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Comprehensively covers conventional and novel drying systems and applications, while keeping a focus on the fundamentals of Drying Phenomena. * Presents detailed thermodynamic and heat/mass transfer analyses in a reader-friendly and easy-to-follow approach * Includes case studies, illustrative examples and problems * Presents experimental and computational approaches * Includes comprehensive information identifying the roles of flow and heat transfer mechanisms on the Drying Phenomena * Considers industrial applications, corresponding criterion, complications, prospects, etc. * Discusses novel drying technologies, the corresponding research platforms and potential solutions
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Cover
Title Page
Preface
Nomenclature
1 Fundamental Aspects
1.1 Introduction
1.2 Fundamental Properties and Quantities
1.3 Ideal Gas and Real Gas
1.4 The Laws of Thermodynamics
1.5 Thermodynamic Analysis Through Energy and Exergy
1.6 Psychometrics
1.7 Heat Transfer
1.8 Mass Transfer
1.9 Concluding Remarks
1.10 Study Problems
References
2 Basics of Drying
2.1 Introduction
2.2 Drying Phases
2.3 Basic Heat and Moisture Transfer Analysis
2.4 Moist Material
2.5 Types of Moisture Diffusion
2.6 Shrinkage
2.7 Modeling of Packed-Bed Drying
2.8 Diffusion in Porous Media with Low Moisture Content
2.9 Modeling of Heterogeneous Diffusion in Moist Solids
2.10 Conclusions
2.11 Study Problems
References
3 Drying Processes and Systems
3.1 Introduction
3.2 Drying Systems Classification
3.3 Main Types of Drying Devices and Systems
3.4 Processes in Drying Systems
3.5 Conclusions
3.6 Study Problems
References
4 Energy and Exergy Analyses of Drying Processes and Systems
4.1 Introduction
4.2 Balance Equations for a Drying Process
4.3 Performance Assessment of Drying Systems
4.4 Case Study 1: Analysis of Continuous-Flow Direct Combustion Dryers
4.5 Analysis of Heat Pump Dryers
4.6 Analysis of Fluidized Bed Dryers
4.7 Conclusions
4.8 Study Problems
References
5 Heat and Moisture Transfer
5.1 Introduction
5.2 Transient Moisture Transfer During Drying of Regularly Shaped Materials
5.3 Shape Factors for Drying Time
5.4 Moisture Transfer Coefficient and Diffusivity Estimation from Drying Curve
5.5 Simultaneous Heat and Moisture Transfer
5.6 Models for Heat and Moisture Transfer in Drying
5.7 Conclusions
5.8 Study Problems
References
6 Numerical Heat and Moisture Transfer
6.1 Introduction
6.2 Numerical Methods for PDEs
6.3 One-Dimensional Problems
6.4 Two-Dimensional Problems
6.5 Three-Dimensional Problems
6.6 Influence of the External Flow Field on Heat and Moisture Transfer
6.7 Conclusions
6.8 Study Problems
References
7 Drying Parameters and Correlations
7.1 Introduction
7.2 Drying Parameters
7.3 Drying Correlations
7.4 Conclusions
7.5 Study Problems
References
8 Exergoeconomic and Exergoenvironmental Analyses of Drying Processes and Systems
8.1 Introduction
8.2 The Economic Value of Exergy
8.3 EXCEM Method
8.4 SPECO Method
8.5 Exergoenvironmental Analysis
8.6 Conclusions
8.7 Study Problems
References
9 Optimization of Drying Processes and Systems
9.1 Introduction
9.2 Objective Functions for Drying Systems Optimization
9.3 Single-Objective Optimization
9.4 Multiobjective Optimization
9.5 Conclusions
9.6 Study Problems
References
10 Sustainability and Environmental Impact Assessment of Drying Systems
10.1 Introduction
10.2 Sustainability
10.3 Environmental Impact
10.4 Case Study: Exergo-Sustainability Assessment of a Heat Pump Dryer
10.5 Conclusions
10.6 Study Problems
References
11 Novel Drying Systems and Applications
11.1 Introduction
11.2 Drying with Superheated Steam
11.3 Chemical Heat Pump Dryers
11.4 Advances on Spray Drying Systems
11.5 Membrane Air Drying for Enhanced Evaporative Cooling
11.6 Ultrasound-Assisted Drying
11.7 Conclusions
11.8 Study Problems
References
Appendix A Conversion Factors
Appendix B Thermophysical Properties of Water
Appendix C Thermophysical Properties of Some Foods and Solid Materials
References
Appendix D Psychometric Properties of Humid Air
Index
End User License Agreement
Chapter 01
Table 1.1 The fundamental quantities of the International System of Units
Table 1.2 Some quantities relevant in thermodynamics
Table 1.3 Fundamental constants and standard parameters
Table 1.4 Simple thermodynamic processes and corresponding equations for ideal gas model
Table 1.5 Description of the van der Waals equation of state
Table 1.6 Comparison of Dalton and Amagat models
Table 1.7 Relevant parameters of ideal gas mixtures
Table 1.8 Standard chemical exergy of some elements
Table 1.9 Components molar fraction and standard chemical exergy for terrestrial atmosphere
Table 1.10 Illustration of the effects of wall assumptions considered at entropy associated with heat transfer
Table 1.11 Energy and exergy efficiency of some important devices for power generation
Table 1.12 Important notions and properties for psychometrics
Table 1.13 The balance equations of basic psychometric processes
Table 1.14 Dimensionless criteria for heat and mass transfer modeling
Table 1.15 Correlations for Nusselt number for various flow configurations
Table 1.16 Mathematical relationships for basic transient heat transfer
Table 1.17 Analytical solutions for transient heat transfer through the semi-infinite solid
Table 1.18 Correlations for Sherwood number
Table 1.19 Analytical solutions for transient mass transfer through the semi-infinite solid
Chapter 02
Table 2.1 Mathematical models for property equations
Table 2.2 Fluid properties for numerical calculations
Chapter 03
Table 3.1 Categorization of numerous moist materials for drying applications
Table 3.2 Dryer types categorized with respect to the moist material handling method
Table 3.3 Heat transfer parameters and heat demand of two types of indirect dryers
Table 3.4 Types of agitated dryers
Table 3.5 Description of gravity-type dryers
Chapter 04
Table 4.1 State point descriptions for the generic drying system described in Figure 4.2
Table 4.2 State point descriptions for the generic drying system described in Figure 4.2
Table 4.3 Assumptions for Example 4.1
Table 4.4 Balance equations for the heat pump dryer shown in Figure 4.5
Table 4.5 Balance equations for the heat pump dryer shown in Figure 4.5
Table 4.6 Energy and exergy efficiencies of system units
Table 4.7 Input data for the system
Table 4.8 Summary of each stream along with their component and properties, for Example 4.2
Table 4.9 Exergy efficiency, rate of exergy destruction, RI, and SI of the major units of the heat pump dryer system
Table 4.10 Input data for Example 4.3
Chapter 05
Table 5.1 Analogue parameters for transient heat transfer and transient mass transfer modeling
