Heat and Mass Transfer Modelling During Drying: Empirical to Multiscale Approaches

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Acknowledgements
Authors
Chapter 1 Introduction to Drying
	1.1 Introduction
	1.2 Materials and Their Characteristics
		1.2.1 Porosity
		1.2.2 Water-Holding Properties
		1.2.3 Structural Homogeneity
	1.3 Common Drying Materials
		1.3.1 Food
			1.3.1.1 Fruits and Vegetables
			1.3.1.2 Grains
			1.3.1.3 Leaf and Spices
			1.3.1.4 Fish and Meat
			1.3.1.5 Dairy
		1.3.2 Timber
		1.3.3 Fabrics
		1.3.4 Pulp and Paper
		1.3.5 Chemical and Pharmaceutical Products
		1.3.6 Leather
		1.3.7 Bricks and Ceramics
		1.3.8 Coal
	1.4 Drying Phenomena and Methods
		1.4.1 Common Drying Methods
			1.4.1.1 Convective Drying
			1.4.1.2 Microwave Drying
			1.4.1.3 Infrared Drying
			1.4.1.4 Vacuum Drying
			1.4.1.5 Freeze Drying
			1.4.1.6 Spray Drying
		1.4.2 Drying Conditions
	References
Chapter 2 The Physics in Drying
	2.1 Introduction
	2.2 Mass Transfer
		2.2.1 Mass Transfer-related Terminologies
			2.2.1.1 Moisture Content
			2.2.1.2 Water Concentration
			2.2.1.3 Critical Moisture Content
			2.2.1.4 Equilibrium Moisture Content
			2.2.1.5 Moisture Sorption Isotherm
			2.2.1.6 Monolayer Moisture Content (MMC)
			2.2.1.7 Phases of Water
			2.2.1.8 Water Potential
			2.2.1.9 Water Activity
		2.2.2 Types of Water
			2.2.2.1 Free Water
			2.2.2.2 Bound Water
			2.2.2.3 Spatial Distribution of Water
	2.3 Heat Transfer Phenomena During Drying
		2.3.1 Conduction Heat Transfer
			2.3.1.1 Steady Conduction
			2.3.1.2 Lump System
			2.3.1.3 Transient Heat Conduction
		2.3.2 Convection Heat Transfer
		2.3.3 Radiation Heat Transfer
			2.3.3.1 Grey Body Heat Radiation
	2.4 Mass Transfer Basics
		2.4.1 Diffusion
			2.4.1.1 Transient Mass Diffusion
		2.4.2 Mass Convection
	2.5 Fluid Flow
	References
Chapter 3 Governing Equations and Material Properties
	3.1 Introduction
	3.2 Heat and Mass Transfer During Different Types of Drying
		3.2.1 Convective Drying
		3.2.2 Vacuum Drying
		3.2.3 Drum Drying
		3.2.4 Freeze Drying
		3.2.5 Spray Drying Process
		3.2.6 Microwave Drying
			3.2.6.1 Maxwell’s Equation for Electromagnetics
			3.2.6.2 Lambert’s Law
		3.2.7 Infrared Drying
		3.2.8 Combined or Assisted Drying
			3.2.8.1 Continuous
			3.2.8.2 Intermittent
	3.3 Boundary Conditions
		3.3.1 Heat Transfer Boundary Conditions
		3.3.2 Mass Transfer Boundary Conditions
	3.4 Thermo-Physical and Transport Properties
		3.4.1 Density
		3.4.2 Porosity
		3.4.3 Specific Heat Capacity
		3.4.4 Thermal Conductivity
		3.4.5 Emissivity
		3.4.6 Dielectric Properties
		3.4.7 Effective Moisture Diffusivity
	References
Chapter 4 Numerical Model Formulation and Solution Approaches
	4.1 Introduction
	4.2 Types of Mathematical Modelling of Drying
		4.2.1 Empirical Modelling
		4.2.2 Single-Phase Modelling
		4.2.3 Multiphase Modelling
		4.2.4 Micro-Scale Modelling
		4.2.5 Conjugated Drying Models
		4.2.6 Drying Model Considering Deformation
		4.2.7 Multiscale Modelling
