scispace - formally typeset
Search or ask a question
Proceedings ArticleDOI

Thermal drying technologies: new developments and future r&d potential

01 Aug 2007-Drying Technology & Equipment (International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics)-pp 1-8
TL;DR: In this paper, the authors summarize the state-of-the-art as far as theoretical understanding of drying processes and provide examples of some new technologies being developed and provide opportunities for challenging fundamental and modeling studies to enhance drying technologies.
Abstract: Thermal dehydration processes are highly energy-intensive and are found in almost all industrial sectors, accounting for 10 to 20 percent on national industrial energy consumption in developed countries. With escalating energy costs and need to mitigate environmental pollution due to emissions from combustion of fossil fuels, it is increasingly important to develop innovative drying technologies. Furthermore, drying also affects quality of the dried product due to physical and/or chemical transformations that may occur during the heat and mass transfer operation. With tens of thousands of products that are dried in hundreds of dryer types, it is a formidable task indeed to develop design and scale-up procedures of wide applicability. Attempts have been made over the past three decades to make fundamental and applied contributions to transport phenomena and material science aspects in drying of various forms of wet solids, pastes and liquids. This presentation will attempt to summarize the state-of-the-art as far as theoretical understanding of drying processes and provide examples of some new technologies being developed. Opportunities for challenging fundamental and modeling studies to enhance drying technologies will be identified. Illustrative results will be presented to show how mathematical modeling of spray, spouted bed and heat pump dryers can be utilized to develop new conceptual designs and to optimize operating conditions as a cost-effective route to intensify innovation in thermal dryer design.

Summary (3 min read)

INTRODUCTION

  • Almost all industrial sectors involve thermal dehydration during one or several phases of their manufacturing processes.
  • This massive energy consumption mainly using fossil fuels directly impacts CO2 emission levels which are being curtailed actively under the Kyoto Protocol.
  • To make matters worse, industrial dryers, most of which were designed during the era of cheap and abundant energy, typically operate at thermal efficiencies in the range 20 to 60 percent.
  • Clearly there is tremendous scope for improvement of industrial drying technologies- a task that must logically begin with R&D to enhance their knowledge base on drying as well as dryers.
  • The latter is a coupled process involving transport phenomena and material science.

MATHEMATICAL MODELS OF DRYING AND DRYERS

  • The authors cannot provide a general overview of the wide assortment of modelling approaches, their relative merits and limitations, within the limited scope of this presentation.
  • The type of model clearly depends on the object of modelling, type of product and drying equipment.
  • Modelling of drying is a microscopic level approach that ideally is independent of the material.
  • Huang (2005) developed a CFD model to predict flow patterns and overall drying performance of different spray dryer designs [5]: the conventional cylinder-on-cone one; the dryer with two pressure nozzles, rotating disk atomizer and ultrasonic nozzle; the dryer with conical, hour-glass shape and lantern shape chambers.
  • The typical flow pattern of the spouted bed is shown in Figure2 (a), where a stable spout, fountain and annulus regions were observed clearly.

Thermo-Mechanical Models of Drying

  • When water is removed during drying processes, pressure imbalance is produced between inner pressure of the material and the external pressure, generating contracting stresses that can lead to material shrinkage or collapse, changes in shape.
  • When rapid drying rate conditions are used and intense moisture gradient through the materials are observed, shrinkage is not uniform resulting in the formation of unbalanced stress.
  • Surface cracking may occur leading to permanent deformation or even failure of the material.
  • To avoid such undesired effects, simulation tools that can handle simultaneously the drying problem and the coupled mechanical problem are necessary.
  • The thermo-mechanical models often comprise of simplified drying models based on the diffusion equation with different coefficients and boundary conditions for the first and second periods of drying.

Distribution of moisture content

  • The distributions of moisture content are often evaluated based on the diffusion model equations.
  • When temporal moisture content distribution is obtained, the shrinkage of materials and stresses can be then determined.

Drying- induced stresses

  • The author assumed that wood beyond the fibre saturation point (FSP) does not shrink and has the lowest mechanical strength despite its moisture content.
  • The shrinkage is then regarded as proportional primarily to the change of moisture content; the volumetric strain due to shrinkage is θε )(3 Xk= .
  • Substituting equation (5) and (7) into the physical relation (9-10), the authors can obtain the differential equation for determining stresses.
  • In summary, the thermo-mechanical model can be used to estimate shrinkage, capillary forces and thermal tensions cause stresses in drying bodies.
  • Table 2 lists the applications of thermo-mechanical models reported in the literature for various materials and its geometries, including organic, inorganic, biological materials.

Multiscale Models for Drying

  • Perre (2002) has discussed the characteristics and needs for multi-scale models in drying of such materials as wood and paper [22].
  • When the overall drying behaviour is influenced by both what happens at the micro scale and what happens at the macro scale, the authors need multi-scale models for proper representation of the drying behaviour.
  • On assuming isothermal conditions and constant total pressure, the microscopic vapour flux can be expressed with the gradient of the boundary-water content as the driving force by equation 12.
  • Vapour diffusion at macro scale will change the state variable (density, moisture content, temperature, etc) of the wood.
  • If the scale levels can not be considered as independent, other strategies have been proposed through which several scales can be considered simultaneously, such as the parallel flow model, mesocopic model [24], distributed microstructure models [25], etc.

R&D NEEDS IN DRYING

  • As is evident from the previous discussion, thermal drying of solids is a complex phenomenon that has defied development of a universal theory.
  • Unlike heat exchangers, design and analysis of the heat and mass exchangers (viz. dryers) is not amenable to use of appropriate software.
  • Kudra and Mujumdar (2001) have discussed a multitude of industrial drying technologies which deserve R&D for optimization [29].
  • Use of bio-gas, bio-diesel instead of oil or natural gas will become more common as petroleum products escalate in price.
  • Changes in technologies in one field will have an impact on technology in a related field.

CONCLUDING REMARKS

  • This paper has focused on a small area of R&D needs in the vast field of thermal drying.
  • As an energy consuming operation responsible for 10-25% of national industrial use in the developed countries, and an increasing fraction in the emerging economies as well, there is strong incentive to understand this operation better.
  • Aside from attempts to develop workable models for drying and dryers, it is also essential to carry out careful experiments on different size equipment to test models for scale-up.
  • Aside from models for heat and mass transfer it is also necessary to develop predictive models for the quality parameters of the dried products.
  • With potential legislations limiting carbon emissions and imposition of carbon tax, it will be essential in the next few decades to come up with ultraefficient, compact drying systems to remain globally competitive.