Table 5.2 Experimental determinations of diffusivity and moisture transfer coefficient for some moist materials
Table 5.3 Dimensionless moisture content data for Example 5.6
Table 5.4 Boundary conditions for simultaneous heat and mass transfer in 2D domain from Figure 5.14
Table 5.5 Time-dependent moisture diffusion equation without source terms in 3D coordinate systems
Table 5.6 Sorption isotherms models
Table 5.7 Parameters for Midilli et al. (2002) model
Table 5.8 Semitheoretical and empirical models for thin-film drying curve
Chapter 06
Table 6.1 Classification of PDEs of two variables
Table 6.2 Numerical methods for systems of ODE of the form
Table 6.3 Runge–Kutta–Nyström method for systems of second-order ODEs
Table 6.4 Weighted residual methods of finite element type
Table 6.5 Equations and boundary conditions for simultaneous heat and moisture transfer in semi-infinite solid
Table 6.6 Explicit finite difference numerical scheme for 2D time-dependent heat and moisture transfer
Table 6.7 Drying parameters of some fruits slices
Table 6.8 Input data for the apple slab of 4.8 × 4.9 × 2.0 cm
Table 6.9 Boundary conditions for simultaneous heat and mass transfer in cylindrical 2D domain with axial symmetry
Table 6.10 Explicit time-dependent finite difference numerical scheme for axisymmetric cylindrical coordinates
Table 6.11 Input data for broccoli drying, Example 6.6
Table 6.12 ADI numerical scheme for heat and moisture transfer on polar coordinates
Table 6.13 Explicit time-dependent finite difference numerical scheme for 2D spherical coordinates
Table 6.14 Process and thermophysical parameters considered for potato drying
Table 6.15 Luikov coefficients for simultaneous heat and moisture transfer with constant thermophysical properties
Table 6.16 Governing equations for the external flow field
Chapter 07
Table 7.1 Parameters for moisture diffusivity correlation (Eq. (7.17)) for various foodstuff subjected to drying
Table 7.2 Moisture diffusivity correlated with lag factor and drying coefficient
Table 7.3 The use of
Bi
m
–
Di
m
correlation to determine the moisture diffusivity and transfer coefficient for foodstuff
Table 7.4 Regression correlations for μ
1
eigenvalues versus lag factor
Table 7.5 The use of
Bi
m
–
S
correlation to determine the moisture diffusivity and transfer coefficient for foodstuff
Chapter 08
Table 8.1 Calculation table for exergy price based on primary energy sources for Canada (data for year 2008)
Table 8.2 Parameters required for an economic analysis
Table 8.3 Equations for economic analysis
Table 8.4 Quantification of environmental impact
Chapter 09
Table 9.1 Parameters utilizable as constraints for drying systems optimization
Table 9.2 Atmospheric pollutants released by combustion systems
Table 9.3 Rough estimation of life cycle air pollution versus GHG indicator for various dryer systems
Chapter 10
Table 10.1 Categories and kinds of indicators influencing the sustainability assessment
Table 10.2 Atmosphere gases and their molar fractions for Gaggioli and Petit (1977) model
Table 10.3 Reference environment described in Rivero and Garfias (2006)
Table 10.4 Atmospheric pollutants released by power generation systems
Table 10.5 The principal greenhouse gases and their approximated concentration in the atmosphere
Table 10.6 The GWP of principal greenhouse gases
Table 10.7 Typical life cycle emissions for power generation from differing sources (g/kW h)
Table 10.8 Estimations of exergetic cost of atmospheric pollutants for Ontario
Table 10.9 Approximated average VOC composition and characteristics in Ontario
Table 10.10 Approximated average PM composition and characteristics in Ontario
Table 10.11 Environmental pollution costs (EPC) and removal pollution costs (RPC) for fossil fuels in Ontario
Table 10.12 Removal pollution cost at power generation in Canada
Table 10.13 Life cycle emissions into the atmosphere for power generation technologies (kg/GJ)
Table 10.14 Embodied energy, pollution, and environmental pollution cost in construction materials
Table 10.15 State points description and parameters for the reference drying system
Table 10.16 Construction materials and the associated sustainability parameters for the reference drying system
Table 10.17 Embedded exergy and environmental pollution costs for reference drying system life cycle
Table 10.18 State descriptions and thermodynamic parameters for the heat pump system
Table 10.19 Embedded exergy and environmental pollution costs for the improved drying system life cycle
Table 10.20 Comparison of the reference and improved drying systems
Chapter 11
Table 11.1 Energy demand comparison of conventional and superheated steam dryers
Appendix B
Table B.1 Thermophysical properties of pure water at atmospheric pressure
Table B.2 Thermophysical properties of water at saturation
Appendix C
Table C.1 Thermophysical properties of some solid materials
Table C.2 Average water content moisture diffusivity of selected foodstuff at room temperature
Appendix D
Table D.1 Properties of air at standard atmospheric pressure
Table D.2 Properties of humid air at standard atmospheric pressure
Chapter 01
Figure 1.1 Illustration of pressures for measurement
Figure 1.2 Illustrating the concept of thermodynamic system
Figure 1.3 Representation of an isolated thermodynamic system
Figure 1.4 Representation of phase diagram of water
Figure 1.5
T–v
diagram for pure water
Figure 1.6
P–v
diagram for pure water
Figure 1.7 Pressure versus temperature diagram of water
Figure 1.8 Ideal gas processes represented in
P–v
diagram
Figure 1.9 Generalized compressibility chart averaged for water, oxygen, nitrogen, carbon dioxide, carbon monoxide, methane, ethane, propane,
n
-butane, iso-pentane, cyclohexane,
n
-heptane
Figure 1.10 Illustrating the first law of thermodynamics written for a closed system
Figure 1.11 Conceptual representation of a heat engine (a) and heat pump (b)
Figure 1.12 Illustrative sketch for mass balance equation
Figure 1.13 Explanatory sketch for the entropy balance equation – a statement of SLT
Figure 1.14 Explanatory sketch for the exergy balance equation
Figure 1.15 Diagram illustrating the concepts of dew point and relative humidity
Figure 1.16 Schematic representation of (a) dry-bulb and (b) wet-bulb thermometers
Figure 1.17 The Mollier diagram of moist air
Figure 1.18 Representation of the adiabatic saturation process
Figure 1.19 Illustration of a latent cooling process of humid air
Figure 1.20 Some basic psychometric processes: (a) Cooling and heating. (b) Dehumidification. (c) Cooling and dehumidification. (d) Adiabatic humidification. (e) Chemical dehumidification. (f) Mixture of two moist air flows
Figure 1.21 Schematic representations of heat transfer modes: (a) Conduction through a solid. (b) Convection from a surface to a moving fluid. (c) Radiation between two surfaces
