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4Modelling of drying processes
for food materials
H.T. SabarezCommonwealth Scientific and Industrial Research Organisation–Food and NutritionFlagship, Werribee, Victoria, Australia
4.1 Introduction
Drying is one of the important unit operations in food manufacturing aimed at reduc-
ing the amount of moisture in food products to levels that ensure preservation by inhi-
biting microbial and enzymatic activity and the associated product quality
deterioration. In basic terms, the process of drying (or dehydration) involves the
removal of water from a wet feedstock by inducing phase changes of water from solid
or liquid into a vapour phase via the application of heat (except in the case of osmotic
dehydration during which the water is removed without a change in phase by the dif-
fusion of liquid water from solid foods to osmotic solution through an osmotic pres-
sure difference). Drying usually consumes large amounts of energy and imparts
significant alterations in product quality attributes due to the exposure to longer drying
times or higher temperatures. Today’s increased competition due to globalisation,
together with the growing consumer demand for better quality products, will continue
to drive innovations in the drying process, leading to further efforts in improving the
performance of the existing drying technologies and the development of new drying
concepts crucial for the future sustainability of the food industry. In drying food mate-
rials, there remains a major challenge in removing water from the material in the most
efficient way, with better control of product quality, minimal impact on the environ-
ment, the lowest capital and operating costs of the process. A further challenge arises
from the fact that many food materials with very diverse physical or chemical prop-
erties need to be dried at different scales of production and with very different product
quality specifications (Mujumdar and Wu, 2010).
Mathematical modelling is a useful tool for simulating and testing the performance
of the drying process, which allows one to generate tangible results for a wide range of
scenarios through a virtual laboratory that would be too expensive or time-consuming
to perform at the conceptual stage. It also enables the modeller to predict outcomes for
the optimisation and scaling-up of the improved and new or untested process designs,
accelerating understanding and decreasing the development costs of the process, with-
out the excessive need for labour-intensive trial-and-error experimentation. However,
food materials are extremely complex in their structure and composition, so there is no
universally acceptable way to model their drying behaviour, as exemplified by the vast
volume of literature published on various modelling approaches (Kostoglou et al.,
2013). This also reflects the extreme diversity of the drying mechanisms in food
Modeling Food Processing Operations. http://dx.doi.org/10.1016/B978-1-78242-284-6.00004-0
© 2015 Elsevier Ltd. All rights reserved.
96 Modeling Food Processing Operations
systems. Mujumdar and Huang (2007) stated that most models are applicable for spe-
cific product-equipment combinations. The development of drying models would
therefore continue to improve our attempts to meet these challenges.
The chapter mainly deals with the basic concept of the drying process of food
materials when considering the removal of water from these materials through vapor-
isation of the liquid or solid by supplying different forms of heat. It starts with a brief
overview of the transport phenomena involved in the drying of food materials and the
drying techniques commonly used in the food industry. The latter part of this chapter
focuses on modelling approaches and strategies, providing a case study on the devel-
opment and application of the modelling approach for the optimisation of an industrial
drying process.
4.2 The drying process
4.2.1 Drying mechanisms
The process of drying food materials is extremely complex, involving coupled tran-
sient mechanisms of heat, mass and momentum transfer processes accompanied by
physical, chemical and phase change transformations (Sabarez, 2012). In drying food
materials, two distinct transport mechanisms occur simultaneously, comprising heat
transfer from the drying medium (or heat source) to the food material and water trans-
port from the interior of the solid product to its surface from which the water is even-
tually transported away by a carrier gas (or by the application of vacuum for
nonconvective dryers). A conceptual representation of the transport phenomena
occurring during the drying of a solid food material is illustrated in Figure 4.1.
Hot airTemp
velocityRH
Internal
External
Heating plate
(liquid/vapour)
Shrinkage
Evaporation
Radiation Convection
Heating plate
Conduction
Diffusion
Capillary flow
Figure 4.1 A conceptual representation of the thermal drying process for a solid food material.
Modelling of drying processes for food materials 97
Energy is required to generate a phase change of water from a liquid to a vapour (or
solid to vapour) and to activate molecular movement. Hot air (the most common dry-
ing medium) is employed both to supply heat (by convection) and as the carrier gas to
take away the moisture. Heat may be also supplied by conduction (i.e. from heated
metal surfaces as a heat source) or radiation, or it may be supplied volumetrically
by placing the wet material in a microwave or radio frequency electromagnetic field.
Drying is a highly energy-consuming unit operation due to the high latent heat of
vaporisation of water and the inherent inefficiency of using hot air as the (most com-
mon) drying medium. The three modes of energy transfer (convection, conduction and
radiation) may be used alone or in combination to supply heat from the heat source to
the food materials. According to Mujumdar and Devahastin (2008), over 85% of
industrial dryers are of the convective type with hot air or direct combustion gases
as the drying medium. All modes of heat transfer, except those using electromagnetic
energy (microwave and radio frequency), supply heat at the boundaries of the drying
material so that the heat must diffuse into the solid primarily by conduction. Also, the
different heat transfer modes may be deployed simultaneously or sequentially depend-
ing on individual application in order to achieve improved energy efficiency in the
drying process.
The mass transfer phenomena during drying may be controlled by either the rate of
moisture diffusion (liquid or vapour) within the food matrix (internal transfer) or the
rate of moisture evaporation from the product surface to the drying medium (external
transfer). The internally controlled drying process is mainly influenced by tempera-
ture and predominates once the rate of replenishment of moisture from the interior
to the surface of the product is slower than the external mass transfer rate. The internal
mass transfer process often involves different mechanisms of moisture movement.