Did you find this useful? Give us your feedback

Content maybe subject to copyright    Report

HEFAT2007
5
th
International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
Sun City, South Africa
Paper number: K3
THERMAL DRYING TECHNOLOGIES: NEW DEVELOPMENTS AND FUTURE R&D
POTENTIAL
Mujumdar A.S.* and Wu Z.H.
*Author for correspondence
Department of Mechanical Engineering and Engineering Science Program,
National University of Singapore,
Singapore, 117575
E-mail: mepasm@nus.edu.sg
; website: http://serve.me.nus.edu.sg/arun
ABSTRACT
Thermal dehydration processes are highly energy-intensive
and are found in almost all industrial sectors, accounting for 10
to 20 percent on national industrial energy consumption in
developed countries. With escalating energy costs and need to
mitigate environmental pollution due to emissions from
combustion of fossil fuels, it is increasingly important to
develop innovative drying technologies. Furthermore, drying
also affects quality of the dried product due to physical and/or
chemical transformations that may occur during the heat and
mass transfer operation. With tens of thousands of products that
are dried in hundreds of dryer types, it is a formidable task
indeed to develop design and scale-up procedures of wide
applicability. Attempts have been made over the past three
decades to make fundamental and applied contributions to
transport phenomena and material science aspects in drying of
various forms of wet solids, pastes and liquids. This
presentation will attempt to summarize the state-of-the-art as
far as theoretical understanding of drying processes and provide
examples of some new technologies being developed.
Opportunities for challenging fundamental and modeling
studies to enhance drying technologies will be identified.
Illustrative results will be presented to show how mathematical
modeling of spray, spouted bed and heat pump dryers can be
utilized to develop new conceptual designs and to optimize
operating conditions as a cost-effective route to intensify
innovation in thermal dryer design.
INTRODUCTION
Almost all industrial sectors involve thermal dehydration
during one or several phases of their manufacturing processes.
Developed economies expend from 12-25% of their national
industrial energy for drying operations depending on the
product mixes they produce. This massive energy consumption
mainly using fossil fuels directly impacts CO
2
emission levels
which are being curtailed actively under the Kyoto Protocol. To
make matters worse, industrial dryers, most of which were
designed during the era of cheap and abundant energy, typically
operate at thermal efficiencies in the range 20 to 60 percent.
Clearly there is tremendous scope for improvement of
industrial drying technologies- a task that must logically begin
with R&D to enhance our knowledge base on drying as well as
dryers.
At the outset it is important to recognize that drying
involves heat and mass transfer but it is only a part of the
problem. It is important to be able to handle the wet material in
the dryer and be able to produce a dried product of prescribed
quality parameters- often not a simple task. In general what is
optimal for heat and mass transfer is not optimal for drying.
The latter is a coupled process involving transport phenomena
and material science. It may involve physical transformations
such as shrinkage, puffing, crystallization, cracking, glass
transitions along with potential chemical or biochemical
reactions. A mathematical model considering all these
phenomena- many unpredictable a priori- is still a distant dream
of drying researchers. A further complication arises from the
fact that some 50,000 materials with very diverse
physical/chemical properties need to be dried at different scales
of production and with very different product quality. No
wonder then that over 500 different types are reported in
technical literature and some 100 types of dryers are available
commercially. Contrast this with heat exchangers which can be
designed reasonably reliably using standard software packages.
No such luxury exists when it comes to heat and mass
exchangers involving wet solids. Indeed, the large body of
research literatures for dry solids becomes quite useless when
one is faced with a corresponding wet solid! It is obvious that
drying R&D presents numerous challenging problems some of
which are amenable to treatment with advanced computational
and analytical tools, but the actual scope of the problem is truly
of gigantic proportion.
The objective of this paper is to discuss some generic
problems encountered in the design and optimization of
industrial dryers, outline with some examples the nature of

problems that can be treated via mathematical modelling and
identify worthwhile R&D needs and opportunities for those
who wish to take up the challenge and make definitive and
useful contribution to the advancement of the science,
engineering and technology of thermal dehydration.
NOMENCLATURE
A [MPa] Elastic bulk modulus of dried materials
A [m
2
] The surface area of dried sample
B=KR/A [-] Coefficient of mass transfer (Biot Number)
c
1
,c
2
, …c
8
[-] Constants
D [m
2
/s] Coefficient of diffusion
f
[kg/m
2
s]
Moisture flux
h [J/kg] Enthalpy
J
0
, J
1
[-] Bessel functions of first kind of zero and first order
k
[kg/m
2
s]
Coefficient of convective vapour exchange
K [MPa] Elastic modulus due to shrinkage
M [MPa] Elastic shear modulus of dried sample
P [Pa] Pressure
r [m] Radial direction
R
[J/molK]
Universal gas constant
T [K] Temperature
t [s] Time
X [kg/kg] Moisture content, dry basis
Y [-] Vapour content in drying air
V [m
3
] Volume of dried sample
v [m/s] Velocity
Special characters
χ
[-] Depth scalar
ε
[-] Volume fraction
ε
[-] Volume strain
κ
(X)
[-] Coefficient of humid expansion
λ
1
, λ
n
[-] Enginvalue for Bessel functions
σ
[Pa] Stress
ρ
[kg/m
3
] Mass density
θ=X-X
r
[kg/kg] Relative moisture content
Α
[kgs/m
3
]
Mass transport coefficient
Subscripts
a Air
b Bulk
e Equilibrium state
eff Effective
g Gas phase
l Liquid phase
s Saturated state
v Vapour
w Water
0 Initial state
INNOVATION IN DRYING
Innovation is the engine that drives R&D and advances in
technologies in general. As the world is getting “flatter”,
following Friedman’s terminology, at an accelerating pace,
global competition will provide the impetus for increased R&D
particularly in areas inevitably dependent on large consumption
of energy. Already developing economies are making more
than their share of drying R&D over the past decades as
reflected by publications on drying R&D. Energy crisis of the
early 70’s drove drying R&D, resulting in several conferences
devoted to drying and even a new journal focused on drying.
As energy costs dropped and levelled off drying R&D
continued but driven by need to reduce costs, improve quality
and meet global competition. Recent hikes in energy costs will
drive a second wave in drying R&D seeking to further improve
the energy efficiency of entire drying/dehydration systems and
potentially use renewable sources of energy where feasible.
With rapidly increasing cost of physical experimentation and
lack of talent, it is obvious that we need to turn to the almighty
computer for cost-effective solutions and even as a way to
intensity the innovation process. After all, we are facing the
Digital Big Bang resulting in explosive growth of computer-
assisted engineering solutions.
There is one major problem that is limiting general
utilization of mathematical models for innovation, design,
operation and optimization of dryers. We do not yet have a
reliable general theory of drying. In fact we do not have
generalized mathematical models for even a particular type of
dryer, for example for spray dryer for liquids or fluid bed dryer
for particles. We must depend on empirical data and lab or even
pilot scale tests to arrive at reliable full scale units; even then
knowhow is of overriding value relative to current knowledge
of these processes. Most models work well with specific
product-dryer type combinations and that too with a significant
amount of empiricism.
In this paper we will provide as examples modelling results
for several dryer types examined at NUS viz. spray dryer for
liquids, a spouted bed dryer of particles, pulse combustion
dryer for liquids or as impingement dryer for sheets and heat
pump dryer for heat-sensitive materials. The idea is to
demonstrate how one can utilize models, even if not general
and fully validated, can be used to innovate and examine new
conceptual designs of dryers. They also show the formidable
challenges ahead, leading to some ideas for future R&D.
MATHEMATICAL MODELS OF DRYING AND DRYERS
We cannot provide a general overview of the wide
assortment of modelling approaches, their relative merits and
limitations, within the limited scope of this presentation. Table
1 is a summary of some of the model types (along with some
references for the benefit of the interested reader). The type of
model clearly depends on the object of modelling, type of
product and drying equipment. Modelling of drying is a
microscopic level approach that ideally is independent of the
material. Even for the simplest well-defined porous material
this poses severe problems. Compared to what we find in the
literatures on porous media, the corresponding drying problem
is complicated by the fact that the porous material can undergo
physical deformation and even chemical reactions, change of
moisture transport mechanisms during drying, can involve glass
transitions, precipitation of solids, micro-crystallization etc.
Some phenomena can occur at the micro-scale while others
may occur at the macro-scale. The material being dried can be
non-homogeneous and anisotropic. There can be porosity
gradients within the product as it dries. Multiple modes of heat
transfer can be applied simultaneously or intermittently to
provide the heat of phase change. Indeed, the operating
temperature and pressure range can range from below the triple
point (freeze drying) to above the critical point (supercritical