Figure 1.22 Schematic illustration of conduction in a slab object
Figure 1.23 A wall subject to convection heat transfer from both sides and heat conduction through wall
Figure 1.24 Simple model transient conduction heat transfer
Figure 1.25 Mass transfer process at an interface, through a mass transfer boundary layer
Chapter 02
Figure 2.1 The drying periods for a solid. (a) Moisture content versus time. (b) Drying rate versus drying time. (c) Drying rate versus moisture content. (The curves are for moist material dried at a constant temperature and relative humidity)
Figure 2.2 Classification of Moist materials
Figure 2.3 Classification of moist materials according to the types of their drying rate curves: (a) boundary layer control, (b) boundary layer and internal diffusion, and (c) internal diffusion control
Figure 2.4 Two forms of unbound moisture. Funicular state is that condition when during a drying process of a capillary porous material air is absorbed into the pores due to capillary suction forces. Pendular state is the state of a liquid in a porous solid when a continuous film of liquid no longer exists around and between discrete particles so that flow by capillary cannot occur. This state succeeds the funicular state
Figure 2.5 Dried apple tissue after 2 h at 70 °C
Figure 2.6 Porosity versus product moisture content for various drying methods (Krokida and Maroulis (1997))
Figure 2.7 Effects of drying temperature on the shrinkage coefficient of grapes (Krokida and Maroulis (1997))
Figure 2.8 Three stages of packed-bed drying (A material zone with initial moisture, B: drying zone, and C: dried material zone)
Figure 2.9 Mass balance at the product element
Figure 2.10 Numerical model for solving the differential equations
Chapter 03
Figure 3.1 Classification criteria of drying equipment and systems
Figure 3.2 Classification of direct-contact dryers
Figure 3.3 Classification of indirect-contact dryers
Figure 3.4 Heat demand ranges for the main types of direct-contact dryers
Figure 3.5 Batch tray dryer with direct contact (forced air circulation)
Figure 3.6 Batch through-recirculation dryer
Figure 3.7 Countercurrent tunnel dryer
Figure 3.8 Parallel flow tunnel dryer
Figure 3.9 Dual-zone tunnel dryer with entrance side exhaust
Figure 3.10 Dual-zone tunnel dryer with central exhaust
Figure 3.11 Sketch of a tunnel dryer of conveyor-screen type
Figure 3.12 Simplified sketch illustrating the operating principle of indirect rotary dryer
Figure 3.13 Sketch showing the mechanical construction of a direct-heat rotary dryer
Figure 3.14 Sketch showing a perspective view of a rotary dryer
Figure 3.15 Drying rate and specific price of industrial direct rotary dryers correlated with surface area
Figure 3.16 Relative drying of various materials in direct heated rotary dryers
Figure 3.17 Schematics of a Roto-Louvre dryer
Figure 3.18 Sketch of an agitated rotating dryer
Figure 3.19 Correlation between heat transfer surface area and specific equipment price for two agitated dryers
Figure 3.20 Sketch of a direct-heat vibrating conveyer dryer
Figure 3.21 Two-stage gravity flow dryer
Figure 3.22 Dispersion dryer: (a) operation principle and (b) sketch showing the spiral path of air and particles
Figure 3.23 Pneumatic-conveyor flash dryer schematics
Figure 3.24 Sketch showing the 3D view of an industrial flash dryer platform
Figure 3.25 System schematics of an extended residence time flash dryer
Figure 3.26 Flash drying system with partial product recirculation
Figure 3.27 Flash drying system with partial air recirculation
Figure 3.28 Countercurrent two-stage flash drying system
Figure 3.29 Flash fluid bed drying system
Figure 3.30 Relative drying of some materials in pneumatic-conveyor dryer
Figure 3.31 Schematic diagram of a ring dryer system
Figure 3.32 Schematics of a P-type ring dryer system
Figure 3.33 Sketch illustrating the operation principle of spray dryer
Figure 3.34 Sketch illustrating the operation principle of well-mixed continuous-flow fluidized bed dryer
Figure 3.35 Sketch showing the system construction of fluid bed dryer
Figure 3.36 Sketch showing the operation principle of drum dryers: (a) single-drum system and (b) sheets drying system
Figure 3.37 Solar cabinet dryer
Figure 3.38 Staircase-type solar dryer
Figure 3.39 Schematic diagram of the reverse absorber cabinet dryer
Figure 3.40 Solar tunnel dryer
Figure 3.41 Solar chimney dryer
Figure 3.42 Solar through dryer with separate air heater
Figure 3.43 PV/T-assisted solar drying tunnel
Figure 3.44 Solar air heaters with corrugated absorber: (a) single glazing and (b) double glazing
Figure 3.45 Schematic illustration for modeling natural drying process
Figure 3.46 Natural drying of agricultural products (grains, rice) in open air on concrete slabs
Figure 3.47 Natural drying of fruits in trays directly exposed to solar radiation
Figure 3.48 Natural drying of wood logs in stacks placed under shelters (use of solar radiation)
Figure 3.49 Comparison of four natural drying technologies for cassava
Figure 3.50 Relative decrease of moisture content (with respect to initial value) at natural drying of some fruits and vegetables
Figure 3.51 Drying of concrete
Figure 3.52 Temporal variation of central temperature and moisture content hydrated high amylose starch powders
Figure 3.53 Forced drying with an air-loop heat-pump dryer
Figure 3.54 Forced drying with a batch tray dryer equipped with a heat pump system
Figure 3.55 Temperature and humidity control with heat pump-based air handling units
Figure 3.56 Forced drying system with heat pump and advanced heat recovery option
Chapter 04
Figure 4.1 Thermodynamic model schematics for a drying process
Figure 4.2 Schematics of a continuous-flow direct combustion dryer of generic type
Figure 4.3 Relative irreversibility for the drying system studied in Example 4.1
Figure 4.4 Comparison of heat pump drying with other conventional drying methods in terms of energy efficiency (
η
) and moisture extraction for kilojoule of heat input
Figure 4.5 Heat pump drying system of simple configuration
Figure 4.6 Heat pump drying system with two-stage evaporators
Figure 4.7 Heat pump drying system with two-stage evaporators
Figure 4.8 Effect of reference temperature on exergetic performance
Figure 4.9 The correlation between the fluidization regime, flow velocity, and bed pressure drop
Figure 4.10 Schematics for the fluidized bed drying modeling
Figure 4.11 Relative reduction of the moisture content of wheat grains during the drying process (given with respect to the initial moisture content)
Figure 4.12 Variation of the energy efficiency during drying of wheat grains