	4.3 Solution Methods
		4.3.1 Finite Element Method (FEM)
		4.3.2 Finite Volume Method (FVM)
		4.3.3 Finite Difference Method (FDM)
		4.3.4 Discrete Element Methods (DEM)
	4.4 Computational Platforms and Validation
		4.4.1 User-Developed Code
		4.4.2 Computational Software
		4.4.3 Validation of the Models
	References
Chapter 5 Empirical Modelling of Drying
	5.1 Introduction
	5.2 Regression Analysis
		5.2.1 Simple Linear Regression
		5.2.2 Multiple Linear Regression
		5.2.3 Non-Linear Regression
	5.3 Empirical Modelling for the Drying Process
		5.3.1 Important Considerations of the Empirical Model
		5.3.2 Drying Kinetics Models
		5.3.3 Empirical Models
		5.3.4 Semi-Empirical Models
			5.3.4.1 Models Derived from Newton’s Law of Cooling
			5.3.4.2 Fick’s Law Based Semi-Empirical Models
	5.4 Quality Kinetics Model
	5.5 Validation and Interpreting Regression Models Output
		5.5.1 Regression Coefficients
			5.5.1.1 P-Value
			5.5.1.2 Chi-Square (˜ 2)
			5.5.1.3 R-Squared
			5.5.1.4 Standard Deviation (SD)
			5.5.1.5 Sum Square Error (SSE)
			5.5.1.6 Root Mean Square Error (RMSE)
	5.6 Limitations
	References
Chapter 6 Single-Phase Diffusion Model
	6.1 Introduction
	6.2 Model Development
		6.2.1 Geometry and Meshing
			6.2.1.1 Meshing Grid Dependency
		6.2.2 Assumptions
		6.2.3 Governing Equations
			6.2.3.1 Heat Transfer
			6.2.3.2 Mass Transfer
		6.2.4 Initial and Boundary Conditions
			6.2.4.1 Heat Transfer Boundary Conditions
			6.2.4.2 Mass Transfer Boundary Condition
	6.3 Input Parameters
		6.3.1 Equilibrium Vapour Pressure
		6.3.2 Effective Moisture Diffusivity
		6.3.3 Temperature-Dependent Effective Diffusivity Calculation
		6.3.4 Moisture-Dependent Effective Diffusivity
		6.3.5 Average Effective Moisture Diffusivity
		6.3.6 Heat and Mass Transfer Coefficient Calculation
		6.3.7 Computation
	6.4 Typical Simulation Results
		6.4.1 Effective Moisture Diffusivity
		6.4.2 Average Moisture Content
		6.4.3 Temperature Evolution
	References
Chapter 7 Multiphase Porous Materials Modeling
	7.1 Introduction
		7.1.1 Porosity
		7.1.2 Tortuosity
		7.1.3 Hygroscopic
	7.2 Feature of Multiphase Drying Model
		7.2.1 Meaning of Multiphase
		7.2.2 Representative Elementary Volume
		7.2.3 Driving Forces of Mass Transfer
		7.2.4 Assumptions
	7.3 Governing Equations
		7.3.1 Conservation of Mass
			7.3.1.1 Mass Conservation of Liquid Water
			7.3.1.2 Mass Conservation of Water Vapour
			7.3.1.3 Mass Fraction of Air
		7.3.2 Continuity Equation to Solve for Pressure
		7.3.3 Energy Equation
		7.3.4 Initial and Boundary Conditions
			7.3.4.1 Initial Conditions
			7.3.4.2 Boundary Condition
	7.4 Input Parameters
		7.4.1 Thermo-Physical Properties
		7.4.2 Porous Structure-Related Properties
			7.4.2.1 Porosity
			7.4.2.2 Permeability
			7.4.2.3 Capillary Diffusivity of Liquid Water
		7.4.3 Gas-Related Properties
			7.4.3.1 The Viscosity of Water and Gas
			7.4.3.2 Effective Gas Diffusivity
		7.4.4 Drying Air Condition (Relative Humidity)