Food materials (e.g. fruits, vegetables) are generally porous media containing solid
matrices having void spaces that are filled with gas or liquid (Prakotmak, 2013). In
this case, the food material is treated to undergo deformation (shrinkage) during
the drying process with the transport of water within the material to include in mul-
tiphases. According to Heldman and Hartel (1997), the moisture within the food prod-
uct can migrate in several ways via a number of different mechanisms (liquid or
vapour phase). The liquid transport mechanisms include capillary flow, surface dif-
fusion and liquid diffusion while the vapour transport mechanisms consist of Knudsen
diffusion, mutual diffusion, Stefan diffusion, Poiseuille flow and condensation-
evaporation (Sablani and Rahman, 2007). In liquid diffusion, the rate at which mois-
ture migrates depends on the nature of the food product, temperature and water
concentration difference. In some cases, vaporisation may occur within the product,
and thus water diffuses in the form of vapour through the food matrix with the differ-
ence in vapour pressure as the driving force for moisture transfer. The differences in
pressure between the drying medium and the internal food structure (pressure flow)
and the differences in temperature between the surface and the interior of the product
(thermal flow) may also influence the internal mobility of moisture. Transport of
moisture within the solid may also occur by a combination of the following mecha-
nisms of mass transfer (liquid diffusion, vapour diffusion, pressure differences). The
moisture must travel to the boundary of the material before it is then transported away
98 Modeling Food Processing Operations
by the carrier gas (or by application of vacuum for nonconvective dryers). The mois-
ture transfer from the solid surface to the drying medium is mainly governed by the
properties of the drying air.
The heat and mass transfer phenomena are usually influenced by both temperature
and water concentration differences, as well as the air velocity field, together with the
properties of the material itself. In convective drying, the coupled transfer of heat,
mass and momentum in at least two distinct subdomains (air and food), which simul-
taneously occur both externally and internally to the food matrix during drying, can be
described as follows (Sabarez, 2012): (1) convective and conductive heat transfer in
the air, (2) convective and diffusive water transfer in the air, (3) heat transfer mainly
by conduction within the solid interior, (4) mass transfer in the solid interior by dif-
fusion (liquid or vapour), (5) moisture evaporation at the air–food interface, and (6)
airflows (laminar or turbulent) around the food material. The external transfer rates
for both heat and mass are greatly influenced by the air velocity field (fluid dynamics)
and other drying air properties (i.e. temperature and relative humidity). The internal
heat and mass transfer processes may be also affected by the physical changes
that may occur in the product, including shrinkage, puffing, crystallization and glass
transitions.
4.2.2 Drying techniques
The removal of water from the food materials during drying can be achieved in dif-
ferent ways, and this variety of methods has led to many drying techniques. There are
also tens of thousands of different foodmaterials with very diverse physical and chem-
ical properties that need to be dried for different product specifications and at different
scales of production (Mujumdar and Wu, 2010). The selection of the drying method
for a particular food product is an important step because the drying technique and
operating conditions affect the quality of the dried product as well as its cost. It
depends on various factors, including the type of feed, the amount of moisture, the
drying kinetics, the heat sensitivity, the physical structure of the material to be dried,
the quality requirements of a dried food, and many other factors (Jangam, 2011). Also,
the selection procedures of a drying system include the cost estimation of various
dryers, including capital and operating costs. Table 4.1 summarises a generalised clas-
sification of conventional drying methods applied for drying food materials. There are
numerous criteria used to classify dryers. The classification in Table 4.1 is a rather
coarse representation, and readers may refer to Jangam (2011) and Bansal and
Chung (2007) for additional information on the classification of dryers applicable
for drying food materials.
Dryers are commonly classified based on the mode of heat transfer (e.g. convec-
tion, conduction, radiation or a combination thereof). The majority of dryers used in
the food industry are of the convective type; in other words, hot air is used to both
supply heat for the evaporation of water and carry away the evaporated moisture from
the product. These are by far the most common drying method despite their relatively
low thermal efficiency. Hot air produced by indirect heating or direct firing is the most
common drying medium, although for some special applications superheated steam
Table 4.1 A generalised classification of thermal dryers forfood materials
Classification Types of dryers (general characteristics and applications)
Type of feed material l Particlesl Slurry/paste/sludgel Liquid suspension
Processing mode l Batchl Continuous
Mode of heat transfer l Convectionl Conductionl Electromagnetic (RF, ohmic, infrared, microwave)l Combination (hybrid)
Energy sources l Electricityl Gas (natural/LPG)l Solar/windl Biomass
Mode of operation l Cyclicl Intermittentl Continuous
Product temperature l Above freezing pointl Below freezing point
Operating pressure l Atmosphericl Vacuuml High pressure
Modelling of drying processes for food materials 99
has been shown to yield higher efficiency and often higher product quality
(Mujumdar, 1987). In this type of dryer, the drying medium contacts the material
to be dried directly.
Another type of dryer involves supplying heat to the dryingmaterial through heated
metallic or nonmetallic solids (molecular vibration) or stationery fluids (primarily by
molecular collision) by conduction (e.g. drum dryers). In this type, the heat is trans-
ferred from the heat transfer medium (hot gas, steam, thermal fluids, etc) through the
hot metal directly in contact with the drying materials. Because no gas flow is pre-
sented on the wet solid side, the system must either apply a vacuum or use gentle
gas flow to remove the evaporated moisture so that the dryer chamber is not saturated
with vapour. Furthermore, vacuum operation lowers the boiling point of the liquid
being removed; this allows drying of heat-sensitive solids at relatively fast rates. Con-
vection (gas flow) or vacuum operation is still needed to remove the evaporated
moisture.