Figure 4.13 Variation of the exergy efficiency during drying of wheat grains
Figure 4.14 Variation of the exergy efficiency during drying of wheat grains
Figure 4.15 Comparison of energy and exergy efficiency for wheat and corn drying when input air temperature is fixed at 65 °C and the moisture content reduction relative to initial value is 45%
Chapter 05
Figure 5.1 General model for moisture diffusion through the infinite slab
Figure 5.2 Dimensionless moisture content variation at the infinite slab median plane with Fourier number for mass transfer at drying of an infinite slab for various
Bi
m
Figure 5.3 Dimensionless moisture content at infinite slab center and surface for
Figure 5.4 Comparison between experimental data (circles) and the drying model predictions based on Dincer number (Eq. (5.22), continuous line) for a case study of sultana grapes drying assumed with cylindrical shape
Figure 5.5 Variation of the normalized dimensionless moisture content with
τ
and Dincer number
Figure 5.6 General model for moisture diffusion through the infinite cylinder
Figure 5.7 Dimensionless moisture content variation at the infinite cylinder axis with Fourier number for mass transfer at drying of an infinite slab for various
Bi
m
Figure 5.8 Comparison of dimensionless moisture content for moist materials of spherical shape, infinite cylinder shape, and infinite slab shape for
Figure 5.9 Ratio of dimensionless moisture contents at material surface and the center during a drying process for a range of Biot numbers
Figure 5.10 Regular tridimensional geometrical objects
Figure 5.11 Variation of shape factor with Biot number for the infinite square rod (
Figure 5.12 Shape factors for spheroids (oblate and prolate)
Figure 5.13 Data regression in a drying experiment to determine the exponential drying curve
Figure 5.14 Sketch for 2D heat and mass transfer time-dependent modeling in Cartesian coordinates
Figure 5.15 Sketch illustrating the hysteresis effect of sorption isotherms
Chapter 06
Figure 6.1 Approximation of a function based on Taylor expansion (Euler method)
Figure 6.2 Approximation of a function based on Taylor expansion (Euler method)
Figure 6.3 The moisture content and the moisture diffusivity variation at a depth of 2 mm in the semi-infinite moist material subjected to drying. The analytical solution for
W
at
D
= constant as given by Eq. (6.30) is compared to the numerical solution for which
D
varies with the temperature
Figure 6.4 The moisture content in the semi-infinite moist material subjected to drying at various depths
Figure 6.5 Moisture content and temperature in the semi-infinite moist material subjected to drying at
Figure 6.6 Distribution of the dimensionless moisture content and temperature at
Fo
= 1 for Example 6.4
Figure 6.7 Dimensionless moisture content variation at three locations for Example 6.4
Figure 6.8 Two-dimensional numerical grid for the time-dependent finite difference scheme
Figure 6.9 Qualitative representation of momentarily temperature and moisture content distributions in a rectangular material subjected to drying
Figure 6.10 Contour plots of 2D temperature and moisture content at drying of fig slice (Table 6.7)
Figure 6.11 Temperature and moisture content surfaces at drying of fig slice (Table 6.7)
Figure 6.12 Contour plots of 2D temperature and moisture content at drying of apple slice (Table 6.7)
Figure 6.13 Temperature and moisture content surfaces at drying of apple slice (Table 6.7)
Figure 6.14 Contour plots of 2D temperature and moisture content at drying of peach slice (Table 6.7)
Figure 6.15 Temperature and moisture content surfaces at drying of peach slice (Table 6.7)
Figure 6.16 Contour plots of 2D temperature and moisture content for Example 6.5
Figure 6.17 Moisture content and temperature variation at the center of the apple slab for Example 6.5
Figure 6.18 Axisymmetric numerical grid for the time-dependent finite difference scheme for heat and moisture transfer in cylindrical coordinates
Figure 6.19 Representation of numerical solutions for temperature and moisture content in cylindrical domain
Figure 6.20 Temperature and moisture surfaces at banana drying, modeled in axisymmetric cylindrical coordinates
Figure 6.21 Contour plots of dimensionless temperature and moisture content for broccoli, Example 6.6
Figure 6.22 Dimensionless temperature at the center of the cylindrical object as function of time for five values of the heat transfer coefficient, for Example 6.6
Figure 6.23 Dimensionless moisture content at the center and at the surface of the cylindrical object variation in time, for Example 6.6
Figure 6.24 Domain discretization for polar coordinates (a) and contours of dimensionless moisture content obtained for a porous material with moisture
exposed to drying (b)
Figure 6.25 Variation of dimensionless moisture content at center and surface during drying of a spherical potato
Figure 6.26 Drying rate variation with time for a spherical potato
Figure 6.27 Discretization of a 3D domain in Cartesian coordinates for the control volume method
Figure 6.28 External flow field and computational domain around a moist slab material
Figure 6.29 Qualitative representation of local heat and moisture transfer coefficients for a slab object in an external flow field
Figure 6.30 Numerical results showing the moisture content (a) and temperature (b) contours in a kiwi fruit slice after 30 min drying in air at 50 °C with a velocity of 0.3 m/s
Chapter 07
Figure 7.1 Drying curve expressing the exponential variation of the dimensionless moisture content at material center (Φ) with respect to the dimensionless time (
Fo
m
)
Figure 7.2 Flow patterns in a spouted bed dryer
Figure 7.3 Experimental (marks) and predicted (line) Biot number for mass transfer as a function of Dincer number for moisture transfer during various foodstuff drying
Figure 7.4 Experimental (marks) and predicted (line) Biot number for mass transfer as a function of drying coefficient during various foodstuff drying
Figure 7.5 Prediction validation of diffusion coefficient using the
correlation
Figure 7.6 Prediction validation of Biot number for mass transfer using the
correlation
Figure 7.7 Graphical determination of moisture transfer parameters in drying of a slab-shaped moist material
Chapter 08
Figure 8.1 System modeling sketch to the application of the EXCEM method
Figure 8.2 Solar dryer system for Example 8.1
Figure 8.3 SPECO method application to a drying system showing the input and output cost stream
Figure 8.4 SPECO method applied for Example 8.2 (heat pump tumbler dryer)
Figure 8.5 Environmental impact of a drying system
Figure 8.6 Relative environmental impact factor for a solar-driven drying system
Figure 8.7 Environmental impact and exergy efficiency for a heat pump dryer
