Analysis of Mathematical Models with Different Aspects of Heat Transfer

Abstract

Various base liquids such as ethylene, oil, water, and glycols etc. have low thermal conductivity. Thus, an improvement in the thermal efficiency of these liquids seems necessary in achieving the engineers and scientists’ expectations. Nanofluid consists of base liquid and nanoscale material (1-100 nm). In thermal engineering, heat exchangers, electronic chemical processes, cancer therapy and biomedicine, nanofluids are found very useful. Nanoparticles include namely 𝛾𝐴𝑙2𝑂3, 𝐶2𝐻6𝑂2,oxides and carbides ceramics and semiconductors. Nanofluids are the new generation coolants which exhibit much better heat transfer performance than the ordinary liquid carrier. Especially two-phase flow problems used abundantly in petroleum, usage of waste water, combustion and smoke emission from automobiles process. Non-Newtonian fluids like second grade fluid model, third grade fluid model Jeffrey fluid model, Williamson and many others are regarded helpful in physiological phenomenon, pharmaceutical etc. Viscous fluid, second grade fluid model, third grade fluid model and Jeffrey fluid model, are incorporated in this thesis. Mechanism of heat transfer has involvement in industries such as nuclear reactor, energy production and mobile device etc. For relatively higher temperature the surfaces heat transfer requires simultaneous study of various heat transporation process. Such process by which heat can be transmitted faster by the fluid are melting, absorption, combustion, conduction, convection and dispersal of radiation. Technologies and industries have widespread utilizations of melting phenomenon. Researchers paid particular attention to improving effective, safe, and energy depot technologies. These technologies are interrelated with the repossession of excess fuel, solar, electricity and food from plants. For example, three energy storage procedures have been introduced including latent, thermal energy and chemical energy. The economically sustainable heat energy storage is latent heat via material phase adjustment. Melting phenomenon has applications in many fields namely heat exchanger coils, based pump, the freeze treatment, solidification, welding processes and many others. The boundary layer flows of viscous/non-Newtonian liquids over a stretched sheet have interest in various fields. Examples of these flows involve polymer sheet sectors, glass sheets, pharmacology, bioengineering, fusion technology, plastic wire making and emulsion of polymeric materials etc. Current product efficiency primarily depends on heat transfer rate and drag forces etc. Keeping all these dimensions in mind the main goal of this thesis is to study mathematical models with different aspect of heat transfer. The structure of this thesis is as follows. Chapter 1 consist of some basic law of conservations. Mathematical model and boundary-layer expressions for Newtonian fluid, second grade, third grade and Jeffrey fluids are incorporated. Three different techniques are used to deal the flow problems. Basic concepts of these techniques namely HAM, OHAM and shooting technique is also provided. Chapter 2 addresses the flow subject to effective Prandtl number and without effective Prandtl number via γAl₂O₃-H₂O and γAl₂O₃-C₂H₆O₂ nanoparticles. The resulting problem are solved through Optimal homotopy method (OHAM). Optimum values are determined for the auxiliary parameters. Impact of emerging parameters are graphically analyzed for (γAl₂O₃ -H₂O and γAl₂O₃ -C₂H₆O₂) nanoparticles. The contents of this chapter are published in Journal of Molecular Liquids 266 (2016) 814-823. Chapter 3 deals the Mixed convective dissipative flow of effective Prandtl number subject to entropy optimization and melting heat. The governing flow expressions with boundary conditions are solved via built-in-Shooting technique. Computational solutions are identified and analyzed utilizing plots. The outcomes are reported in International Communications in Heat and Mass Transfer 111(2020) 104454. Chapter 4 reports computational aspects for Entropy generation in MHD flow of viscous fluid subject to aluminum and ethylene glycol nanoparticles. Thermal radiation and Joule heating are examined. Electric field is absent. Uniform magnetic field is applied normal to the sheet. The relevant equation are solved via built-in- Shooting method. The various flow parameters are graphically discussed. The outcomes of this chapter are published in Computer methods and programs in biomedicine 182(2019) 105057. Chapter 5 examines Thermal radiation and heat source/sink impacts in stagnation point flow of viscous nanomaterial. Radiative heat and convective conditions are also analyzed. Inclined magnetic field is taken. Homotopy analysis method is employed to find the serious solution. The contents of this chapter are available in Indian Journal of Physics 94(2019) 657–664. Chapter 6 presents Computational analysis of 3D radiative Darcy-Forchheimer flow subject to suction/injection. Porous medium is characterized by Darcy-Forchheimer relation. Radiation, convective condition and slip effect are addressed. Stagnation point flow is examined. Non-linear ordinary differential system are solved through shooting method. Graphical results are portrayed and scrutinized with distinct values of dimensionless variables. The chapter key results can be found in Computer Methods and Programs in Biomedicine 184(2020) 105104. Chapter 7 describes Utilization of entire modern aspect of Cattaneo-Christov model in mixed convective entropy optimized flow by Riga wall. Brownian motion and thermophoresis are adopted. Cattaneo-Christove model for heat and mass fluxes are used to examine the heat and mass transfer. Entropy generation is modeled. The numerical solutions are developed through ND solve technique. Graphical illustrations are given for the influence of sundry parameters. The outcomes of this chapter are submitted in Numerical Method for Partial Differential Equations for possible publication. Chapter 8 discloses a novel perspective of Cattaneo-Christov model in MHD second grade nanofluid flow. Heat and mass transfer are based upon Cattaneo-Christov (CC) theory. Results are developed via OHAM. The outcomes of this chapter are published in International Communications in Heat and Mass Transfer 119(2020) 104824. Chapter 9 describes Melting heat in Jeffrey fluid flow through permeable space. Energy equation is considered in the existence of melting heat and heat absorption/ generation. The results are constructed via OHAM. The outcomes of this chapter are published in Thermal Science 23(2019) 3833-3842. Chapter 10 includes the Impact of entropy generation on third grade nanofluid flow over a stretchable Riga wall with Cattaneo-Christov double diffusions. Formulation also consists of heat generation and mixed convection. The key results of this chapter are submitted in Numerical Method for Partial Differential Equations for possible publication