Dryers are also classified according to the radiant energy supplied in various forms
of electromagnetic waves categorised according to where they lie in the electromag-
netic spectrum (e.g. radio frequency, infrared, microwave). Radiation does not
100 Modeling Food Processing Operations
require a medium and uses the electromagnetic waves emitted by an object for
exchanging heat, and, thus, this is the only form of heat transfer present in vacuum.
The electromagnetic spectrum classifies radiative heat transfer according the wave-
lengths of radiation. In food drying applications, the main types of radiation applied
are infrared (IR), microwave (MW) and radio frequency (RF), which employ a
completely different heating mechanism. This type of heating mode (termed thermalradiation to distinguish it from other forms of radiation such as x-rays and gamma
rays) must be used in conjunction with convection or under vacuum to remove the
evaporated moisture. Radio waves have long wavelengths and therefore have good
penetration. Microwave heating is similar to RF heating because both methods are
quick and consistent, and they target water molecules, resulting in fast volumetric
heating (from the inside out). In most drying operations, energy is transferred from
the surface to the centre of the wet material, with the exception of radiofrequency
and microwave drying, during which the energy supplied generates internal heat
within the solid.
In some cases, the combination of the three modes of heat transfer (convection,
conduction and radiation) is applied for a more energy-efficient drying process.
The refractance window (RW) dehydration method, developed by MCD Technolo-
gies, Inc. (Tacoma, Washington, USA), is a good example of a drying technique that
utilises all the three modes of heat transfer (Figure 4.2). The technology is suitable for
producing dried products from liquid and semiliquid foods (Bolland, 2000). It uses
water as a drying medium to transmit heat into the product to be dried. The product
is evenly applied to the surface of a conveyor belt system (usually an infrared-
transparent plastic) that floats on the surface of heated circulating water. The RW
drying technology utilises the refractive principle of the surface of water, which is
harnessed by creating a window for the passage of infrared energy. In this technology
the three modes of heat transfer occur between the drying medium (water) and
the material to be dried. A number of studies were found to be relevant to the RW
drying process (Ochoa-Martinez et al., 2012; Caparino et al., 2012; Nindo et al.,
2003a; Abonyi et al., 2001; Bolland, 2000; Nindo et al., 2003b, 2004; Clarke,
2004). According to Abonyi et al. (1999), products can be dried in a few minutes with
this technology, unlike hot air or tunnel dryers that can take several hours. Nindo et al.
(2003a) reported that the drying of pumpkin puree from 80% to 5% moisture content
(wet basis) was achieved in less than 5 minutes in both pilot- and commercial-scale
RW dryers with a circulation water temperature of 95 °C, with a 52–70% energy effi-
ciency of the RW drying system.
The other common classification of dryers is based on the type of feed material. For
example, for liquid feed, spray drying is still the most common drying method,
although rotary drum dryers are also popular (Jangam, 2011). Spray drying is a very
expensive technique to use for low-value products, mainly because of its low energy
efficiency (Jangam, 2011). This method has several advantages, including rapid dry-
ing, large throughput and continuous operation (Duffie and Marshall, 1953). How-
ever, due to the relatively high temperatures involved in spray drying processes,
this drying technique (spray drying) may cause losses of certain quality and sensory
attributes, especially vitamin C, b-carotene, flavours and aroma (Dziezak, 1988).
Figure 4.2 Photos of (a) a commercial-scale RW dryer facility (RWD5 Model, MCD
Technologies, USA), (b) the wet-feed end of the dryer, and (c) the dried-product exit end of the
dryer (Sabarez and Chessari, 2006).
Modelling of drying processes for food materials 101
102 Modeling Food Processing Operations
The RW drying technology is also a suitable drying method for producing dried
products from liquid and semi-liquid foods (Bolland, 2000).
Other drying techniques evolved due to the need to produce high-quality dried
products that are ultra-heat-sensitive. Such drying systems include the utilisation of
subfreezing temperature and vacuum for the operating pressure (e.g. freeze drying).
Freeze drying (also known as lyophilisation) is a drying process in which the food is
first frozen then dried by direct sublimation (i.e. phase changes from solid to vapour)
of the ice under reduced pressure (Oetjen and Haseley, 2004; Barbosa-Canovas,
1996). Freeze drying is generally considered to be the best method for the production
of high-quality dried products (Ratti, 2001). But, it suffers from high production costs,
high energy consumption and low throughput (Ratti, 2001; Hsu et al., 2003). The cost
of low-temperature vacuum processing is many times higher than that of other con-
vection dryers, which makes it less attractive for most products (Jangam, 2011).
In recent years, a number of innovative food processing technologies have been
investigated and developed with the aim of improving or replacing conventional pro-
cessing technologies. These novel or emerging technologies take advantage of other
physical phenomena such as sound waves, pressures and electromagnetic fields,
which can be applied for the development of new drying concepts for improving
the quality of food products through gentle processing. In particular, the application
of ultrasonic energy to assist the drying of food materials has been explored for several
decades. It has been known for many years that the energy generated by sound pres-
sure waves could enhance a wide range of processes due to a series of mechanisms
activated by the ultrasonic energy, such as heat, diffusion, mechanical rupture,
chemical effects, and so on (Gallego-Juarez et al., 2007).
Several studies have reported the application of ultrasonic technology in combina-
tion with convective drying processes. A number of investigations have shown the
potential of power ultrasound to improve the drying process of various food materials.