CO
2
extraction of water form hydrogels). Drying times can
range form milliseconds (inkjet droplets) to several months (in
some drying kilns for wood). From this it is clear that it is
unrealistic to expect to develop a generalized theory drying
based only on fundamental properties of the material.
Table 1 Mathematical model for the drying process
Table 2 Mathematical models for dryers
Model Type Description Applications
Response
surface
methodology
A statistical technique that uses
regression analysis to develop a
relationship between input and
output parameters
Process
optimization[8],
finding significant
factors
Multivariate
analysis
A collection of statistical
procedures that involve
observation and analysis of
multiple measurements
Optimization,
finding significant
factors
Data mining Automatic searching of large
volumes of data to establish
relationships and identify
patterns
Statistical
techniques,
machine learning
Neural
networks
An artificial neural network
model is an interconnected
group of functions that can
represent complex input-output
relationships
Process control [9-
10], product
quality, wider
applications
Genetic
algorithms
Search algorithms in a
combinational optimization
problem
Parameters
optimization [11],
process control
method [12]
Fuzzy logic Fuzzy set theory that permits
the gradual assessment of the
membership of elements
Dryer selection
[13], control [14]
Indeed, mathematical models also help with scale-up and
optimization of operating conditions. Furthermore, model-
based control is becoming increasingly popular to ensure good
thermal efficiency, safe operation and product quality. Thus,
out thesis is that mathematical models of dryers are a valuable
prelude to arriving at innovative designs of dryers. Following
are a couple of recent examples from our laboratory.
It should be noted at the outset that modelling of dryers
basically requires two sub-models, viz. a drying model and an
equipment model. The former deals with the drying
characteristics of the material being dried and the latter deals
with the manner in which the material is handled in the
equipment which affects the heat and mass transfer rates and
residence times the material sees within the dryer. Both types of
models today need considerable amount of empirical data e.g.
drying kinetics over parameter ranges to be encountered in the
dryer, behaviour of the material in the equipment under a range
of parameters the dryer may be operated under etc. The need to
model solids and solids flow, that too when the solids are wet
and hence maybe sticky with tendency to form lumps or
agglomerates, presents unusually complex problem to
modellers. We will consider just a few examples in this
presentation.
Huang (2005) developed a CFD model to predict flow
patterns and overall drying performance of different spray dryer
designs [5]: the conventional cylinder-on-cone one; the dryer
with two pressure nozzles, rotating disk atomizer and ultrasonic
nozzle; the dryer with conical, hour-glass shape and lantern
shape chambers. Furthermore, the CFD model was used to
Model Descriptions Applications
Lattice
Boltzmann
Simulation
Complex fluid phenomena at the
mesoscopic scale systems;
Simplicity, powerful method for
simulating flow in porous media;
Efficient to parallel computing
Emulsification;
micro-filtration
process; few
application in drying
Population
balances
Modelling discrete or particulate
materials using a population density
function;
Accuracy and convenience in
description of particle properties
Expensive in computation
Particulates in
fluidized beds [1].
Particle formation ,
breakage , etc
Discrete
element
model
Tracking the motion of individual
particles.
Accuracy in description of
dynamics of particulate phase.
Expensive in computation cost
Particle mixing in a
drum[2], particle
dynamics in fluid,
spray bed, etc.
Pore
network
model
Simulating flow in porous bodies.
Influence of Pore- structures on
drying kinetics.
Microscopic description of transport
phenomena
Increased model performance.
Drying of Porous
materials [3]
Fractal
analysis
Powerful tool for characterizing
materials and processes.
Self-similarity theory.
Complex and chaotic problem.
Efficiency in predicting particle
properties
Difficulty in estimation of fractal
dimension
Particle diameter
distribution, material
properties[4]
Computati
onal fluid
dynamics
(CFD)
model
Comprehensive model for
engineering problem.
Governing equations + boundary
and initial equations.
Higher sophistication when coupled
with other models
Available in commercial software
packages.
Active in system design and process
optimization
Spray, fluid, spouted
bed drying[5-6],
wider applications
Finite
element
analysis
Modelling moisture transfer in wet
solid.
No need for additional equation to
assure continuity cross common
boundaries.
Easily handle complex geometries
and mesh gradation.
Easily handle mixed boundary
conditions
Easily programmed.
Grains, soybean, rice
drying, thin-layer
drying, etc [7]

