Understanding Heat Conduction

Description

"The first chapter of this book proposes an analytical Fourier series solution to the equation for heat transfer by conduction in a spherical shell with an internal stone consisting of insulating material as a model for the kinetic of temperature in stone fruits both as a general solution and a mass average value. The chapter also considers an internal heat source linearly reliant on temperature. The second chapter focuses on the sensitivity of the numerical modeling technique for conjugate heat transferinvolving high speed compressible flow over a cylinder. The last chapter presents an overview of the fundamental solution (FS) based finite element method (FEM) and its application in heat conduction problems. First, basic formulations of FS-FEM are presented, such as the nonconforming intra-element field, auxiliary conforming frame field, modified variational principle, and stiffness equation. Then, the FS-FE formulation for heat conduction problems in cellular solids with circular holes, functionally graded materials, and natural-hemp-fiber-filled cement composites are described"-- Contents Preface Chapter 1 Cooling Kinetics in Stone Fruits Abstract General Introduction: Some Concepts in Heat Transfer Estimations and Applications Cooling/Heating Times Example I (from Reference [5]) Solution Modelling Thermal kinetics in stone fruits Mathematical Background Estimations and Applications Cooling/Heating Times Thermal Flow Indirect Measurement of Thermal Diffusivity and Surface Heat Transfer Coefficient Example II (from Reference [13]) Experiment Description Equivalent Sphere Determination of Biot Number and Thermal Diffusivity Asymptotic Aproximation to Dimensionless Slope ,,𝛿-1.-2. Maximum Values of , 𝜹-𝒏. Example III. Prediction of Cooling Times in Example II Modelling Thermal Kinetics Considering Internal Linearly Temperature Dependent Heat Generation Mathematical Background General Solution for Simple Geometries Average Value Estimations and Applications Cooling/Heating Times Displacement Correction Summary of the Procedure Example IV (from Reference [48]) Maximum Value at the Core Threshold Biot Number Estimation to ,𝐹𝑜-𝑀., ,𝑌-𝑀. and ,𝐵𝑖-𝑇ℎ. Modelling Thermal Kinetics in Stone Fruits Considering Heat of Respiration Linearly Reliant on Temperature Mathematical Background Maximum Value at the Core Threshold Biot Number Estimations and Applications Cooling/Heating Times Displacement Correction Other Indirect Determinations Heat Transfer Coefficient Heat Generation Constants Indirect Measurement of Thermal Diffusivity and Surface Heat Transfer Coefficient Example V References Chapter 2 Sensitivity of Numerical Modeling Technique for Conjugate Heat Transfer Involving High Speed Compressible Flow over a Cylinder Abstract Introduction Methods System Investigated Governing Equations Material Properties Modeling Method Studies Model Validation Results Modeling Method Variations Case A: Time Discretization Method Case B: Timestep Case C: Upwinding Case D: Gradient Calculations Case E: Gradient Limiter Case F: Compressibility Effects with  Model Case G: Standard- Turbulence Model Case H: Non-Equilibrium Wall Treatment Turbulence Model. Case I: Enhanced Wall Treatment – - Turbulence Model Moving Cylinder Modeling Method Velocity = 250 m/s Velocity = 500 m/s Velocity = 1000 m/s Conclusion References Chapter 3 Advances in Heat Conduction Analysis with Fundamental Solution Based Finite Element Methods Abstract Introduction Basic Formulation of FS-FEM Basic Equation of Heat Conduction Basic Formulation of FS-FEM Nonconforming Intra-Element Field Auxiliary Conforming Frame Field Modified Variational Principle Stiffness Equation Recovery of Rigid-Body Motion FS-FEM for Cellular Solids with Circular Holes Fundamental Solutions Fundamental Solution without Circular Hole Fundamental Solution with a Centered Circular Hole FS-FEM with Special Fundamental Solutions FS-FEM for Graded Materials Fundamental Solution in Functionally Graded Materials Generation of Graded Element Special n-Noded Voronoifiber/Matrix Element Micromechanical Model of Clustered Composite Special n-Sided Voronoi Fiber/Matrix Element Results and Discussion Validation of Element Property Effect of Degree of Fiber Clustering Effect of Global Fiber Volume Fraction Conclusion and Future Developments References Index