In these studies, the ultrasonic energy was transmitted as either airborne to the surface
of food material (Garcia-Perez et al., 2009; Carcel et al., 2007, 2011a,b; Garcia-Perez
et al., 2007a,b, 2010; Khmelev et al., 2008, 2011; Ozuna et al., 2011; Soria and
Villamiel, 2010) or in direct contact between the product and the vibrating element
(Gallego-Juarez et al., 2007; Gallego-Juarez, 2010; Schossler et al., 2012). In partic-
ular, a promising approach for the application of ultrasound to assist in the convective
food drying of apple slices was developed and tested by Sabarez et al. (2012). This
study was carried out to investigate the effect of ultrasound on drying kinetics and
product quality attributes using the alternative approach for the application of ultra-
sonic energy in the convective drying process. The approach is based on the transmis-
sion of ultrasonic energy using a vibrating stepped-plate ultrasound technique that
relies on combined transmission through air and a series of solid contacts between
the ultrasound element and the product tray as the ultrasonic vibration transmitting
surface (Figure 4.3). The results from this work indicate a significant reduction in dry-
ing time (up to 57%) with the simultaneous application of ultrasound on the convec-
tive drying of apple slices (Figure 4.4). This corresponds to a reduction of energy
consumption by up to 54% with the ultrasound-assisted convective drying process.
The processing variables (i.e. drying temperature, product thickness, ultrasonic
Front viewComputer
Refrigeration
Sensors (x16)
Airf
low
Actuator
Transducer
Vibrating plate
Balance
PLC
Generator
Sample tray(movable)
PLC
Water tank
Cooling coil
Heater
Motor
Exhaust
Fan
Steamgenerator
Inlet
Side view
Figure 4.3 Schematic diagram of a computerised ultrasound-assisted convective drying system
(Sabarez et al., 2012).
Drying time (h)
−US (0 W)
+US (75 W)
+US (90 W)
0 1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
Moi
stur
e co
nten
t (%
w.b
.)
60
70
80
90
Figure 4.4 Effect of ultrasound on the drying kinetics of apple slices at different ultrasonic
power levels (T¼40 °C; RH¼25%; u¼1.0 m/s; 5 mm thickness) (Sabarez et al., 2012).
Modelling of drying processes for food materials 103
104 Modeling Food Processing Operations
power level) appeared to substantially influence the magnitude of the ultrasonic
energy’s effect in enhancing the drying process, indicating the necessity to establish
the optimum drying conditions for specific product and ultrasonic applications. In par-
ticular, the ability of ultrasound to improve the efficiency of convective drying pro-
cesses seems to be maximised when using low temperature and a high ultrasonic
power level.
In a further study (Beck et al., 2014), the application of a specially designed ultra-
sonic horn for a completely airborne ultrasound transmission to assist in the convective
drying of a model food system was investigated. This work involved investigations
of the impact of airborne ultrasound at various power levels and different levels of dry-
ing air conditions (i.e. temperature, relative humidity and velocity), using a response
surface methodology (RSM) approach to examine the possible interactions between
these parameters and to find the combination of these factors that yields the best
response. The airborne ultrasound equipment tested in this work was found to enhance
the conventional hot air drying process by significantly reducing the overall drying time
(i.e. by more than 60%). The process parameters (temperature, air humidity, air speed
and ultrasound power level) and their interactions substantially affected the drying pro-
cess, with optimum conditions found using the RSM approach.
In general, the findings from these studies offer a promising alternative to facilitate
the adaptability of the technology in industrial-scale operations because there is no
direct contact between the ultrasound element and the food sample to be dried. Further
research efforts to optimise the technology for application in industrial food drying
and the application to other drying techniques, together with future advancements
in ultrasonic technology, should provide the basis for developing a new ultrasonic dry-
ing technology for adoption in industrial drying practise.
4.3 Modelling approaches
The literature presents different approaches for modelling various drying processes. In
general, the models for the drying of food materials can be categorised into two major
groups: (a) those involving empirical equations and (b) those based on the fundamen-
tal physics of the drying processes. The level of model complexity must be balanced
with the time and cost required to develop and implement it while ensuring that an
adequate accuracy is achieved. In some cases, models are either too simplistic (i.e.
deviating significantly from real processes) or too complex to have any practical
application. It is therefore essential to develop a model that is not only meaningful
and relatively simple to use, but also accurate enough to predict the processes (and
that can be applied in industrial situations beyond those in which experiments were
conducted).
The empirical models (sometimes referred to as characteristic drying rate curves)
are system specific and cannot be generalised, because they do not involve any
physical basis. The most common model under this category is the Page model.
The empirical models, resulting from simple fitting to the experimentally determined
Modelling of drying processes for food materials 105
drying curves (Mujumdar and Huang, 2007; Togrul, 2005), are widespread due to their
simple implementation and adequate description of the specific drying processes.
Although empirical models would produce good results for engineering applications
in the food industry, they frequently do not allow the simulation of experiments car-
ried out under conditions different from those used to identify the model parameters
(Ah-Hen et al., 2013). These models are generally based on simplifying hypotheses
that may not be applicable in some situations (e.g. complex food geometries) and
changing operating conditions during the drying process (i.e. industrial scale). During
the drying process, variation in moisture content and temperature as a function of both
time and space exists inside the material, but this is not included in empirical models,
which may limit their practical application to drying. The dependence of thermophy-
sical and transport properties on product temperature and moisture content is not taken
into account. Also, the models consider only either the internal or external resistance
to mass transfer in an isothermal process (i.e. the analysis of heat transfer is neglected),
and product shrinkage is not considered. Singh et al. (2012), Menges and Ertiken
(2006) and Yaldiz et al., 2001 presented a comprehensive review of the application
of such models in the drying of various food materials.