evaluate an innovative one-stage and two-stage, two
dimensional horizontal spray dryer (HSD) concept. Figure 1
shows predicted particle trajectories inside various chamber
geometries design in one stage HSD dryer, where Figure1 (A)
show a basic rectangular box design similar to a commercial
horizontal spray dryer (Ceroges, 2004). From Figure 1, it can
be seen that the chamber volume is not fully used in Case A
and B. The particle deposit on bottom wall is reduced and the
chamber volume is fully utilized in Case C. However, a
recirculation zone near the outlet will lead to backflow of
ambient air. Condensation may occur and it may cause large
deposit and poor product quality. Case D and E can be
considered as good conceptual designs: high chamber volume
utilization ratio, reduced wall deposits, sufficient particle
residence time, etc. If the evaporation rate per unit volume is
considered, Case D gives better performance, about 25%, more
than case E. Thus, Case D is the best one among proposed
geometry designs
Figure 1 Predicted flow stream and particle trajectories for
various one stage HSD designs
A CFD two-fluid model was developed by Wu to describe
the gas-particle flow behaviours of a cylindrical spouted bed
under a steady spouting jet [6]. The typical flow pattern of the
spouted bed is shown in Figure2 (a), where a stable spout,
fountain and annulus regions were observed clearly. Calculated
particle velocities and concentrations agree well with the
published experimental data. The CFD model was also used to
evaluate the influence of operation parameters such as particle
size, density, and pulsating jet, etc on flow pattern of the bed.
Figure2 (b) show a bubble generate inside the bed under a
pulsating jet and is moving to the freeboard. The bubble size
and shape is related to the frequency of the pulsating jet and
bubbles will disappear when frequency exceeds a critical value.
Bubble formation and resulting flow instabilities were also
described. The drying kinetics of grains in the spouted bed
dryer was also investigated computationally. Figure 3(b) shows
the predicted mass fraction of vapour inside the bed after a
drying time of 1.2 second. Similar distributions can also
obtained for gas temperature, particle temperature, moisture,
density, water evaporation rate, etc at different drying times.
Such predictions can provide important information on the flow
field within the spouted beds for process design and scale-up.
Figure 2 Particle concentration distribution insider the
bed under steady (a) and unsteady spouting jet (b) and mass
fraction distribution of vapor at drying time of 1.2 s
(H=0.325m, ρ
s
= 2500 kg/m
3
, d
s
=1.41mm, U
ms
=0.54 m/s)
Thermo-Mechanical Models of Drying
When water is removed during drying processes, pressure
imbalance is produced between inner pressure of the material
and the external pressure, generating contracting stresses that
can lead to material shrinkage or collapse, changes in shape.
When rapid drying rate conditions are used and intense
moisture gradient through the materials are observed, shrinkage
is not uniform resulting in the formation of unbalanced stress.
In this condition, surface cracking may occur leading to
permanent deformation or even failure of the material. To avoid
such undesired effects, simulation tools that can handle
simultaneously the drying problem and the coupled mechanical
problem are necessary.
The thermo-mechanical models often comprise of simplified
drying models based on the diffusion equation with different
coefficients and boundary conditions for the first and second
periods of drying. The drying models enable estimation of
moisture content distribution in the dried sample. The
magnitude of stresses/shrinkage depends inter alia on the
moisture distribution gradient. Different models for drying-
induced stresses and shrinkages have been developed to
estimate these mechanical effects.
Distribution of moisture content
The distributions of moisture content are often evaluated
based on the diffusion model equations. Taking a pine-wood
disk as an example [15], the moisture transfer during the first
period of drying, also called the constant drying rate period, is
described by the following differential equation

+
=
rr
r
D
t
II
I
I )(
2
)(2
)(
)(
1
ϑϑϑ
(1)
The boundary and initial condition is given by:
0
0
)(
=
=r
I
t
ϑ
(2)
()
constYYk
t
A
an
I
Rr
I
I
==
=
)(
)(
)(
ϑ
(3)
const
t
I
==
=
0
0
)(
θϑ
(4)
where Y
n
and Y
a
are the vapour contents in the drying air close
to and far form the disk surface, and k
(
Ι
)
is the coefficient of
convective vapour exchange between the dried disk and the
ambient air, respectively.
The solution of the above initial-boundary value problem
was constructed by Kowalski (2005) with the help the
separation of variables method and its final form is described as
()
+=
=
0
0
2
0
)(
)(
0
,
)(
)(
2
)(
)/(
12
n
t
t
e
nn
n
I
I
tr
I
I
n
J
RrJ
t
t
CRB
λ
λλ
λ
θϑ
(5)
where
)()()(
/
III
ARkB =
,
()
RYYC
an
/=
,
)(2)(
/
II
DRt =
and λn is the n-th eigenvalue calculated from the characteristic
equation
() {}{ }
.....,0
211
λ
λ
λ
λ
==
nn
J
,
(6)
Here J
0
and J
1
are Bessel functions of the first kind of zero and
first order, respectively.
Similarly, the moisture distribution in the disk during the
second period of drying reads
()
()
()
[]
()
+
×
+
+=
Π
Π
=
ΠΠΠ
)(
2
0
2
)(2
0
0
)(
2
)(
,
)(
exp
/
2
4
12
t
tt
a
aJBa
RraJ
B
a
aBb
s
n
nn
n
n
n
ee
tr
ϑθθ
(7)
Here a
n
is the nth enginvalue calculated from the characteristic
equation of the form
()
()
() {}{ }
.....,
2101
aaaaJ
a
B
aJ
nn
n
n
==
Π
Hence, equations (5) and (7) enable estimation of moisture
content distribution in the dried sample in several instants of
time. When temporal moisture content distribution is obtained,
the shrinkage of materials and stresses can be then determined.
Shrinkage
The moisture content of materials decreases during drying,
resulting in a decrease of its volume-shrinkage. Generally,
mathematical models for shrinkage can be classified as
empirical and fundamental ones. Empirical models are
relatively simple methods which develop an empirical
correlation between shrinkage and moisture content, including
occasionally the relevant process parameters like temperature
and humidity of air. The correlation can be linear: Lozano et al
(1980) used the equation
XccD
R 21
+= to model shrinkage
of the cylindered apple [16]. The reduced dimension D
R
refers
to volume; it can also be non-linear:
Vazquez, et al (1999)
applied the equation
)exp(
76
2/3
543
XccXcXccD
R
+++= to simulate
shrinkage of the slab garlic [17]. The reduced dimension is
thickness. These empirical models usually give good fit to
experimental data, but their use is limited because of their
dependence on the drying conditions and on the material
characteristics. They require extensive experimental testing and
should not be extrapolated.
Fundamental models, based on mass balances, density and
porosity definitions, assume in most cases additivity of the
volumes of the different phases of the system. That is,
shrinkage compensates for moisture loss. Suzuki, et al (1976)
used a linear equation to model the shrinkage of cube carrot,
potato, sweet potato, and radish:
1
7
0
+= Xc
V
V
where
e
XX
c
c
=
0
8
7
1
and
()
()
e
e
X
X
c
ρ
ρ
1
1
0
0
8
+
+
=
[18]. The reduced
dimension is area:
3/2
00
=
V
V
A
A
. Other types of
fundamental models for shrinkages were summarized in
Reference [19]. Compared with empirical models, it is not
usually necessary for fundamental models to obtain
experimental shrinkage values at every process condition. It
also allows the prediction of moisture content and/ or change in
volume to be obtained without complicated mathematical
calculations. However, the quality of the fundamental models
fitted to experimental data is relatively low.
Drying- induced stresses
Kowalski (2004, 2007) discussed the drying induced stress
during the wood drying process [15, 20]. The author assumed
that wood beyond the fibre saturation point (FSP) does not
shrink and has the lowest mechanical strength despite its
moisture content. Unsaturated wood, on the other hand, shrinks
when the moisture content decreases. The shrinkage is then
regarded as proportional primarily to the change of moisture
content; the volumetric strain due to shrinkage is
θε
)(
3
X
k=
.
The coefficient of humid expansion fulfils the following
criterion
=
se
X
s
X
k
k
θθθ
θθθ
)(
0
0
)(
0
(8)

