Modeling and analysis for nonlinear flows due to stretched surface

Abstract

Preface The flows of nonlinear liquids are recognized in the manufacturing systems of modern technological advancement and industries. Rheological features of nonlinear fluids is a major concern of various industrial processes like polymer processing, pharmaceutical industries, petroleum reservoirs, ceramics, food production etc. Many materials like apple sauce, sugar solutions, polymers of higher and lower molecular weights, drilling muds, blood, shampoos, certain oils lubricants, colloidal suspensions and many others are common examples of nonlinear fluids. Further the stretched flows of nonlinear liquids have great demand in metal and plastic processes such as thinning/annealing of copper wires, fiber spinning, plastic and rubber sheets manufacturing, polymer sheet extruded from dye, drawing of stretched sheets. The analysis and simulation of flows of nonlinear liquids present interesting challenges to the recent engineers and mathematicians. Rheological characteristics of nonlinear fluids give rise to constitutive relations which are very complex and highly complicated. Various models of nonlinear liquids are developed in past according to their physical behavior and shear. Heat transfer in flow of nonlinear liquids is quite relevant to industrial applications. The analysis of heat transport phenomenon through cooling rate is very essential to achieve the end products of desired quality. In addition the generalized concepts of heat and mass fluxes by Cattaneo-Christov theory resolve various issues associated with paradox of heat conduction. With these motivations in mind, the present thesis is organized as follows. Having all the above aspects in mind, in this thesis, we visualized the aspects of various type nonlinear fluids under different conditions and laws. The Fourier’s and Fick’s laws and their advanced forms are used for better modeling of heat and mass transport processes. The structure of this thesis is governed as follows. Literature review regarding previous published attempts, description of solution procedure and relations for conservation of mass, linear momentum and energy are given in chapter one. Chapters two to five model the flows of non-Newtonian fluids subject to Cattaneo-Christov heat flux. Chapter two addresses the flow of generalized Burgers liquid by moving surface considering variable conductivity. Energy expression for heat transfer is modeled implementing novel heat flux theory known as Cattaneo-Christov theory. The concept of boundary-layer is utilized for modeling of considered physical problem. Relevant variables are introduced to convert the developed partial differential system into the ordinary ones. Graphs are created for the influences of distinct variables versus velocity and temperature. It is declared that larger Prandtl number and thermal relaxation factor correspond to lower temperature and related thickness of thermal boundary layer. The observations of this chapter have been published in Journal of Molecular Liquids 220 (2016) 642–648. Analysis of chapter two is extended for tangent hyperbolic and Eyring-Powell fluids in chapters three to five. Novel concepts considered in these chapters include variable thickness, stretching cylinder, stagnation point and improved Fick’s relation. Materials of these three chapters have been published in Neural Computing & Applications (2017) DOI: 10.1007/s00521-017-3016-6, Results in Physics 7 (2017) 446-450 and Chinese Journal of Physics 55 (2017) 729-737 respectively. Chapters six to nine highlight stratification and mixed convection effects in flows of non-Newtonian fluids. Explicitly influence of thermal stratification in mixed convective Oldroyd-B fluid flow is described. Stretching plate bounds the fluid. Characteristics of heat transfer are elaborated through heat generation/absorption. Application of apposite transformations provide ODEs through PDEs. The homotopy scheme is applied for the computation of nonlinear systems. Features of emerging variables versus velocity and temperature are scrutinized. Rate of heat transport is computed and exhibited in the tabular form. We noticed increasing trend for velocity and heat transport rate subject to larger thermal buoyancy factor. Furthermore temperature is diminished when heat absorption variable and Prandtl number are increased. Obtained results are also compared in a limiting manner and found in exceptional agreement. The findings of this chapter have been published in Nuclear Engineering and Technology (in press). Flow analysis presented in chapter six is modified in chapters seven to nine for Oldroyd-B, Burgers and thixotropic materials respectively. Additionally the concepts of nanofluid and magnetohdrodynamics are utilized. The results of these chapters have been published in Results in Physics (2017) 10.1016/j.rinp.2017.06.030, The European Physical Journal Plus 131 (2016) 253 and International Journal of Heat and Mass Transfer 102 (2016) 1023-1029. Thermal radiation effect in chapters ten to twelve is explored for boundary layer flows of non-Newtonian fluids. In fact chapter ten describes the Brownian motion and thermophoresis aspects in nonlinear flow of micropolar nanoliquid. Stretching surface with linear velocity creates the flow. Energy expression is modeled subject to thermal radiation. Effect of Newtonian heating is considered. The utilization of transformation procedure yields nonlinear differential systems which are computed through homotopic approach. The important features of several variables like material parameter, conjugate parameter, Prandtl number, Brownian motion parameter, radiation parameter, thermophoresis parameter and Lewis number on velocity, micro-rotation velocity, temperature, nanoparticles concentration, surface drag force and heat and mass transfer rates are discussed through graphs and tables. The presented analysis reveals that the heat and mass transfer rates are enhanced for higher values of radiation and Brownian motion parameters. Present computations are consistent with those of existing studies in limiting sense. This material is published in “International Journal of Hydrogen Energy 42 (2017) 16821-16833”. Chapter eleven explores the magnetohydrodynamic (MHD) flow of Carreau nanoliquid by an exponentially convected stretchable surface. Formulation and computations are presented for Brownian motion and thermophoresis. Concentration by zero mass flux condition is reported. Consideration of thermal radiation characterizes the heat transfer process. Transformation procedure is utilized for reduction of PDEs into ODEs. Highly nonlinear complex problems are computed numerically through bvp4c technique. Salient characteristics of local Weissenberg number, Hartman number, Biot number, thermophoresis parameter, Prandtl number, thermal radiation parameter and Schmidt number on the velocity, temperature, nanoparticles concentration, surface drag force and Nusselt number are reported. The results reveal that velocity distribution for local Weissenberg number in case of shear thinning liquid reduces whereas it increments for shear thickening liquid. Temperature and thermal layer thickness are increasing functions of thermal radiation. A comparative study reveals that presents results are in very good agreement with the existing limiting solutions. The obtained results are published in Computer Methods in Applied Mechanics and Engineering 324 (2017) 640-653. Chapter twelve extends the analysis of previous chapter for Williamson fluid. Modeling is presented through nonlinear convection, Joule heating and heat generation/absorption. Nonlinear version of thermal radiation is opted. The outcomes of this chapter are published in The European Physical Journal Plus 132 (2017) 280.