The second approach is mainly based on models utilising the fundamental laws of
conservation of mass, momentum and energy. These mechanistic (classical) models
couple the fundamental transport equations with the thermodynamically interactive
fluxes and phase equilibrium expressions (Hayakawa and Furuta, 1988). The approach
comprises the physics involved in the drying process, largely represented by coupled
heat and mass transfer equations. For convection-based drying processes, the external
heat and mass transfer rates at the air–food interface could play a significant role in
controlling the drying process, depending on the drying conditions, which are, in turn,
strongly dependent on the drying air velocity field (Sabarez, 2012). It is therefore
important to further account for the momentum transport dynamics to improve the
predictive precision of the model. Besides, the incorporation of fluid dynamics in
the drying process is important for characterising the effect of heat and mass transfer
from the material to the drying medium (i.e. termed as equipment models) for design-
ing a dryer for a particular task. The equipment model describes the transfer process in
the drying system and predicts the instantaneously changing drying conditions of air at
any location in the drying system (i.e. drying chamber). However, there are different
mechanisms proposed under the mechanistic models (e.g. single or multiple phases),
and, generally, these models involve highmathematical complexity and determination
of too many parameters.
A more comprehensive modelling approach involves the numerical computation of
a theoretical model describing the simultaneously coupled transfer of momentum (air
only), heat and mass (both air and food) under transient conditions occurring during
the convective drying of food materials (Sabarez, 2012; Curcio et al., 2008). These
models are based on the fundamental physical principles of the drying process and
take into account the variability of air flows (fluid dynamics) around the food
material. For example, Sabarez (2012) successfully used a similar approach to predict
the moisture content and temperature distributions within prunes during drying.
Aversa et al. (2007) also employed a similar modelling approach to describe the
106 Modeling Food Processing Operations
transport phenomena occurring during the drying of carrot slabs. These models did not
make any distinction between the transport of liquid water and that of vapour within
the food matrix. More recently, Curcio and Aversa (2014) presented and successfully
validated a multiphase transport model for describing the drying process of a porous
material undergoing deformation by considering the conservation of liquid water,
vapour and energy in food, coupled to the conservation of vapour and energy in the dry-
ing air. However, a detailed analysis of the inherent complexity of the coupled transient
phenomena (i.e. heat, mass, momentum and deformation) involved in the drying process
is often regarded as time consuming for practical purposes. Hence, it is necessary to
have a simple, accurate and robust mathematical model with minimum mathematical
complexity to reduce the computational time. With the advent of increasing computing
power it is now possible to undertake simulations of these complex phenomena in less
time. The challenge is to optimise the level of simplification (model complexity) with
the level of accuracy to satisfactorily explain the real system.
4.4 Modelling of the drying process
The development and delivery of a product to market can be a long and expensive
journey. Industrial R&D now extensively employs mathematical modelling
approaches to evaluate new concepts to reduce costs, to minimise time needed and
to intensify innovation. Together with advances in computing capability, the develop-
ment of computational models to accurately simulate complex processes in less time is
one of the great advances in process engineering research. This enables the modeller to
predict outcomes for performance evaluation, optimisation and the scaling-up of new
and untested process designs, without the excessive need for expensive and labour-
intensive trial-and-error experimentation (and the models are not time consuming to test
experimentally). Computational modelling can also be utilized to develop improved
conceptual designs and to optimise operating conditions as a cost-effective route to
intensifying improvements in existing conventional dryers. The extensive characterisa-
tion of drying behaviour using a strictly experimental approach constitutes a formidable
challenge due to the excessively large number of variables that must be considered.
Modelling allows one to conduct a wide range of tests that would be too expensive
or time-consuming to perform, reducing the number of prototypes required. It is also
important to develop a tool that can simulate the product’s drying behaviour and there-
fore allow one to extend understanding beyond the results of experimental drying inves-
tigations. Modelling a drying process (as with modelling any other processes) involves
several steps, includingmodel conceptualisation, mathematical formulation, determina-
tion of model parameters, methods of solution and experimental validation.
4.4.1 Model conceptualisation
Modelling starts by conceptually defining the system and the physics associated with
the process using a geometric representation. The computational domain can be
solved in various dimensional coordinates (i.e. 2D or 3D), depending on the geometric
Modelling of drying processes for food materials 107
complexities of the system, allowing one to satisfactorily depict the real system. At
this stage, it is also important to clarify howmany details and assumptions are required
in order to reach a practical solution and satisfy the need of the application by provid-
ing the level of information required.
A conceptual representation of a convection-based drying process of a solid food sys-
tem is illustrated in Figure 4.1. In this example, themodel food is viewed as a continuum
system with a composite ellipsoidal body comprising two materials with different prop-
erties, representing typical fruit drying. A 2-dimensional (2D) solution is considered to
satisfactorily describe the physics occurring in two distinct subdomains (air and food).
In this example, the drying process is described by the simultaneous transfer of coupled
momentum (air only), heat and mass (air and food) phenomena.
4.4.2 Mathematical formulation
The conceptual model development is followed by the formulation of mathematical
equations that describe the physics of the process. The approach takenwhen formulating
a mathematical model generally depends on the problem being considered. In food dry-
ing processes, two distinct transport mechanisms occur simultaneously, involving heat
transfer from the drying medium to the food material and water transport from the inte-
rior of the solid product to its surface and eventually to the air through evaporation. For
robustness and accuracy, the governing partial differential equations (PDEs) describing
the simultaneous transfer of heat, mass and momentum in two distinct subdomains (air
and food) during the drying of a solid food material are employed.