Citations
More filters
Book ChapterDOI
01 Jan 2015
TL;DR: In this paper, the basic concepts of the drying process of food materials, detailing the transport mechanisms involved in the food drying process and the drying techniques commonly used in food industry are discussed.
Abstract: This chapter covers the basic concepts of the drying process of food materials, detailing the transport mechanisms involved in the drying process and the drying techniques commonly used in the food industry. It describes the different approaches employed for modelling various drying processes and the developmental steps involved in modelling the drying process of food materials. The chapter also presents a case study to demonstrate the application of modelling approach for optimisation of an industrial drying process. Finally, it highlights future development and application of modelling in food drying.

23 citations

Book ChapterDOI
01 Jan 2016
TL;DR: In this article, an overview of the transport mechanisms involved in convective drying of food materials and the drying techniques commonly used in the food industry is presented. And the influence of airborne ultrasound on the drying kinetics and on the changes of the product's structural and quality attributes, and phenomena associated with the application of ultrasound responsible for these effects.
Abstract: This chapter deals with the application of airborne ultrasound for convective drying intensification of food materials. It starts with an overview of the transport mechanisms involved in convective drying of food materials and the drying techniques commonly used in the food industry. The latter part of the chapter focuses on the influence of airborne ultrasound on the drying kinetics and on the changes of the product's structural and quality attributes, and the phenomena associated with the application of ultrasound responsible for these effects. Finally, the chapter examines the effects of various process parameters for efficient application of airborne ultrasound and highlights the future outlook of the technology.

17 citations

Book ChapterDOI
31 Aug 2016
TL;DR: The contribution of some drying techniques employed in the development of functional foods to increase the sustainability of the feeding process is discussed in this paper, where some measurements taken by the food industry to ensure the supply of bioactive nutrients to as many individuals as possible, assuring the global sustainability.
Abstract: Nowadays, the sustainability of a product, a process or a system is assessed according to three dimensions: environmental, social and economic. Sustainability challenges occur at all stages in the food system from production through processing, distribu‐ tion and retailing to consumption and waste disposal. The promotion of organic and local food is not the only way to reach the sustainability. There is other possibility that implies to continue the production hegemony. Increasing research is being focused on the development of healthy, quality and safety food products adapted to consumer’s needs and more environment-friendly processes, that is, processes consuming energy more efficiently, generating less waste and emitting less greenhouse effect gases. Drying technology is applied in the food industry not only for preservation but also to manufacture foods with certain characteristics. Drying technology operations need to be precisely controlled and optimized in order to produce a good-quality product with the highest level of nutrient retention and flavor together with microbial safety. This chapter contains detailed information about some measurements taken by the food industry to ensure the supply of bioactive nutrients to as many individuals as possible, assuring the global sustainability. More specifically, the contribution of some drying techniques employed in the development of functional foods to increase the sustaina‐ bility of the feeding process is discussed.

16 citations


Cites background from "Thermal drying technologies: new de..."

  • ...The problems of drying are diverse as various food materials with very diverse physical/ chemical properties need to be dried at different scales of production and with very different product quality specifications [13]....

    [...]

Book ChapterDOI
01 Jan 2015
TL;DR: In this article, the authors provide an overview of the drying process of food materials and provide a brief history of food drying and then describe the techniques commonly used in the food industry, focusing on the new/novel developments in food drying.
Abstract: This article provides an overview of the drying process of food materials. It starts with a brief history of food drying and then describes the techniques commonly used in the food industry. The latter part of this article focuses on the new/novel developments in food drying and finally highlights the future outlook of food drying.

14 citations

Journal ArticleDOI
TL;DR: In this paper, a closed loop heat pump drying (CLHPD) system with a relatively high circulating air temperature was proposed and established, and the effect of compressor speeds on the air temperature, coefficient of performance (COP), moisture extraction rate (MER), and specific moisture extraction ratio (SMER) of the system were experimentally studied.

