Drying Phenomena - Ibrahim Dincer - ebook

Drying Phenomena ebook

Ibrahim Dincer

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Opis

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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Table of Contents

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

List of Tables

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

List of Illustrations

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

Guide

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DRYING PHENOMENA

THEORY AND APPLICATIONS

İbrahim Dinçer

and

Calin Zamfirescu

University of Ontario Institute of Technology, Oshawa, ON, Canada

This edition first published 2016© 2016 John Wiley & Sons, Ltd.

Registered OfficeJohn Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

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Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought.

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.

Preface

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

Nomenclature

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

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

Greek Letters

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

Subscripts

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

Superscripts

average value

saturation condition

0

reference state with respect to dry air

ch

chemical

discretized time index

Q

heat