Numerical Modelling in some Non-linear Flow problems

Abstract

Academic curiosity and latest technology application has generated considerable interest in researchers towards non-Newtonian rheological problems. In recent years, numerous examinations have been reported on non-Newtonian fluids due to their generous and treasured utility in industrial mechanism, power engineering, petroleum production and in broad spectrum chemical processes. Nanofluids are modern type of fluids, which are combination of base fluid and nano-sized metal particles. The basic principle of including these particles is to efficiently manage the heat transfer process and reduce to drag them. Because it is observed that mostly fluids (water, oil, ethylene glycol, engine oil etc.) which are traditionally utilized in thermal processes having low thermal conductivity. Recently, nanofluids are found very useful in bio-medicine and bio-engineering. Thus due to substantial importance, this phenomenon has motivated to explore these important features of fluid flows in current work. Since Sisko fluid, Prandlt and Prandlt_Eyring fluid models have great importance in industry. However, the models of such type that involve stretching in cylinder/sheet has not been discussed so far. Thus, major focus of present work is on these models. Numerical solutions are obtained through robust numerical technique i.e. Shooting method. This thesis comprises on seven chapters. The layout of this thesis is as follows: Literature review of present work is presented in chapter 0. Boundary layer flow of MHD Sisko fluid model over a stretching cylinder, under the effect of viscous dissipation is investigated in chapter 1. The cylindrical polar coordinates are used to model this physical problem. The modeling yields a nonlinear set of partial differential equations. Modelled equations are transferred to non-dimensional form after application of appropriate similarity transformations. The obtained equations are solved numerically with the aid of shooting technique in conjunction with Runge Kutta fifth order scheme. The expressions for velocity and temperature are computed under different conditions and deliberated in graphical manner. The local Nusselt number and wall friction coefficient are calculated and described in quantitative sense through graphs and tables. The contents of this chapter are published in AIP Advances 6, 035009 (2016), Doi:10.1063/1.4944347 The physical aspects of mixed convection, axisymmetric stagnation point and Joule heating on boundary layer flow of MHD Sisko fluid towards a stretching cylinder are analysed in chapter 2. The modelled partial differential equations are transfigured into ordinary differential equations with the aid of scaling group of transformations. Computed numerical solutions depicts impact of flow controlling parameters on velocity, temperature, coefficient of wall friction and wall heat flux is delineated via graphical and tabular manners. A comparison is made to ensure the validity of computed results. The contents of this chapter are published in Results in Physics 7(2017) 49-56. Chapter 3 focuses on including work presented in chapter 2 by factoring nonlinear-thermal radiation, heat generation/absorption, variable thermal conductivity and convective boundary conditions effects into account. Here, silent features of mixed convection and non-linear thermal radiation for non-Newtonian Sisko fluid over a linearly stretching inclined cylindrical surface are anticipated. The effect of pertinent flow parameters on these quantities are displayed with the help of graphs. Physical phenomenon in vicinity of stretching surface are explained with the help of skin friction coefficient and local Nusselt number. Also, effect of physical parameters are depicted with the assistance of graphs and tables. The comparison of present and previous results exhibits good agreement which leads to validate the presented model. The contents of this chapter are published in European Physical Journal Plus 132(9) (2017), DOI:10.1140/epjp/i2017-11645-y. Computational study has been established to explore the combined physical aspects of melting heat transfer and chemical reaction on electrically conducting Prandtl fluid flow towards an inclined stretching cylinder in chapter 4. The effect of relevant physical parameters on velocity, temperature and concentration profiles are taken into account. The contents are accepted in Canadian Journal of Physics (cjp-2018-0582.R1). Chapter 5 focuses on MHD boundary layer flow of Prandtl nanofluid over a linearly stretching cylinder. The effect of chemical reaction is also accounted in this case. The governing boundary layer equations regarding the flow are converted into a system of ordinary differential equations after using similarity transformation, which has been solved numerically by applying shooting method. The contents of this chapter are published in Journal Mathematical Problems in Engineering. doi.org/10.1155/2021/5162423 Chapter 6 spotlight the effect of Navier slip and convective boundary conditions on MHD Prandtl-Eyring nanofluid over stretching sheet under the influence of chemical reaction. The modelled problem comprises highly nonlinear partial differential equations under prescribed boundary conditions. To facilitate the computation process, an appropriate group of similar variables is utilized to transfigured governing flow equations into dimensionless form. Numerical results obtained through shooting technique are accomplished. The interesting aspects of velocity, temperature and concentration profiles are visualized via graphs by varying values of physical parameters. The contents of this chapter are published in Mathematical Methods in the Applied Sciences (2018) Doi.org/10.1002/mma.5319.