14 citations

References
More filters
BookDOI
08 Nov 2006
TL;DR: In this article, Arun S. Mujumdar and Zdzislaw Pakowski discuss the fundamental principles, classification, and selection of spray dryers for various industrial spray drying processes.
Abstract: Section I - Fundamental Aspects Principles, Classification, and Selection of Dryers Arun S. Mujumdar Experimental Techniques in Drying Karoly Molnar Basic Process Calculations and Simulations in Drying Zdzislaw Pakowski and Arun S. Mujumdar Transport Properties in the Drying of Solids Dimitris Marinos-Kouris and Z.B. Maroulis Spreadsheet-Aided Dryer Design Z.B. Maroulis, G.D. Saravacos, and Arun S. Mujumdar Section II - Description of Various Dryer Types Indirect Dryers Sakamon Devahastin and Arun S. Mujumdar Rotary Drying Magdalini Krokida, Dimitris Marinos-Kouris, and Arun S. Mujumdar Fluidized Bed Dryers Chung Lim Law and Arun S. Mujumdar Industrial Spray Drying Systems Iva Filkova, Li Xin Huang, and Arun S. Mujumdar Theoretical Modeling and Numerical Simulation of Spray Drying Processes Maksim Mezhericher, Avi Levy, and Irene Borde Drum Dryers Wan Ramli Wan Daud Freeze Drying Athanasios I. Liapis and Roberto Bruttini Microwave and Dielectric Drying Robert F. Schiffmann Solar Drying Laszlo Imre and Arun S. Mujumdar Spouted Bed Drying Elizabeth Pallai, Tibor Szentmarjay, Sachin V. Jangam, and Arun S. Mujumdar Impingement Drying Arun S. Mujumdar Pneumatic and Flash Drying Irene Borde and Avi Levy Conveyor Dryers Dan Poirier Infrared Drying Cristina Ratti and Arun S. Mujumdar Superheated Steam Drying Arun S. Mujumdar Special Drying Techniques and Novel Dryers Tadeusz Kudra and Arun S. Mujumdar Intermittent Drying Karim Allaf, Sabah Mounir, Mohamed Negm, Tamara Allaf, Hanintsoa Ferrasse, and Arun S. Mujumdar Pulse Combustion Drying Wu Zhonghua and Arun S Mujumdar Section III - Drying in Various Industrial Sectors Drying of Foodstuffs Shahab Sokhansanj and Digvir S. Jayas Drying of Fish and Seafood M. Shafiur Rahman Grain Drying Vijaya G.S. Raghavan and Venkatesh Sosle Grain Property Values and Their Measurement Digvir S. Jayas and Stefan Cenkowski Drying of Rice Somkiat Prachayawarakorn, Chaiyong Taechapairoj, Adisak Nathakaranakule, Sakamon Devahastin, and Somchart Soponronnarit Drying of Fruits and Vegetables D. K. Das Gupta and K. S. Jayaraman Drying of Herbal Medicines and Tea Guohua Chen and Arun S. Mujumdar Drying of Potato, Sweet Potato, and Other Roots Shyam S. Sablani and Arun S. Mujumdar Osmotic Dehydration of Fruits and Vegetables Piotr P. Lewicki and Andrzej Lenart Drying of Pharmaceutical Products Zdzislaw Pakowski and Arun S. Mujumdar Drying of Nanosize Products Baohe Wang, Li Xin Huang, and Arun S. Mujumdar Drying of Ceramics Yoshinori Itaya, Shigekatsu Mori, and Masanobu Hasatani Drying of Peat and Biofuels Roland Wimmerstedt Drying of Fibrous Materials Roger B. Keey Drying of Textile Products Wallace W. Carr, H. Stephen Lee, and Hyunyoung Ok Drying of Pulp and Paper Osman Polat and Arun S. Mujumdar Drying of Wood: Principles and Practices Patrick Perre and Roger B. Keey Drying of Biomass Shusheng Pang Drying in Mineral Processing Arun S. Mujumdar Dewatering and Drying of Wastewater Treatment Sludge Guohua Chen, Po Lock Yue, and Arun S. Mujumdar Physicochemical Aspects of Sludge Drying Sachin V. Jangam, Tolga Tuncal and Arun Mujumdar Drying of Biotechnological Products Janusz Adamiec, Wladyslaw Kaminski, Adam S. Markowski, and Czeslaw Strumillo Drying of Coated Webs James Y. Hung, Richard J. Wimberger, and Arun S. Mujumdar Drying of Polymers Arun S. Mujumdar and Mainul Hasan Drying of Enzymes Ana M.R. Pilosof and Virginia E. Sanchez Drying of Proteins M. Amdadul Haque and Benu Adhikari Product Functionality-Oriented Drying Process related to Pharmaceutical Particle Engineering Meng Wai Woo and Arun Mujumdar Drying of Coal Jerzy Pikon, Sachin V. Jangam, and Arun S. Mujumdar Section IV - Miscellaneous Topics in Industrial Drying Dryer Feeding Systems Rami Y. Jumah and Arun S. Mujumdar Dryer Emission Control Systems Rami Y. Jumah and Arun S. Mujumdar Energy Aspects in Drying Czeslaw Strumillo, Peter L. Jones, and Romuald Zylla Heat Pump Drying Systems Chou Siaw Kiang and Chua Kian Jon Safety Aspects of Industrial Dryers Adam S. Markowski and Arun S. Mujumdar Control of Industrial Dryers Rami Y. Jumah, Arun S. Mujumdar, and Vijaya G.S. Raghavan Solid-Liquid Separation for Pretreatment of Drying Operation Mompei Shirato and Masashi Iwata Frying of Foods Vassiliki Oreopoulou, Magdalini Krokida, and Dimitris Marinos-Kouris Use of Simprosys in Drying Flowsheet Calculations Z. X. Gong, Sachin V. Jangam, and Arun S. Mujumdar Life Cycle-Assessment of Drying Systems Nawshad Haque, Sachin V. Jangam, and Arun Mujumdar Thermo-Hydro-Mechanical Aspects of Drying Stefan J. Kowalski and Andrzej Rybicki Supercritical Fluid-Assisted Drying Marzouk Benali and Yacine Boumghar Industrial Crystallization Seppo Palosaari, Marjatta Louhi-Kultanen, and Zuoliang Sha Cost-Estimation Methods for Drying Zbigniew T. Sztabert and Tadeusz Kudra