	7.5 Typical Simulation Results
		7.5.1 Average Moisture Content
		7.5.2 Liquid and Gas Saturation
		7.5.3 Temperature Evolution and Distribution
		7.5.4 Evaporation Rate and Vapour Pressure
	7.6 Challenges and Possible Simplifications
		7.6.1 Challenges
			7.6.1.1 Shrinkage
			7.6.1.2 Properties of Porous Material
		7.6.2 Simplification
	References
Chapter 8 Micro-Scale Drying Model
	8.1 Introduction
		8.1.1 Defining Micro-Scale
		8.1.2 Micro-Scale Domain
		8.1.3 Transport Phenomena at the Micro-Scale
		8.1.4 Micro-Scale Modelling Approaches
			8.1.4.1 Discrete Models
			8.1.4.2 Continuum Models
	8.2 FEM Approach of Micro-Scale Modelling
		8.2.1 Governing Equation
		8.2.2 Initial and Boundary Conditions
		8.2.3 Input Parameters
	8.3 Typical Results and Discussion
		8.3.1 Temperature Distribution
		8.3.2 Moisture Distribution
	8.4 Challenges in Micro-Scale Modelling
		8.4.1 Domain Development
		8.4.2 Boundary Conditions
		8.4.3 Unavailability of Micro-Level Properties
		8.4.4 Too Much Information
		8.4.5 Higher Computational Cost
	References
Chapter 9 CFD Modelling of Drying Phenomena
	9.1 Introduction
		9.1.1 Fluid Flow in the Drying
		9.1.2 Computational Fluid Dynamics
		9.1.3 Conjugate Drying Model
		9.1.4 Assumptions
	9.2 CFD-Coupled Heat and Mass Transfer Model
		9.2.1 Governing Equations
			9.2.1.1 Turbulent Model
		9.2.2 Boundary Conditions
		9.2.3 Input Parameters
	9.3 Typical Results and Discussion
		9.3.1 Temperature Distribution
		9.3.2 Liquid Water Content
		9.3.3 Relative Humidity
		9.3.4 Air Velocity
	References
Chapter 10 Modelling of Deformation During Drying
	10.1 Introduction
	10.2 Factors Associated with Deformation during Drying
		10.2.1 Water Migration and Distribution
		10.2.2 Structural Mobility
		10.2.3 Phase Transition (Multiphase)
	10.3 Mathematical Models for Deformation
		10.3.1 Empirical Models
		10.3.2 Semi-Theoretical Models
		10.3.3 Theoretical Models
	10.4 Challenges
		10.4.1 Moisture Dependent on Internal Stress
		10.4.2 Appropriate Material Model
		10.4.3 Real-Time Mechanical Properties
		10.4.4 Coupling of Deformation and Transport Phenomena
		10.4.5 Multiscale Nature of Deformation
	References
Chapter 11 Multiscale Drying Modelling Approaches
	11.1 Introduction
		11.1.1 The Hierarchical Structure of Materials
		11.1.2 Structure–Properties–Drying Kinetics Relationship
		11.1.3 Imaging: Structure and Properties Quantification
	11.2 Modelling at a Different Scale
		11.2.1 Atomic Scale Simulation
		11.2.2 Molecular Dynamics Simulations
			11.2.2.1 Monte Carlo Methods
			11.2.2.2 Coarse-Grained Models
			11.2.2.3 Lattice-Boltzmann Method
	11.3 Multiscale Modelling Approaches: Bridging between Scales
		11.3.1 Problem Formulation
			11.3.1.1 Concurrent Approach
			11.3.1.2 Hierarchical Approach
			11.3.1.3 Hybrid Multiscale Modelling
		11.3.2 Solution Approach
	11.4 Challenges in Current Multiscale Paradigms
	11.5 Prospects: Multiscale Modelling–Artificial Intelligence Integration
	References
Index