Chapter 09
Figure 9.1 Thermodynamic representation of an ideal (reversible) drying process
Figure 9.2 Energy balances for an actual (irreversible) drying process (finite time/finite size process)
Figure 9.3 GHG emission indicator for Canadian grids
Figure 9.4 Life cycle exergetic emission indicator for various energy sources usage (approximated for Canada)
Figure 9.5 Drying process optimization as a trade-off problem of balancing between moisture diffusion through the material and convective moisture transfer at the surface
Figure 9.6 Optimization of drying time for levelized product price or total cost minimization
Figure 9.7 Tray dryer configuration for optimization Example 9.1
Figure 9.8 Example of a 2D convex function
Figure 9.9 Graphical representation of parametric minimization process of a 2D objective function
Figure 9.10 Graphical representation of parametric minimization process of a 2D objective function
Figure 9.11 Pareto frontier for the parametric optimization problem from Example 9.2
Figure 9.12 Multiobjective optimization of multigeneration systems: (a) two-dimensional Pareto fronts and (b) three-dimensional optimal representation
Figure 9.13 Example of an irregular Pareto frontier of a three-objective optimization problem
Figure 9.14 Example of an irregular Pareto frontier of a three-objective optimization problem
Figure 9.15 Three-objective optimization of the dryer analyzed in Example 9.2 with respect to drying time (
t
drying
), mass flow rate of dry product (
), and total tray area (m
2
)
Chapter 10
Figure 10.1 The DPSIR model for sustainability assessment
Figure 10.2 Sustainability assessment model for a drying process, based on material and energy balances
Figure 10.3 Energy and exergy efficiency of basic drying systems and other thermal processes
Figure 10.4 Representation of the exergy at the confluence of energy, environment, and sustainable development
Figure 10.5 The correlation between environmental impact index and sustainability index
Figure 10.6 Exergetic life cycle modeling diagram for sustainability assessment of a drying system (continuous arrows mean material flow, dashed arrows mean heat or work fluxes)
Figure 10.7 Thermodynamic model for the terrestrial environment showing the interactions among the main subsystems (biosphere is partially represented by anthropogenic biosphere)
Figure 10.8 Anthropogenic environmental impact affecting the atmosphere and global climate
Figure 10.9 The residence of gaseous effluents in the atmosphere expressed as the temporal decrease of mass relative to the initial moment
Figure 10.10 The radiative forcing in 2005 with respect to year 1750, due to various causes of change
Figure 10.11 Anthropogenic GHG emissions by sectors (a) and major gas type (b)
Figure 10.12 Thermodynamic representation of the drying process indicating the waste stream
Figure 10.13 Illustrating the concept of greenization applied to drying systems
Figure 10.14 Wood chips drying process in an industrial rotary kiln dryer
Figure 10.15 Wood chips drying process in an industrial rotary kiln dryer
Figure 10.16 Model for life cycle operations for drying system manufacture, scrapping, and fuel production
Figure 10.17 Heat pump for improved wood chips drying system
Chapter 11
Figure 11.1 Schematic of a drying system with superheated steam
Figure 11.2 Example of a chemical heat pump dryer
Figure 11.3 Solar chemical heat pump dryer with the CaCl
2
/NH
3
pair or MgCl
2
/NH
3
pair
Figure 11.4 Setup for spray drying of aqueous cupric chloride at UOIT
Figure 11.5 Photograph of the low-temperature spray drying system for CuCl
2
(aq) dehydration (taken at Clean Energy Research Laboratory (UOIT))
Figure 11.6 SEM images of CuCl
2
particles formed by spray drying at UOIT: (a) low-temperature experiments, (b) high-temperature experiments
Figure 11.7 Principle of operation of the vibrating membrane atomizer
Figure 11.8 Principle of operation of the electrostatic separator for nanoparticles
Figure 11.9 Configuration of the main types of microcapsules
Figure 11.10 Spray drying setup for microencapsulation
Figure 11.11 Emerging air-conditioning system with membrane air dryer integrated with evaporative cooling
Figure 11.12 Cooling process representation in Mollier diagram for the membrane air dryer integrated with evaporative cooling
Figure 11.13 Ultrasound-assisted vacuum drying system
Figure 11.14 Relative moisture removal after 90 min of vacuum drying under ultrasound exposure at various intensities
Appendix D
Figure D.1 Psychometric chart of humid air
Cover
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İbrahim Dinçer
and
Calin Zamfirescu
University of Ontario Institute of Technology, Oshawa, ON, Canada
This edition first published 2016© 2016 John Wiley & Sons, Ltd.
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Library of Congress Cataloging-in-Publication Data
Dinçer, İbrahim, 1964– author.Drying phenomena : theory and applications / İbrahim Dinçer and Calin Zamfirescu. pages cm Includes bibliographical references and index.
ISBN 978-1-119-97586-1 (cloth)1. Drying. I. Zamfirescu, Calin, author. II. Title. TP363.D48 2016 664′.0284–dc23
2015025655
A catalogue record for this book is available from the British Library.
Drying, as an energy-intensive process, plays a major role in various sectors, ranging from food industry to wood industry, and affects economies worldwide. Drying applications consume a noticeable part of the world’s produced energy and require a careful attention from microlevel to macrolevel applications to make them more efficient, more cost effective, and more environmentally benign. Bringing all these dimensions into the designs, analyses, and assessments of drying systems for various practical applications is of paramount significance.
This book offers a unique coverage of the conventional and novel drying systems and applications while keeping a focus on the fundamentals of drying phenomena. It includes recent research and contributions in sustainable drying systems and integration with renewable energy. The book is expected to serve the drying technology specialists by providing comprehensive tools for system design, analysis, assessment, and improvement. This is essentially a research-oriented textbook with comprehensive coverage of the main concepts and drying systems designs. It includes practical features in a usable format for the design, analysis, multicriteria assessment, and improvement of drying processes and systems which are often not included in other solely academic textbooks. Due to an extensive coverage, practicing engineers, researchers, and graduate students in mainstream engineering fields of mechanical and chemical engineering can find useful information in this book.