1,711 citations

Book
27 Sep 2012
TL;DR: In this article, the authors proposed a percolation model for Porous Media, based on a distributed microstructure model and showed that it is possible to obtain a homogenization of the Buckley-Leverett system.
Abstract: 1 Introduction.- 1.1 Basic Idea.- 1.2 First Examples.- 1.2.1 One-Dimensional Diffusion.- 1.2.2 Resistor Networks.- 1.2.3 Layered Media.- 1.3 Diffusion in Periodic Media.- 1.3.1 Formal Asymptotic Expansion.- 1.3.2 Application to Layered Media.- 1.3.3 Estimates of the Effective Conductivity Tensor.- 1.3.4 Media with Obstacles and Diffusion in Perforated Domains.- 1.4 Formal Derivation of Darcy's Law.- 1.5 Formal Derivation of a Distributed Microstructure Model.- 1.6 Remarks on Networks of Resistors, Capillary Tubes, and Cracks.- 1.6.1 Monte-Carlo Simulations.- 2 Percolation Models for Porous Media.- 2.1 Fundamentals of Percolation Theory.- 2.2 Exponent Inequalities for Random Flow and Resistor Networks.- 2.3 Critical Path Analysis in Highly Disordered Porous and Conducting Media.- 3 One-Phase Newtonian Flow.- 3.1 Derivation of Darcy's Law.- 3.1.1 Presentation of the Results.- 3.1.2 Proof of the Homogenization Theorem.- 3.1.3 A Priori Estimate of the Pressure in a Porous Medium.- 3.2 Inertia Effects.- 3.2.1 Darcy's Law with Memory.- 3.2.2 Nonlinear Darcy's Law.- 3.3 Derivation of Brinkman's Law.- 3.3.1 Setting of the Problem.- 3.3.2 Principal Results.- 3.4 Double Permeability.- 3.5 On the Transmission Conditions at the Contact Interface between a Porous Medium and a Free Fluid.- 3.5.1 Statement of the Problem and Existing Results from Physics.- 3.5.2 Statement of the Mathematical Results and Comparison with the Literature.- 4 Non-Newtonian Flow.- 4.1 Introduction.- 4.2 Equations Governing Creeping Flow of a Quasi-Newtonian Fluid.- 4.3 Description of a Periodic s-Geometry, Construction of the Restriction Operator, and Review of the Results of Two-Scale Convergence in Lq-Spaces.- 4.4 Statement of the Principal Results.- 4.5 Inertia Effects for Non-Newtonian Flows through Porous Media.- 4.6 Proof of the Uniqueness Theorems.- 4.7 Uniform A Priori Estimates.- 4.8 Proof of Theorem A.- 4.9 Proof of Theorem B.- 4.10 Conclusion.- 5 Two-Phase Flow.- 5.1 Derivation of the Generalized Nonlinear Darcy Law.- 5.1.1 Introduction.- 5.1.2 Obtaining Macroscopic Laws by Volume Averaging.- 5.1.3 Obtaining Macroscopic Laws by Homogenization.- 5.2 Upscaling Two-Phase Flow Characteristics in a Heterogeneous Reservoir with Capillary Forces (Finite Peclet Number).- 5.2.1 Introduction.- 5.2.2 Definition of the Homogenization Problem.- 5.2.3 General Homogenization Result.- 5.2.4 Some Special Cases.- 5.2.5 Randomly Heterogeneous Porous Media.- 5.3 Upscaling Two-Phase Flow Characteristics in a Heterogeneous Core, Neglecting Capillary Effects (Infinite Peclet Number).- 5.3.1 Introduction.- 5.3.2 Homogenization of the Buckley-Leverett System.- 5.3.3 Propagation of Nonlinear Oscillations.- 5.4 The Double-Porosity Model of Immiscible Two-Phase Flow.- 5.4.1 Introduction.- 5.4.2 The Microscopic Model.- 5.4.3 Compactness and Convergence Results.- 6 Miscible Displacement.- 6.1 Introduction.- 6.2 Upscaling from the Micro-to the Mesoscale.- 6.2.1 Diffusion, Convection, and Reaction.- 6.2.2 Adsorption.- 6.2.3 Chromatography.- 6.2.4 Semipermeable Membranes.- 6.3 Upscaling from the Meso-to the Macroscale.- 6.3.1 Mobile and Immobile Water.- 6.3.2 Fractured Media.- 6.4 Discussion.- 7 Thermal Flow.- 7.1 Introduction.- 7.2 Basic Equations.- 7.3 Natural Convection in a Bounded Domain.- 7.4 Natural Convection in a Horizontal Porous Layer.- 7.5 Mixed Convection in a Horizontal Porous Layer.- 7.6 Thermal Boundary Layer Approximation.- 7.7 Conclusion.- 8 Poroelastic Media.- 8.1 Acoustics of an Empty Porous Medium.- 8.1.1 Local Description and Estimates.- 8.1.2 Macroscopic Description.- 8.2 A Priori Estimates for a Saturated Porous Medium.- 8.3 Local Description of a Saturated Porous Medium.- 8.4 Acoustics of a Fluid in a Rigid Porous Medium.- 8.5 Diphasic Macroscopic Behavior.- 8.6 Monophasic Elastic Macroscopic Behavior.- 8.7 Monophasic Viscoelastic Macroscopic Behavior.- 8.8 Acoustics of Double-Porosity Media.- 8.8.1 A Priori Estimate.- 8.8.2 Double-Porosity Macroscopic Models.- 8.9 Conclusion.- 9 Microstructure Models of Porous Media.- 9.1 Introduction.- 9.2 Parallel Flow Models.- 9.2.1 Totally Fissured Media.- 9.2.2 Partially Fissured Media.- 9.3 Distributed Microstructure Models.- 9.3.1 Totally Fissured Media.- 9.3.2 Partially Fissured Media.- 9.4 A Variational Formulation.- 9.5 Remarks.- 9.5.1 Homogenization.- 9.5.2 Further Remarks.- 10 Computational Aspects of Dual-Porosity Models.- 10.1 Single-Phase Flow.- 10.1.1 The Mesoscopic and Dual-Porosity Models.- 10.1.2 Numerical Solution.- 10.2 Two-Phase Flow.- 10.2.1 The Mesoscopic and Dual-Porosity Models.- 10.2.2 Numerical Solution.- 10.3 Some Computational Results.- 10.3.1 Single-Phase.- 10.3.2 Two-Phase.- A Mathematical Approaches and Methods.- A.1.1 F-Convergence.- A.1.2 G-Convergence.- A.1.3 H-Convergence.- A.2 The Energy Method.- A.2.1 Setting of a Model Problem.- A.2.2 Proof of the Results.- A.3 Two-Scale Convergence.- A.3.1 A Brief Presentation.- A.3.2 Statement of the Principal Results.- A.3.3 Application to a Model Problem.- A.4 Iterated Homogenization.- B Mathematical Symbols and Definitions.- B.1 List of Symbols.- B.2 Function Spaces.- B.2.1 Macroscopic Function Spaces.- B.2.2 Micro-and Mesoscopic Function Spaces.- B.2.3 Two-Scale Function Spaces.- B.2.4 Time-Dependent Function Spaces.- C References.

1,005 citations


"Thermal drying technologies: new de..." refers background in this paper

  • ...If the scale levels can not be considered as independent, other strategies have been proposed through which several scales can be considered simultaneously, such as the parallel flow model, mesocopic model [24], distributed microstructure models [25], etc....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a physical description of the shrinkage mechanism and a classification of the different models proposed to describe this behaviour in food materials undergoing dehydration is presented. But, the authors do not consider the effect of porosity change on the quality of the dehydrated product and should be taken into consideration when predicting moisture and temperature profiles in the dried material.

