Rheology of the Rate Type Fluid Models with Heat Transfer: ' Analytical and Numerical Treatment

Abstract

The significant features of an engineering and technological field can be realized by its worth in relation to other engineering sciences. Transport phenomena in fluid mechanics have prominent aspects in chemical, thermal and mechanical engineering sciences. This field of research has enormous applications in biotechnology, microelectronics, nanotechnology, crystal growth, paper production, wire drawing, food processing etc. By getting inspiration from such broad applications, scientists and engineers have done extensive studies in this field. The strength of this subject is mainly depending on the fundamental laws of conservation. The transport phenomena like momentum, heat and mass transfer are important since they govern the velocity, temperature and concentration profiles. It has been apprehended that main attention in the preceding years has been given to the rheological problems relating to the differential type non-Newtonian fluid models. In this dissertation, the rate type non-Newtonian fluid modeis have been examined and the effects of heat transfer on various flow situations have been presented. Moreover, heat transfer problems have been coupled with mass transfer to investigate double diffusion. Also influence of magnetic field, suction/injection and radiations have been studied. Chapter 1 addresses the literature review of the two and lhree dimensional non-Newtonian fluid models. Conservation laws and the adopted computational methodologies have been briefly describes. Advantages of different techniques which have been implemented for the analytical and numerical computations have been also discussed. In chapter 2, investigation has been made to study the dual numerical solutions for the flow of an upper convected Maxwell (UCM) fluid in a porous medium. The influence of intern(ll heat generation/absorption effects, chemical reaction phenomenon and magnetic field have taken into account. Stream function and similarity transformations have been employed on the governing mathematical model which results into the system of nonlinear ordinary differential equations. Shooting technique has been implemented efficiently to obtain numerical results. It has been analyzed that the dual numerical results exist in case of shrinking surface while a unique solution Occurs for the stretching sheet. Results have been given to study the skin friction, local Nusselt and Sherwood numbers. The contents of this chapter have been published in Journal of Molecular Liquids, 232 (2017) 361-366. In chapter 3, we have examined double-diffusivity for the Sakiadis flow of UCM nanofluid in the presence of magnetic field and heat source/ sink effects. The effects of thermal radiations have been incorporated in addition. Set of nonlinear ordinary differential equations have been achieved by applying the suitable transformations on the governing partial differential equations. Analytic and numerical solutions have been computed via homotopy analysis method and finite difference approach respectively. Comparison between the results have been presented in tabular form and seems to be in a nice agreement. Results have also been portrayed to vi~ualize temperature and concentration profiles for the involved parameters. The contents of this chapters have been published in Journal of Molecular Liquids, 241 (2017) 570-576. Chapter 4 presents the three dimensional rheology of an upper-convected Maxwell (UCM) fluid over a bidirectionally stretched surface with temperature dependent thermal conductivity effects. Flow over an exponentially stretched wall has been considered and the cases of prescribed surface temperature (PST) and prescribed surface heat flux (PSHT) have been analyzed in detail. Series solutions have been evaluated via homotopy analysis method. Results have been presented in a graphical and tabular form to visualize the effect of different physical parameters. The contents of this chapter have been submitted for publication. Chapter 5 explores the Sakiadis rheology of Oltlroytl-B fluid in the presence of magnetiC field. Convective heating process has been analyzed under the effects of thermal radiations. Appropriate transformations have been invoked for conservation of partial differential equations into coupled nonlinear ordinary differential equations. Numerical as well as analytic solutions have been computed for the velocity and temperature distributions. Graphical results have been prepared observe the behavior of physical parameters. Error analysis is also presented in order to validate the obtained solutions. Bar charts have been designed to show the heat flux analysis. Comparison between the results obtained by homotopy analysis method (HAM) and finite difference method (FDM) has been given in a tabular form. The contents of this chapter are published in Thermal Sciences (2018) Doi.org/10.2298ITSCI180426284A. In chapter 6, the features of Cattaneo-Christov heat flux for the flow of Burgers' fluid have been analyzed. Mathematical modelling is performed using laws of momentum and energy under the order analysis to transform the problem into the set of equations. It is shown that the term for the hydro-magnetic rheology of the viscous model is "() B~ uJ p" while the generalized m~gnetic field term (as revealed in Eq. 6.2) is for the Burgers' model which is used in the present study. For the solution computation, homotopy analysis method is applied to compute results. Results are depicted in graphs to visualize the effect of physical parameters. Values of skin friction with heat transfer rate have been displayed in the tables. The contents of this chapter are published in Scientia Iranica 26 (2019) 323-330. Chapter 7 explores the study for Jeffery nanofluid with thermophoresis and Brownian motion properties. The combined effects of viscous dissipation and heat generation/absorption have been considered. Entropy generation and inclined magnetic field for the Jeffery fluid have been analyzed. Mathematical formulations have been performed and solutions have been computed by using a homotopy approach in the spatial domain. Results have been illustrated in graphical and tabular form to study the effect of flow parameters. It is analyzed that magnetic field is a flow reducing parameter whereas Biot number behaves like a boosting factor to increase the fluid temperature. The contents of this chapter are submitted for publication. In chapter 8, three-dimensional flow properties of an Oldroyd-B fluid model have been discussed while incorporating the effects due to the existence of nanoparticles. The present physical problem is studied under influence of nonlinear radiations. During mathematical formulation, the heat and concentration equations have been studied under thermophoresis effect and Brownian motion. Bidirectional stretching phenomenon have been taken to study the three-dimensional fluid deformation. Some suitable transformations have been utilized for conversion of derived partial differential system into coupled nonlinear ordinary differential system. Solutions are computed via homotopy approach. Several graphical and numerical illustrations have been prepared to present the behavior of involved physical quantities. The contents of this chapter are published in Results in Physics, 8 (2018) 1038-1045.