In convection-based drying processes (e.g. hot air drying, spray drying, etc.), the
heat and mass transfer rates depend on both temperature and concentration differ-
ences, as well as on the air velocity field. The nonisothermal turbulent flow of air
in the drying chamber is described according to the standard k-e model (C.O.M.S.
O.L. Multiphysics, 2007). The equations for the momentum transport and continuity
are the following:
r@u
@t�r � + r
Cmk2
ske
� �� ru+ ruð ÞT� �� �
+ ru�ru+rP¼ 0 (4.1)
@r@t
+r ruð Þ¼ 0 (4.2)
turbulence energy equation is given by
Ther@k@t
�r � + rCmk2
e
� �rk
� �+ ru�rk¼ 1
2rCm
k2
eru+ ruð ÞT
� �2
�re (4.3)
the dissipation equation by
andr@k@t
�r � + rCmk2
e
� �re
� �+ ru�re¼ 1
2rCe1k ru+ ruð ÞT
� �2
�rCe2e2
k(4.4)
108 Modeling Food Processing Operations
The energy balance in the food material for a generalised geometry leads to the tran-
sient heat transfer equation according to Fourier’s law of heat conduction, as shown by
Equation (4.5):
rCp@T
@t
� �+r �krTð Þ¼QM +QU (4.5)
advantage of the numerical approach is that the PDEs can be solved, covering the
Thepresence of various mechanisms and source terms. With MW applications, the volu-
metric rate of thermal energy generation (QM) is provided by the dissipated MW
power, which can be evaluated according to the electric field distribution resulting
from solving Maxwell’s equations (Equation (4.6)) (Oliveira and Franca, 2002;
Knoerzer et al., 2008). This field depends on the dielectric properties of the food mate-
rial and, thus, on the temperature and moisture content fields and vice versa (i.e. tem-
perature and moisture content fields depend on the electric field) at any point in the
material (Feng et al., 2012), coupling the governing equations (heat and mass transfer,
electromagnetism). A further challenge is the complicated responses of dielectric
properties to the porosity and compositional changes of the material, in addition to
the travelling microwaves that can also decay, focus and superimpose to further
complicate the calculation (Feng et al., 2012). As a result, the modeller must rely
on significant computational effort and tricky computational strategy to efficiently
solve, in a parallel manner, these coupled equations. Modellers can now overcome
this limitation due to the development of powerful computers, which can handle large
amounts of data, and advanced numerical techniques. Feng et al. (2012) presented
the basics of dielectric heating and drying, examined the heat and mass transfer
models developed for the simulation of microwave drying processes, and discussed
dielectric properties of selected food products as influenced by moisture, temperature,
and porosity. On the other hand, the heat generation rate (QU) imparted to the material
by ultrasonic irradiation dissipated as heat can be estimated according to Equation (4.7)
(Du et al., 1981; Lin, 1995; Zhao and Chen, 2011):
QM ¼ 2pf e0e00r E2 (4.6)
QU ¼ 2I1:1f 1=2
c1grm
� �(4.7)
e same time, the energy balance in the drying air, accounting for both convective
At thand conductive contributions, is given in Equation (4.8):
raCpa@T2@t
� �+r �karT2ð Þ+ raCpaurT2 ¼ 0 (4.8)
transient moisture transport within the foodmatrix is modelled using the basic law
Thegoverning the movement of moisture according to Fick’s law of diffusion
Modelling of drying processes for food materials 109
(Equation (4.9)), while the water mass balance in the drying air, taking into account
for both convective and diffusive contributions is given in Equation (4.10):
@c
@t
� �+r �Drcð Þ¼ 0 (4.9)
@c2@t
� �+r �Drc2ð Þ+ urc2 ¼ 0 (4.10)
rticular, the boundary condition at the air–food interface (at t>0) for heat trans-
In pafer, considering the mass transfer at the air–food interface, thus coupling the heat and
mass transfer equations simultaneously is given in Equation (4.11). This means that
the heat transported by convection and conduction from the drying air to the food is
partly used to raise the food temperature by conduction and partly for water evapo-
ration at the food surface. To account for the effect of IR, which is mainly taken at
the boundary condition, the last term of Equation (4.11), which is described by the
Stefan-Boltzmann law of thermal radiation, can be added. This allows for the absorp-
tion of the infrared energy (radiative heat flux) across the boundary layer of the prod-
uct (Sabarez and Chessari, 2006). We write this equation as:
�n �krTð Þ¼ lkc c2� csð Þ+ hc T2�Tsð Þ+ e1s T4R�T4
s
� (4.11)
boundary condition at the air–food interface for mass transfer is given in Equa-
Thetion (4.12), which accounts for the balance between the diffusive flux of liquid water
coming from the interior of the product and the flux of vapour from the food surface to
the drying air:
�n Drcð Þ¼ kc c2� csð Þ (4.12)
dition, the development of mathematical models incorporating the associated
In adimpact on product quality attributes (e.g. colour) is crucial in achieving the optimum
design and operating conditions of a drying system that maximises the retention of the
desired quality attributes of the product. The quality changes (e.g. colour) of the prod-
uct during drying can be modelled using a general kinetic reaction equation:
dC
dt
� �¼�kCn (4.13)
e n is the order of reaction, and k is the reaction rate constant. The positive-or-
whernegative sign in Equation (4.13) indicates the formation and degradation in the quality
parameter with time, respectively. The kinetic model predicts the development of the
quality parameter in the product on each grid or cell during the drying process, with
the reaction rate depending on the temperature and moisture content of the product,
110 Modeling Food Processing Operations
thus coupling the changes in the product quality parameter with the local heat and
mass transfer calculations (Sabarez, 2014).
