A Computational Approach for the Thermal Aspects in Boundary Layer Flows

Abstract

The main theme of this dissertation is about the computational approach for the flows at boundary layer in concern with heat transfer rate by invoking various effects to the energy equation which includes heat absorption/generation, Joule heating, thermal radiation and nano fluids etc. The nano particles are the major source to enhance heat transfer rate in fluid flows. Nano-fluid is the advance type of fluid which shows the combination of base fluid and nano sized particles. These nano particles include metals like silicon, copper and aluminum etc. Beside this, three main sources of heat transfer are the conduction, convection and radiation. The researchers of recent times have been examining the heat transfer rate in different perspectives. As in this dissertation, the heat transfer phenomena is observed by using Cattaneo-Christov heat flux model. This type of heat flux is the generalized shape of Fourier’s law which helps to transform heat equation into hyperbolic form. This law is used to determine the thermo-elastic and concentration elastic effects in Newtonian as well as non-Newtonian fluid models. The study of behavior of concentration of fluid is an important feature to be discussed in fluid dynamics. For this purpose, the concentration equation is debated through Homogeneous-Heterogeneous chemical reactions. The mathematical model for the problem is designed by considering the laws of conservation. The equations of motion are presented as Navier-Stokes equation which reflects as a Partial Differential Equations (PDE’s). The equipment which is used to alter these equations into Ordinary Differential Equations (ODE’s) is a well know similarity transformation technique. This technique helps to reduce independent variables that appears in PDE’s and provides a system of ODE’s. The obtained set of equations are then converted to system of first order ODE’s as it is simpler to deal with or we convert them into initial value problem by using suitable substitutions. The missing initial conditions are supposed to take as some particular values. These supposed values against the missing initial conditions are taken on a hit and trial bases which is known as shooting technique. The numerical solutions are calculated by using Runge-Kutta Fehlberg method in shooting scheme. The impacts of numerous physical quantities upon velocity of fluid, temperature of fluid and concentration of fluid are portrayed through graphs by using MATLAB. The main purpose of representing the graphs is to determine how the base fluids are affected by considering certain effects in the momentum energy and concentration equation. The heat transfer rate or Nusselt number and mass transfer rate that is Sherwood number are examined. Moreover, their numerical values are computed and compared with the previous results. The comparison shows an excellent match with the existing literature which provides the consistency and accuracy of the computational approach. The transfer of heat and mass phenomena by way of Carreau steady two-dimensional infinite shear rate viscosity model over moving wedge is analysed in chapter 1. The results for dilatant and pseudoplastic fluids are reported. The independent variables are reduced from partial differential equations in order to get ordinary differential equations by applying admissible similarity transformation technique. This system is sorted out in a numerically by means of Runge-Kutta methodology associated by shooting algorithm. The reduction in the temperature of Carreau fluid is captured due to greater values of viscosity ratio parameter in case of shear thickening and reverse trend is examined for the shear thinning case. Further, the concentration in Carreau fluid declines against wedge angle parameter for shear thickening and thinning. The headnotes of this chapter are published in “Case Studies in Thermal Engineering, 12(2018): 126-136”. https://doi.org/10.1016/j.csite.2018.04.007 The Carreau viscosity model with heat absorption /generation and chemical reaction, a steady flow at a boundary layer for moving wedge is studied in chapter 2. The mathematical shape is designed in coupled partial differential equations and then sorted out in a numerical way by implementing shooting scheme charted with Runge-Kutta Fehlberg technique. The graphs depict the consequence of physical parameters upon fluid concentration, velocity and temperature. The temperature readings are observed for positive and negative values of parameter of heat generation. Further, the Carreau fluid concentration is inspected for parameter of chemical reaction. The executive summary of the chapter is presented in “Case Studies in Thermal Engineering, 12 (2018): 462–469”. https://doi.org/10.1016/j.csite.2018.06.006 The chapter 3 includes the results for Jeffery fluid with thermal stratification effects at a stagnation point. The thermal energy characteristics are studied through the generalized Fourier’s law of heat flux. The flow is magnified by the stretching cylinder. The homogeneous heterogeneous chemically reactive species are considered. The steady state flow of a boundary layer is examined when the reactants and auto-catalyst have equal diffusion coefficient. The concerned mathematical problem is developed by laws of conservation of momentum, mass and energy which provides coupled partial differential equation. The order of these equations is reduced by way of similarity transformation. Later, the set of reduced coupled equations are computed numerically by implementing Runge-Kutta Fehlberg technique with shooting algorithm. The curves for temperature and velocity of fluid are plotted for different engineering parameters. The coefficient of skin friction is examined, and the obtained outcomes are comparison with existing literature. This pagination is delineated in “Physica A: Statistical Mechanics and its Applications, 542 (2020): 123428”. https://doi.org/10.1016/j.physa.2019.123428 The Jeffery fluid past a point of stagnation towards a cylindrical surface with the homogenous heterogeneous reactions, magnetic field and heat generation effects are elaborated in chapter 4. The heat transport process is debated by Cataneo-Christov heat flux concerned to thermal stratification. The consequential PDE’s descend to ODE’s by carrying out the set of similarity transformation. These equations are sorted out in a numerical procedure named as Runge-Kutta Fehlberg method with shooting approach. The consequences of involved parameters are analysed by means of graphs. The obtain outcomes are validated with an existing published work. The table of contents for this chapter are published in “Canadian Journal of Physics, 97(7) (2019): 735-741”. https://doi.org/10.1139/cjp-2018-0491 The chapter 5 emphasizes on magneto-hydrodynamics, heat generation/absorption and slip effects over a Newtonian flow field with homogeneous-heterogeneous chemical reactions induced by the rotating disk. The concerned steady state flow is examined in case when reactants and auto-catalyst possess equality in coefficients of diffusion. The Cattaneo-Christov approach is proposed to derive the energy equation and heat transfer phenomena. The consequential PDE’s (Partial Differential Equations) descend to ODE’s (Ordinary Differential Equations) by insinuating similarity transform. Further, these equations are sorted out by way of numerical scheme called Runge-Kutta Fehlberg method with shooting scheme. The influence of arising parameters towards fluid velocity, temperature and concentration is observed through graphs. Further, the computational results for the friction coefficient and the rate of heat transfer are examined. The main results of this paper is published in “Physica Scripta, 94 (2019): 085217 (9pp), https://doi.org/10.1088/1402-4896/ab11ff A Newtonian nanofluid flow field is demonstrated in chapter 6 with thermal radiation and heat generation/absorption. Further, in this study mixed convection, magnetic field, stagnation point, temperature stratification, Joule heating, concentration stratification and chemical reaction are included. The flow field is caused by the inclined stretching cylinder. The mathematical shape is developed in coupled partial differential framework and is descended to coupled ordinary differential framework by means of admissible transformation. The numerical findings are presented by Runge-Kutta Fehlberg method along with shooting scheme. The temperature trend towards higher values of heat absorption/generation and thermal radiation is studied and analysed in detail. Further, the guesstimates for local Nusselt number as well as the skin friction coefficient are presented. The detailed summary is published in “Physica A, 553 (2020): 124026”. https://doi.org/10.1016/j.physa.2019.124026