Flows of Nanomaterials by Stretching Boundaries

Abstract

Many non-linear materials (polymers, blood, sauce, drilling muds, sugar solutions, colloidal suspensions, shampoos, lubricants etc) deviates Newtonian’s law of viscosity. The significance of topic can be perceived by its numerous industrial and engineering applications such as petroleum reservoirs, pharmaceutical industries, ceramics, polymer processing, metallurgy and many others. The fluids in all such applications are single type. Therefore viscous and non-Newtonian models like Sisko, Williamson and second grade materials are adopted here. Nanoliquid is further formed by adding nano-dimensions of tiny particles in traditional liquids. It remarkably intensifies low thermal efficiency of materials. It can be utilized in both non-Newtonian and viscous materials. Nanoparticles comprising of carbides, semiconductors, metals, oxides ceramics, CNTs and many other composites are submerged in traditional liquids like engine oil, water, kerosene oil and ethylene glycol to improve heat transport capability. Nanoliquids are extensively utilized in nanotechnologies such as atomic force microscope, conductive plastic, gas storing, nuclear power magnifying lens, electromechanical devices and industrial cooling applications. Hybrid nanoliquids consist of more than one type of nanoparticles. Novel concept of hybrid nanofluid greatly motivated the researchers due to its better thermal feature, excellent stability and physical strength. Therefore main emphasis here to given to inspect the flows of nano and hybrid nanoliquids by stretching boundaries. Phenomenon of heat transport is characterized via various mechanisms. Concept of thermodynamic second law is utilized for entropy production. Thus intension here is to develop mathematical modelling for flows of nano and hybrid nanomaterials using various nanoparticles. The problems are addressed by preserving natural aspects intact and then tackled via different techniques. The chapter wise arrangement of this thesis is as follows. Chapter one consists the expressions for fundamental laws and literature review. Mathematical development of Sisko, Williamson, second grade and Buongiorno models are addressed. Basic concept regarding the solution techniques is provided. Chapter two explores the consequences of nanoparticles on three-dimensional mixed convention flow of Sisko fluid over a stretched surface. Salient aspects of thermophoresis and Brownian motion are addressed. Convective conditions are imposed at the boundary. Boundary layer concept is utilized for mathematical modelling. Homotopic technique is ii implemented for solutions convergence. Graphs of embedded variables on velocity, temperature and concentration are deliberated. Finally heat and mass transfer rates are also studied. Findings of this chapter are reported in International Journal of Mechanical Sciences, 133 (2017) 273-282. Chapter three communicates the chemical reaction and double stratification in MHD stagnation point flow of Williamson nanoliquid towards a stretched sheet. Flow is generated due to non-linear stretching sheet of variable thickness. Non-uniform magnetic filed is implemented in transverse direction. Aspects of Brownian motion, radiation, thermophoresis and viscous dissipation are addressed. Additionally chemical reaction is present. Relevant mathematical formulations are made through boundary layer concept. Homotopic technique is implemented for the solutions procedure. Rate of heat transfer is estimated. Research of this chapter is published in Radiation Physics and Chemistry, 152 (2018) 151–157. The aim of chapter four is in fourfolds. Firstly to formulate magnetized nanomaterials squeezed flow of viscoelastic (second grade) fluid between two parallel disks. Such consideration has relevance in industrial and biomedical utilizations like spintronic devices, catalysis and MEMS etc. Secondly to scrutinize nonlinear thermal radiation for heat transfer analysis. Flows through such consideration are useful in numerous processes like nuclear plants, combustion chambers and solar power technology. Thirdly, the novel chemical species model which elaborates activation energy impact. Activation energy describes least energy required through chemical shape with potential reactants to develop a chemical reaction. Fourth to compute solutions for nonlinear problems utilizing homotopic scheme. Graphical and tabular outcomes are portrayed and elaborated in detail for involved variables. The data of this research is publication in Journal of Heat Transfer, 142(2020) 082501. Chapter five addresses the comparative analysis for radiated flow of nano and hybrid nanomaterials by stretchable disk. Both thermal and velocity slips are considered. Water based liquid containing Aluminum alloy (AA7072 − A7075) nanoparticles is considered. Further exponential heat source is present. Transformations are implemented for conversion of PDEs into ODEs. Non-linear problems are treated through NDSolve scheme. Features of sundry variables for both nano and hybrid nano phases are computed and discussed. Major outcomes are listed in conclusions. The contents of this research are published in Physica Scripta, 94 (2019) 125708. iii Chapter six discusses the nonlinear radiative flow of ethylene-glycol based CNTs suspended in Darcy-Forhheimer porous medium. Xue model is implemented for the transportation of nanomaterials. Ethylene-glycol (EG) is used as a base liquid. The characteristics of nanoparticles volume fraction have been considered. A concise depiction about the entropy of system is presented. Implementation of suitable variables yields dimensionless system. Numerical scheme is employed in order to solve the nonlinear systems. The behaviours of many regulatory flow variables are explained through plots. In addition, the variation of some valuable engineering quantities is interpreted via tabulated values. The results of this chapter are accepted in Journal of Non-Equilibrium Thermodynamics. Chapter seven is generalized version of chapter six in view of hybridization of CNTS. Thus this chapter explicitly provides the comparative analysis for two different types of nanofluids namely regular nanofluid (SWCNT/engine oil) and hybrid nanofluids (SWCNT-MWCNT/engine oil) past a stretching cylinder. Xue model is modified for the modeling of hybrid nanofluid. Effects of melting, viscous dissipation and radiation are studied. To overcome the level of entropy production in a system and irreversibility arising due to pressure drop, mixing and heat transfer, an entropy number is utilized. Dimensionless variables convert the partial differential systems to ordinary one. The reduced systems are then solved numerically by means of NDSolve approach. Graphical analysis is made to visualize the physical characteristics of interesting variables. Moreover analysis of various parameters at surface in terms of skin friction and Nusselt number is also provided. Finding of this chapter is accepted in Modern Physics Letters B. Main emphasis in chapter eight is to differentiate the heat transportation rate in hybrid nanofluid (SWCNT-MWCNT/kerosene oil) and regular nanofluid (SWCNT/kerosene oil) suspended in Darcy-Forchheimer porous space. Whole system is in a rotating frame. Entropy analysis is incorporated. Energy equation is modelled via heat source, convective condition and dissipation. Obtained non-linear systems are tackled by employing numerical approach (NDSolve shooting technique). The physical features of various sundry variables for both types of nanomaterials are depicted graphically and via table. It is noteworthy to point out that analytical model of hybrid nanoliquid is novel achievement of available models based on single-nanoparticles. With great confidence this modified Xue model can be used to assess the heat transport and flow of hybrid nanomaterials in any configuration. The outcomes achieved in this study are important in industrial research, academics and discussion about entropy analysis for flow of two types of nanoliquids by keeping the regular fluid fixed. The outcomes of current chapter are accepted for publication in Journal of Thermal Analysis and Calorimetry.