The book consists of 11 chapters which amalgamate drying technology aspects starting from basic phenomena to advanced applications, by considering energy, exergy, efficiency, environment, economy, and sustainability issues. The first chapter covers in broad manner introductory topics of thermodynamics, energy, exergy, and transient heat transfer and mass transfer, so as to furnish the reader with sufficient background information necessary for the rest of the book.
Chapter 2 covers the basics of drying, introducing the drying phases and the related phenomena of heat and moisture transfer. The moist materials are characterized and classified (e.g., hydroscopic, nonhygroscopic, capillary, etc.) in relation with the mechanisms of moisture diffusion and associated phenomena such as shrinkage. Introduction to diffusion modeling through porous media and moist solids is provided.
Chapter 3 comprehensively classifies and describes drying devices systems. Two- and three-dimensional explanatory sketches are presented to facilitate the systems explanation. The most relevant processes occurring in drying systems and devices are presented for natural and forced drying.
Chapter 4 introduced the energy and exergy analyses for drying processes and systems. There are only few studies in the literature that treat the exergy analysis of drying processes and system; most of the published research limit to energy analyses only. Therefore, this chapter aims to fill this gap and provides a comprehensive method for irreversibility analysis of drying using exergy as a true method to identify the potentials for system improvement. Performance assessment of drying systems based on energy and exergy efficiency is explained in detail. Some relevant drying systems are analyzed in detail such as direct combustion dryers, fluidized bed dryers, and heat pump dryers.
Chapter 5 focuses on analytical methods for heat and moisture transfer. The solutions for moisture transfer in basic geometries such as infinite slab, infinite cylinder, and sphere are given. Parameters such as drying coefficient and lag factor which are essential for analytical modeling of the processes are introduced. The chapter also teaches about the analytical expressions for drying time of object with regular and irregular geometry and the so-called shape factors for drying time. One important aspect is represented by determination of moisture transfer diffusivity and moisture transfer coefficient in drying operation. A comprehensive method to determine these parameters based on the experimental drying curve is introduced. Also, the chapter allocates sufficient space to the analytical formulation and treatment of the process of simultaneous heat and moisture transfer. In this respect, the Luikov equations and other formulations for simultaneous heat and moisture transfer are presented and the impact of sorption–desorption isotherms is explained. A summary of drying curve equations and models is given.
Numerical heat and moisture transfer is treated extensively in Chapter 6. Finite difference schemes and three types of weighted residual numerical methods (finite element, finite volume, and boundary element) are introduced in sufficient detail. The subsequent part of the chapter is structured in three sections corresponding to one-, two-, and three-dimensional numerical analysis of heat and moisture transfer covering Cartesian, cylindrical, polar, and spherical coordinate systems. The influence of external flow field on heat and moisture transfer inside the moist material is also discussed.
Drying parameters and correlations are presented in Chapter 7. Selected correlations are introduced for quick, firsthand calculation of essential drying parameters such as drying time, moisture diffusivity, moisture transfer coefficient, binary diffusion coefficient, drying coefficient, and lag factor. An interesting and useful graphical method for moisture transfer parameters determination in drying processes is given.
Chapter 8 introduces the exergoeconomic and exergoenvironmental analyses for drying processes and systems. Here, the economic value of exergy is emphasized together with its role in economic analysis and environmental impact assessment of drying technologies. Two exergoeconomic methods and their application to drying are presented, namely, the energy–cost–exergy–mass and the specific exergy cost methods. The use of exergy and exergy destruction for environmental impact assessment of drying systems is explained.
Chapter 9 concentrates on optimization of drying processes and system. Optimization is crucial for the design of better systems with improved efficiency, effectiveness, more economically attractive and sustainable, and having a reduced environmental impact. It is important to formulate technical, economic, and environmental objective functions, and this aspect is extensively explained in the chapter. Single-objective and multiobjective optimizations are discussed.
Chapter 10 is about sustainability and environmental impact assessment of drying systems. Here, sustainability as a multidimensional parameter is defined and the most important sustainability indicators are introduced. An exergy-based sustainability assessment method is proposed which accounts for energy, environment, and sustainable development. Various aspects are discussed such as reference environment models and environmental impacts and the role of exergy destruction-based assessment of environmental impact of drying systems. A case study is treated comprehensively regarding the life cycle exergo-sustainability assessment of a heat pump dryer.
Some selected novel drying systems and applications are presented in Chapter 11 based on a literature review. The use of superheated steam as drying medium appears very promising and consists of a novel development trend on drying technology. Chemical heat pump-assisted dryers emerged as a technology push. Very impressive developments in spray drying are reported to cover drying and production of nanoparticles and microcapsules. These emerging technologies are relevant in medicine for nanotherapeutics, in pharmaceutical industry for drug delivery, and in food industry for foodstuff encapsulation. Other emerging technologies and applications such as ultrasonic drying and membrane-assisted air conditioning are reviewed.
The book comprises a large number of numerical examples and case studies, which provide the reader with a substantial learning experience in analysis, assessment, and design of practical applications. Included at the end of each chapter is the list of references which provides the truly curious reader with additional information on the topics yet not fully covered in the text.
We hope that this book brings a new dimension to drying technology teaching and learning, promoting up-to-date practices and methods and helping the community implement better solutions for a better, more sustainable future.
We acknowledge the assistance provided by Dr. Rasim Ovali for drawing various illustrations of the book.
We also acknowledge the support provided by the Natural Sciences and Engineering Research Council of Canada and Turkish Academy of Sciences.
Last but not least, we warmly thank our wives, Gulsen Dincer and Iuliana Zamfirescu, and our children Meliha, Miray, Ibrahim Eren, Zeynep, and Ibrahim Emir Dincer and Ioana and Cosmin Zamfirescu. They have been a great source of support and motivation, and their patience and understanding throughout this book have been most appreciated.
