, for the boundary layer flow over a lubricated surface one needs to solve nonlinear differential equations subject to nonlinear boundary conditions. These nonlinearities in boundary conditions make the system more complicated and analytic solutions are hard with the standard analytical methods. Furthermore, governing equations of non-Newtonian fluids have higher order then the available boundary conditions and in the stretching and stagnation point flows, the coefficient of the leading derivative vanishes at the starting point of the domain. Due to this fact the numerical solutions by a standard integration scheme is not possible. Researchers have adopted different methods to tackle such difficulties. In the second part of this thesis we have discussed the boundary layer flows of second and third grade fluids over a lubricated surface with a power law lubricant. For handling nonlinear boundary conditions we have used the combination of homotopy analysis and shooting methods. The literature is scarce for the flow of non-Newtonian fluids over a lubricated surface. This encourages us to consider flow and heat transfer of non-Newtonian fluids over a lubricated surface. In view of the above mentioned discussion, the thesis is structured as follows. Chapters one covers the literature survey and laws of conservation of mass, momentum and energy. Boundary layer equations of second grade, third grade, Maxwell and Oldroyd-B fluids are also presented. Solution methodology via homotopy analysis method (HAM) and hybrid homotopy analysis method (HHAM) is also given in this chapter. Chapter two addresses the unsteady three-dimensional flow of an incompressible viscous fluid over an unsteady stretching surface in a porous medium. Fluid is electrically conducting and a constant magnetic field is applied in the transverse direction. Heat transfer through constant temperature (CT) and constant heat flux (CH) is also considered. Governing equations are simplified first by applying boundary layer approximations and then by a suitable similarity transformations. Analytical technique (HAM) is used to solve the nonlinear problems subject to linear boundary conditions. A comparison with the existing solutions is also presented for the special case. The leading results of this chapter are published in the journal “Thermal Science”. In chapter three, we have extended the analysis of chapter two for a Maxwell fluid. Boundary layer equations for the three-dimensional flow are used to discuss the flow and heat transfer phenomena. The results are discussed for the influence of pertinent parameters involved in the problem. The contents are accepted for publication in the “Journal of the Brazilian Society of Mechanical Sciences and Engineering”. Chapter four provides the three-dimensional flow and heat transfer of an Oldroyd-B fluid past an unsteady bidirectional stretching surface with constant temperature and constant heat flux. Boundary layer equations are developed for the three-dimensional flow. Similarity solutions are obtained using HAM and convergence of the series is discussed explicitly. The effects of emerging parameters on the velocity and temperature profiles are investigated through graphs and tabular data. Comparison of obtained and previously published work is found in excellent agreement. The results of this chapter are accepted for publication in “Journal of Applied Fluid Mechanics”. Chapter five is prepared to examine the flow and heat transfer analysis of second grade fluid over a lubricated surface. The power law lubricant is assumed to have a thin layer of variable thickness. The interface conditions between second grade fluid and power law lubricant give rise to nonlinear slip condition which is imposed on the boundary. Solutions for this problem are developed using hybrid homotopy analysis method which combines the features of homotopy analysis and shooting methods. Residual errors are computed to validate the obtained solutions. Numerical values of local Nusselt number are examined. The part of the chapter including the flow phenomena is accepted for publication in “European International Journal of Sciences and Technology” while the heat transfer problem is published in “American Journal of Heat and Mass Transfer”. Chapter six extends the flow analysis of chapter five for a third grade fluid. The contents of this chapter are published in “Advances in Mechanical Engineering”. Magnetohydrodynamic Stagnation-point flow and heat transfer analysis of a third grade fluid over a lubricated surface is analyzed in chapter seven. Boundary layer equations for the two dimensional flow are solved subject to a nonlinear slip condition. The corresponding boundary value problems for flow and heat are solved using hybrid homotopy analysis method. Obtained results are validated by plotting residual error curves. The results are discussed for the variations of different parameters appearing in the problem. The work carried out for the flow phenomena is published in “AIP Advances” and the work related to heat transfer analysis is submitted for possible publication in “Journal of Mechanics”.