667 citations


"Thermal drying technologies: new de..." refers background in this paper

  • ...fundamental models for shrinkages were summarized in Reference [19]....

    [...]

  • ...Other types of fundamental models for shrinkages were summarized in Reference [19]....

    [...]

Book
12 Oct 2001
TL;DR: In this article, the authors discuss the need for advanced drying technologies and the requirements for advanced technologies for drying and dewering on Inert Particles Impinging Stream Drying Drying in Pulsed Fluid Beds Superheated Steam Drying Airless Drying In Mobilized Beds Drying with Shock Waves Vacu Jet Drying System Contact-Sorption Drying Sonic Drying Pulse Combustion Drying Heat Pump Drying Fry-Drying
Abstract: GENERAL DISCUSSION: CONVENTIONAL AND NOVEL DRYING CONCEPTS Need for Advanced Drying Technologies Classification and Selection Criteria: Conventional versus Novel Technologies Innovation and Trends in Drying Technologies SELECTED ADVANCED DRYING TECHNOLOGIES Drying on Inert Particles Impinging Stream Drying Drying in Pulsed Fluid Beds Superheated Steam Drying Airless Drying Drying in Mobilized Beds Drying with Shock Waves Vacu Jet Drying System Contact-Sorption Drying Sonic Drying Pulse Combustion Drying Heat Pump Drying Fry-Drying SELECTED TECHNIQUES FOR DRYING AND DEWATERING Mechanical Thermal Expression Displacement Drying Vapor Drying Slush Drying Atmospheric Freeze-Drying Spray-Freeze-Drying Refractance Window Carver-Greenfield Process HYBRID DRYING TECHNOLOGIES Microwave-Convective Drying with Cogeneration Microwave-Vacuum Drying Filtermat Drying Spray-Fluid Bed-Vibrated Fluid Bed Dryer Combined Filtration and Drying Radio-Frequency Drying with 50 O Technology Radio Frequency-Assisted Heat Pump Drying Radio Frequency-Vacuum Drying Miscellaneous Hybrid Technologies OTHER TECHNIQUES Special Drying Technologies Index

387 citations


"Thermal drying technologies: new de..." refers background in this paper

  • ...Kudra and Mujumdar (2001) have discussed a multitude of industrial drying technologies which deserve R&D for optimization [29]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a simple procedure has been implemented to measure porosity of apples as a function of moisture contents, and it is shown that the pores which for biological reasons are open, i.e. connected to the outside, remain so until X = 1.5 g/g.
Abstract: A simple procedure has been implemented to measure porosity of apples as a function of moisture contents. The method has been applied to apples with change in moisture contents by conventional air drying. It is shown that the pores, which for biological reasons are open, i.e. connected to the outside, at the onset of dehydration, remain so until X = 1.5 g/g. As dehydration proceeds the pores are split into two families of pores: externally connected pores and locked-in bores. Both total and open pore porosity can be predicted from experimental correlations. Alternatively, the total porosity can be estimated from data on bulk volume shrinkage and the average composition of the tissue by means of equations presented. The interpretation of experimental data using this approach confirms that there is a significant change in the three-dimensional arrangement of the cellular tissue below X = 1.5 g/g. The two approaches lead to the conclusion that, probably due to cellular collapse, the open structure that characterizes the fresh foodstuff changes into a structure with locked-in pores. This fact may help to explain the slow and difficult re-hydration which characterizes air-dried foodstuffs. This hypothesis will be followed up in future work. The information developed should be of help in qualitative and quantitative modeling of processes involving moisture changes.

197 citations


"Thermal drying technologies: new de..." refers methods in this paper

  • ...The correlation can be linear: Lozano et al (1980) used the equation XccDR 21 += to model shrinkage of the cylindered apple [16]....

    [...]

Frequently Asked Questions (15)
Q1. What have the authors contributed in "Thermal drying technologies: new developments and future r&d potential" ?

This presentation will attempt to summarize the state-of-the-art as far as theoretical understanding of drying processes and provide examples of some new technologies being developed. The objective of this paper is to discuss some generic problems encountered in the design and optimization of industrial dryers, outline with some examples the nature of problems that can be treated via mathematical modelling and identify worthwhile R & D needs and opportunities for those who wish to take up the challenge and make definitive and useful contribution to the advancement of the science, engineering and technology of thermal dehydration. It may involve physical transformations such as shrinkage, puffing, crystallization, cracking, glass transitions along with potential chemical or biochemical reactions. A further complication arises from the fact that some 50,000 materials with very diverse physical/chemical properties need to be dried at different scales of production and with very different product quality. 

More efficient combustion technologies which also provide thrust for gas movement in dryer, e.g. pulse combustion, will become more common. 

Use of low rank coal which contains large volume of water (similar to peat) will increase along with the need to dewater and dry coal costeffectively possibly using superheated steam. 

With potential legislations limiting carbon emissions and imposition of carbon tax, it will be essential in the next few decades to come up with ultraefficient, compact drying systems to remain globally competitive. 

The thermo-mechanical models often comprise of simplified drying models based on the diffusion equation with different coefficients and boundary conditions for the first and second periods of drying. 

The CFD model was also used to evaluate the influence of operation parameters such as particle size, density, and pulsating jet, etc on flow pattern of the bed. 

As energy costs dropped and levelled off drying R&Dcontinued but driven by need to reduce costs, improve quality and meet global competition. 

Solar dryers utilizing photovoltaics and possibly wind energy to boost the drying rates and efficiency will become more popular even in developed countries. 

Even in conventional areas like drying of paper, ceramics, wood etc there is scope to make the processes more energy-efficient, environmentally friendly and safe. 

the multiscale model shows high application potential in drying, especially of porous materials such as wood, ceramics, etc. 

In the coming decade one should see more industrial technologies utilizing superheated steam as the drying medium because of its numerous inherent advantages. 

the CFD model was used toevaluate an innovative one-stage and two-stage, two dimensional horizontal spray dryer (HSD) concept. 

Compared to what the authors find in the literatures on porous media, the corresponding drying problem is complicated by the fact that the porous material can undergo physical deformation and even chemical reactions, change of moisture transport mechanisms during drying, can involve glass transitions, precipitation of solids, micro-crystallization etc. 

If the scale levels can not be considered as independent, other strategies have been proposed through which several scales can be considered simultaneously, such as the parallel flow model, mesocopic model [24], distributed microstructure models [25], etc. 

In summary, the thermo-mechanical model can be used to estimate shrinkage, capillary forces and thermal tensions cause stresses in drying bodies.