İbrahim Dinçer and Calin Zamfirescu
Oshawa, September 2015
a
empirical constant
a
acceleration, m/s
2
a
general parameter
a
thermal diffusivity, m
2
/s
a
regression coefficient
a
1
,
a
2
constants
a
w
water activity
A
area (general; or area normal to the flow of heat or mass), m
2
A
discretization parameter
A
factor in
Eq. (7.8)
discretization matrix
AC
annual consumption
AI
annual income, $
A
n
factor in
Eq. (5.10)
AP
annual production, units
Ar
Archimedes number
AR
aspect ratio
ASI
aggregated sustainability index
b
general parameter
b
regression coefficient
numerical scheme parameter
B
driving force
B
discretization parameter
Bi
Biot number
Bi
m
Biot number for moisture transfer
B
n
factor in
Eq. (5.10)
c
speed of light in vacuum, m/s
C
specific heat, J/kg K
C
coefficients for numerical schemes
C
molar concentration, mol/l
cost, $
cost rate, $/h
CEF
consumed energy fraction
exergy price, $
CExF
consumed exergy fraction
CIEx
exergy based capital investment effectiveness
C
m
moisture (or mass) concentration, kg/m
3
COP
coefficient of performance
C
p
specific heat, J/kg K
CP
capital productivity
CRF
capital recovery factor
CSF
capital salvage factor
C
v
specific heat at constant volume, kJ/kg K
d
diameter, m
d
constant
D
diffusion coefficient, m
2
/s
D
moisture diffusivity, m
2
/s
D
c
binary diffusion coefficient for water vapor in air, m
2
/s
DDTOF
dimensionless drying time objective function
DE
drying effectiveness
D
eff
effective diffusion coefficient, m
2
/s
DEI
dryer emission indicator
D
h
hydraulic diameter, m
Di
Dincer number
Di
m
Dincer number for mass transfer
DPV
drying product value
DQ
drying quality
D
T
Soret coefficient for thermal diffusion, kg/m s K
e
specific energy, kJ/kg
e
elementary charge, C
e
mass specific energy, kJ/kg
E
shape factor
E
energy, J
energy rate, W
EcI
eco-indicator
EE
embodied energy, GJ/t
EEOF
energy efficiency objective function
EF
ecological footprint
EI
environmental impact
E
in
OF
energy input objective function
EPC
environmental pollution cost, $/kg
EPC
ex
exergetic environmental pollution cost, $/GJ
ex
specific exergy, kJ/kg
Ex
exergy amount, kJ
exergy rate, kW
ExCI
specific exegetic capital investment
ExCDR
construction exergy expenditure to lifecycle exergy destruction ratio
ExIE
exergetic investment efficiency
ExEOF
exergy efficiency objective function
EUR
energy utilization ratio
f
friction coefficient
f
function
distribution of pores radius
F
force, N
F
Faraday constant, C/mol
F
function
F
radiative forcing, W/m
2
dimensionless parameter
F
1
,
F
2
series expansions for shape factors
Fo
Fourier number
F
obj
objective function
Fo
m
Fourier number for mass transfer (dimensionless time)
g
gravity constant (= 9.81 m/s
2
)
g
specific Gibbs free energy, kJ/kg
G
basis weight
GC
generated capital, $
GEI
grid emission indicator, g/kW h
GF
greenization factor
Gr
Grashof number
Gu
Gukhman number
GWP
global warming potential
Gz
Graetz number
h
specific enthalpy, kJ/kg
h
Planck constant, kJ s
H
enthalpy, kJ
h
m
moisture transfer coefficient, m/s
HR
Hausner ratio
HT
halving time
h
tr
or
h
heat transfer coefficient, W/m
2
K
i
inflation rate
I
irradiation, W/m
2
I
electric current, A
Ind
indicator
I
v
luminous intensity, cd
j
diffusive mass flux, kg/m
2
s
mass flux, kg/m
2
s
J
0
zeroth-order
J
Bessel function
J
1
first-order
J
Bessel function
J
m
mass flux, kg/m
2
s
boundary intervals
k
thermal conductivity, W/m K
k
drying rate, s
−1
K
1,2
parameters
constant; coefficient, or parameter
k
B
Boltzmann constant, J/K
k
m
mass transfer coefficient, s
−1
l
(characteristic) length, m
L
length, characteristic length or thickness, m
L
bed height, m
L
c
(characteristic) dimension, m
LCC
levelized cost of consumables, $/unit
LCEI
ex
Life cycle exergetic emission indicator, g/kW h
LCSI
lifecycle sustainability index
Le
Lewis number
LF
lag factor
LHV
lower heating value, MJ/kg
LPP
levelized product price $
LPPOF
levelized product price objective function
LT
life cycle time, years
m
index
m
mass, kg
mass ratio
mass flow rate, kg/s
mass flux, kg/m
2
s
m
,
n
,
p
number of elements (vector)
M
molecular weight, kg/kmol
M
a
relative molecular mass of air, kg/kmol
MEPC
molar environmental pollution cost, $/kmol
M
v
molecular mass of vapor, kg/mol
n
index, exponent, number
n
empiric exponent
n
mole number, kmol
n
adiabatic exponent
n
system lifetime
normal to surface
N
number of particles
N
A
Avogadro’s number
NH
number of halving times
n
hour
number of hours of operation, h
NI
net income, $
NSI
normalized sustainability index
Nu
Nusselt number
P
pressure, kPa
P
a
partial pressure of air, Pa
P
am
mean of partial pressures of air over the product surface and in drying air, Pa
PBP
payback period, years
Pe
Péclet number
PoI
point of impingement
PP
performance parameter
Pr
Prandtl number
P
v
partial pressure of vapor, Pa
P
va
partial pressure of vapor in drying air, Pa
saturated vapor pressure, Pa
PVF
present value factor
P
vm
mean of partial vapor pressures of vapor over the product surface and in drying air, Pa
P
vo
vapor pressure over the product surface, Pa
PWI
present worth income, $
PWF
present worth factor
q
heat rate per unit area, W/m
2
; flow rate per unit width or depth
heat flux, W/m
2
heat flux, W/m
2
Q
heat flux, J or kJ
Q
quantity (amount)
heat transfer rate, W
heat flux per unit of surface, W/m
2
QP
quality parameter
r
radial coordinate; radius, m
r
aerodynamic resistance, m/s
r
real discount rate
r
latent heat, J/kg
r
particle coordinate, m
r
distance normal to the flow of heat, m
mesh parameter
R
loss ratio
R
radius, radius of a single particle, m
universal gas constant, kJ/kg K