4.4.3 Model parameters
The solution of the governing partial differential equations requires knowledge of the
thermophysical and transport properties of the product and air. Many of these param-
eters cannot be assumed constant through the drying process but depend on the tem-
perature or moisture content, if precise drying kinetic predictions are to be achieved
(Sloth et al., 2006). The thermophysical properties of the product (i.e. thermal conduc-
tivity, specific heat capacity and density) are assumed to be dependent on product
composition (i.e. water, protein, fat, carbohydrate and ash) expressed as a function
of the local temperature (ASHRAE, 1995; Choi and Okos, 1987; Sabarez, 2012).
The majority of model parameters for drying processes are shown in Table 4.2. Some
parameters are physically measurable and others are quite difficult and sometimes not
available for food systems.
The transport coefficients for heat and mass required in the boundary condition are
usually estimated from empirical equations involving dimensionless numbers. The
convective heat transfer coefficient required for the boundary condition in the heat
transfer equation is calculated using the Nusselt–Reynolds–Prandtl correlation for
local convective heat transfer for a particular geometry of the food material given
by Heldman and Lund (2007). The mass transfer coefficient, which describes the con-
vective mass transfer at the surface of the product, is obtained using the Sherwood–
Reynolds–Schmidt correlation for average convective mass transfer for a particular
geometry of the food material (Heldman and Lund, 2007). The heat and mass transfer
coefficients can vary significantly depending on the drying parameters (i.e. food size,
air velocity, etc.).
The effective diffusion coefficient is the main parameter for the characterisation of
mass transfer phenomena in solid foods. It is regarded as a lumped property that does
not really distinguish between the transport of water by liquid or vapour diffusion, or
capillary or hydrodynamic flow due to pressure gradient set up in the material during
drying (Mujumdar and Devahastin, 2008). The effective diffusivity depends on geo-
metric shapes and drying conditions, and it is strongly a function of both temperature
and moisture content. In some cases, the well known Arrhenius equation is used to
quantify the influence of temperature on moisture diffusivity (Sablani and Rahman,
2007). However, care should be taken in applying effective diffusivity correlations
obtained experimentally with simple geometric shapes (e.g. slab, cylinder or sphere)
to the more complex shapes because this may lead to incorrect calculated results
(Gong et al., 1997). It is apparent from the relationships reported in the literature that
the effective diffusivity values gradually increased with temperature and decreased
with the decrease in moisture content. In general, the moisture diffusivity values
reported in the literature are in the range of 10�9–10�11 m2/s for drying of food
materials (Sacilik et al., 2006).
Table 4.2 Thermophysical and transport properties usedin modelling drying process.
Parameter Expression/dependence References
Thermophysical properties (food):
Density ¼Sb1 + b2T + b3T
2ð Þi
Xwi
where:
b1,b2,b3 ¼Constants of ith component
Xwi ¼weightfractionof ith component
Choi and Okos
(1987),
Sabarez (2012)
Specific heat
capacity
¼S c1 + c2T + c3T2ð ÞiXw
i
where:
c1,c2,c3 ¼Constantsof ith component
Xwi ¼weightfractionof ith component
Choi and Okos (1987),
Sabarez (2012)
Thermal
conductivity
¼S a1 + a2T + a3T2ð ÞiXv
i
where:
a1,a2,a3 ¼Constantsof ith component
Xvi ¼ volumefractionof ith component
Choi and Okos (1987),
Sabarez (2012)
Transport properties:
Heat transfer
coefficient
¼ f (Nu, Re, Pr, geometry, velocity) Heldman and Lund
(2007)
Mass transfer
coefficient
¼ f (Sh, Re, Sc, geometry, velocity) Heldman and Lund
(2007)
Diffusion
coefficient
¼ f (temperature, moisture content) Sabarez (2012)
Sabarez and Price
(2001)
Thermodynamic properties of moist air:
Density ¼ f (temperature) Pakowski et al. (1991)
Thermal
conductivity
¼ f (temperature) Pakowski et al. (1991)
Specific heat
capacity
¼ f (temperature) Pakowski et al. (1991)
Viscosity ¼ f (temperature) Pakowski et al. (1991)
Note: i¼ food components (protein, fat, carbohydrate, fibre, ash and water).
Modelling of drying processes for food materials 111
4.4.4 Methods of solution
For regularly shaped geometries (infinite cylinder, infinite slab, and sphere) with
proper initial and boundary conditions, together with appropriate simplifications
and assumptions of the mathematical models of a system, it is possible to derive infor-
mation about the system by analytical means, which directly produce general solu-
tions. However, for complex geometries and equations, it is necessary to use
112 Modeling Food Processing Operations
numerical computational methods to provide approximate solutions for the problem
under investigation. The fundamental concept of numerically solving the complex
systems is the discretisation of the geometry of interest to a number of finite elements
or cells, thus reducing the complex governing equations to sets of simple linear or
polynomial equations by employing appropriate approximation techniques. The
numerical methods produce solutions in steps, with each step providing the solution
for one set of conditions and the calculation repeated to expand the range of solutions.
The numerical methods most commonly used to solve complex equations in drying
processes include finite difference, finite element, and finite volume methods. More
details of these methods in relation to solving complex equations in food processes can
be found elsewhere (Patankar, 1980).