Ra
Rayleigh number
RC
specific resource consumption
RD
relative drying
Re
Reynolds number
RI
relative irreversibility
ℜ
n
residual function
R
pai
practical application impact ratio
RPC
removal pollution cost
R
si
sectorial impact ratio
R
ti
technological impact ratio
R
v
gas constant for water vapor, J/kg/K
s
specific entropy, kJ/kg
entropy rate, kW/K
S
entropy, kJ/K
S
drying coefficient, s
–1
S
surface, m
2
entropy rate, W/K
Sc
Schmidt number
SE
specific GHG emissions, kg
GHG
/GJ
SEI
sustainability efficiency indicator
S
g
gas phase saturation
Sh
Sherwood number
SI
exergetic sustainability index
SIOF
sustainability index objective function
SP
span
SPI
sustainable process index
SRW
specific reversible work
SR
shrinkage ratio
St
Stanton number
SV
salvage value, $
t
time, s
tortuosity factor
T
temperature, K
temperature function, K
t
05
halftime, h
t
c
tax credit
TCD
tax credit deduction, $
TExDOF
total exergy destruction objective function
t
i
tax on income
TI
taxable income, $
T
m
mean temperatures of product surface and drying air, °C
T
ma
mean absolute temperatures of product surface and drying air, K
T
o
surface temperature, K
TOI
tax on income, $
t
op
operational time, h
TOP
tax on property, $
t
p
tax on property
t
s
tax on salvage
u
specific internal energy, kJ/kg
u
velocity in
x
direction
displacement, m
U
internal energy, kJ
U
flow velocity of drying air, m/s
U
economic utility
v
specific volume, m
3
/kg
v
velocity in
y
direction
velocity, m/s
V
volume, m
3
V
velocity, m/s
volumetric flow rate, m
3
/s
V
0
standard ideal gas volume, m
3
/kmol
u
velocity (speed), m/s
w
mass specific work, kJ/kg
w
weighting factors
W
work, kJ
work rate, kW
moisture content function, kg/kg dry basis
W
moisture content kg water/kg dry material
average moisture content, kg/kg
x
quality, kg/kg
x
Cartesian coordinate, m
x
s
degree of saturation
X
v
volumetric moisture content, m
3
/m
3
y
mole fraction
y
Cartesian coordinate, m
dimensional coordinate, m
Y
characteristic dimension (length), spatial dimension, m
z
Cartesian coordinate, m
z
axial coordinate, thickness, m
Z
compressibility factor
α
volume fraction of air
β
enhancement factor
β
volume-shrinkage coefficient
β
length ratio
γ
parameter
γ
quality factor
γ
climate sensitivity factor
δ
thickness, length, coordinate, m
δ
space increment, m
δ
thermal gradient coefficient, K
−1
Δh
lv
latent heat of vaporization, J/kg
Δ
t
time step, s
ε
void fraction
ε
phase conversion
ε
volumetric fraction of vapor
ζ
dimensionless coordinate
η
energy efficiency
η
dynamic viscosity, Pa/s
η
dimensionless space variable
θ
total specific energy of flowing matter, kJ/kg
θ
dimensionless temperature
μ
dynamic viscosity, kg/ms
μ
chemical potential, kJ/kg
μ
diffusion resistance factor; root of the transcendental characteristic equation
μ
1
first eigenvalue
μ
n
n
th eigenvalue
ν
kinematic viscosity, m
2
/s
ξ
M
specific mass capacity (kg mol/kJ)
ξ
T
specific temperature coefficient (kg/kg K)
ρ
density, kg/m
3
ρ
dr
bone dry density, kg/m
3
σ
Stefan–Boltzmann constant, W/m² K
4
σ
surface tension, N/m
σ
standard average
τ
time constant, s
τ
residence time, s
τ
atmospheric lifetime, s
ϑ
contact
contact angle
φ
relative humidity
φ,
Φ
dimensionless moisture content
Φ
s
sphericity
ϕ
total specific exergy, kJ/kg
ϕ
porosity, m
3
/m
3
ϕ
relative humidity
ϕ
zenith angle
ϕ
trial function
ψ
exergy efficiency
ψ
test function
ω
humidity ratio
Ω
domain of decision variables
0
reference state
0
dry material
0.5, 1, ½, ¼, ⅛, 2
indices
0.5
half time
bulk
a
(dry) air; medium; surroundings
act
activation
acum
accumulated
air
air
am
air mixer
ap
air penetration process
AP
air pollution
avg
average
b
boundary, dry bulb, bulk
b
fluidized bed
bw
bounded moisture
c
characteristic, critical, convection
c
cyclone
cap
capital
ch
chemical
CIE
capital investment effectiveness
cmp
compressor
comb
combustor
cond
condenser
conc
concentration
CO
carbon monoxide
cons
consumed
csteel
carbon steel
cv
control volume
cyl
cylinder
d
destroyed, dew point, drying
da
drying air
dissip
dissipation
dr
dryer
deliv
delivered
e
equilibrium
Eef
effective effusion
ef
effective
en
energetic
ex
exergy, exergetic
evap
evaporator
f
fluid; final; flow; force; formation, fuel
fa
fan
fc
feeder/conveyor
fg
liquid–vapor equilibrium
fi
filter
g
gas, global, generation
gen
generated
gt
gas turbine generator
H
high-temperature
ha
humid air
hp
heat pump
i
,
j
,
k
indices
i, in
initial
in
input
int
internal
k
conduction
ke
kinetic energy
l
liquid, lateral
lam
laminar
lc
lifecycle
liq
liquid
loss, lost
lost
lv
liquid–vapor
L
low-temperature
m
mass, environment, material, moisture, moist material, market
m
monolayer
ma
material-to-air (binary coefficient)
mat
materials
mf
minimum fluidization
mm
moist material
mr
moisture removal
n
normal direction
nf
nonflow
oc
other cost
occ
other cost creation
o&m
operation and maintenance
opt
optimum
out
output
p
particle
p, prod
product
pe
potential energy
ph
physical
pr
pollutant removal
pw
pollutant waste
Q
heat
r
reduced
r
refrigerant
r
removed moisture
R
radius
rec
recovered
ref
reference
rev
reversible
rf
recirculation flap
s
surface; solid, saturation, dry solid surface
sat
saturation
sc
supplementary combustor
sep
separator
shape
shape
slab
slab
sph
sphere
ssteel
stainless steel
surface
surface
sys
system
tot
total
tr
heat transfer
turb
turbulent
tv
throttling valve
used
utilized or used
v
vapor
w
wet bulb, water, wind, moisture, vapor
wb
wet bulb
wm
wet material
x
x
direction
y
y
direction
average value
″
saturation condition
0
reference state with respect to dry air
ch
chemical
discretized time index
Q
heat