To account for shrinkage (deformation) in the material, the resulting systems of
highly coupled nonlinear PDEs in the space-time domain, together with the set of initial
and boundary conditions, are numerically solved coupled to different spatial discretisa-
tion techniques. The most commonly used spatial discretisations are the Lagrange,
Euler, ALE (Arbitrary Euler Lagrange) and mesh-free methods such as smooth particle
hydrodynamics (SPH) (Quan et al., 2003). In the case of ALE, for example, the bound-
ary conditions control the displacement of the moving mesh with respect to the initial
geometry dependent on the moisture content of the material. The moving boundary dis-
placement is propagated throughout the domain to obtain a mesh deformation every-
where using a Laplace smoothing technique (C.O.M.S.O.L. Multiphysics, 2007).
A number of commercial modelling software packages (e.g. COMSOL Multi-
physics) are currently available for the solution of the resulting systems of linear and
nonlinear equations using the appropriate solver. In some cases, a computer program
written in various programming languages (Delphi, C++, Fortran, etc.) is specifically
developed to iteratively solve the equations used to describe the system (Sabarez,
2014; Sabarez and Chessari, 2006). A user-friendly interface of the computer simulation
tool can also be developed especially in object-oriented programming languages (e.g.
Dephi, C++) for the implementation of the mathematical models. This allows the users
to assess the performance of the drying system as a function of the design and opera-
tional parameters of the drying system, as well as the product properties.
Usually, grid independency tests are carried out to ensure that the solution is inde-
pendent of grid or cell size and to verify whether the numerical solution basically
remains the same with further grid or cell refinements. In numerical solutions, the prob-
lem is approximated by discretising the computational domain into a number of points
(or grids). The associated approximation error depends on the number of discretisation
points, meaning that increasing the number of discretisation points can substantially
reduce the error, but with the expense of additional computer time requirement.
4.4.5 Experimental validation
Experimental validation is an essential step in modelling aimed at ensuring that the
mathematical description of the process captures reality. The outputs generated by
a mathematical model must be comparable to the real world system under investiga-
tion. The quality of representing the real behaviour is confirmed during this validation
phase of model development. Differences in model outputs and those gathered from a
Modelling of drying processes for food materials 113
real system are indicators of the level of simplification of the real world problem. By
optimising the level of simplification (model complexity) with the level of accuracy, a
real world problem can be explained satisfactorily. All models must therefore be val-
idated and verified against good experimental data. This involves the comparison of
predicted values (e.g. temperature, moisture content, etc.) with experimentally
measured data.
The validity of the drying models to represent real systems is usually verified by
determining the mean relative percentage deviation (%P) between experimental and
the predicted values, using the expression described elsewhere (Lomauro et al., 1985;
Madamba et al., 1996; Palipane and Driscoll, 1994). According to Kaymak-Ertekin
and Gedik (2005) andMcLaughlin andMagee (1998), a model is acceptable, or a good
fit, when P<10%. Figure 4.5 shows an example of the comparison of changes in the
average moisture content between the experimental and predicted values during the
finish drying of trellis-dried sultanas performed at three drying air temperature levels,
while keeping the same levels of air velocity (2.0 m/s) and relative humidity (10%).
As can be seen from this figure, the simulated results agreed well with the experimen-
tal data. The%Pwas found to be in the range of 0.3–1.1%, confirming the acceptabil-
ity of the model for describing the finish drying process of sultanas at different
temperature levels. In some cases, the validity of the models is evaluated by compar-
ing the predicted values in any particular drying conditions with the experimental data
(Yaldiz et al., 2001; Togrul and Pehlivan, 2003; Sabarez, 2014). The accuracy of the
model predictions is then evaluated on how closely the measured and predicted values
banded around the straight line, which is indicated by the R2 value. For example,
Figure 4.6 shows the experimental drying curves together with the predicted results
from the model at different levels of relative humidity of the drying air with
R2¼0.9941, indicative of the suitability of the model for describing the drying
Drying time (min)
Moi
stur
e co
nten
t (%
w.b
.)
012.0
12.5
13.0
13.5
14.0
14.5
15.0
15.5
16.0
20 40 60 80 100
T = 60 �C (expt)
T = 70 �C (expt)
T = 80 �C (expt)
T = 60 �C (pred)
T = 70 �C (pred)
T = 80 �C (pred)
120 140
Figure 4.5 Experimental versus predicted drying curves at different air temperatures during
finish drying of trellis-dried sultanas (RH¼10%; u¼2.0 m/s; Mi¼15.2%) (Sabarez, 2014).
Experimental moisture content (%w.b.)12 13 14
Pre
dict
ed m
oist
ure
cont
ent (
%w
.b.)
15
y = 0.8732x + 2.0428; R 2 = 0.9941
RH = 10%RH = 30%RH = 50%Linear fit
16 17 18 19 2012
13
14
15
16
17
18
19
20
Figure 4.6 Experimental versus predicted moisture content at different air relative humidity
levels during finish drying of trellis-dried sultanas (T¼70 °C; u¼2.0 m/s; Mi¼18.8%)
(Sabarez, 2014).
02
4
6
8
10
12
14
60 50 30 20 40 60300
302
304
306
308
310
40x (mm) x (mm)y (mm)
y (mm)40 30 20
5
10
15
z (m
m)
z (�
2 m
m)20
25
30
Simulation MeasurementT ( K)
Figure 4.7 Visual comparison between the simulated (left) and the measured (right) heating of
a model food cylinder (at a discrete time) (Knoerzer et al., 2008).
114 Modeling Food Processing Operations
behaviour of sultanas at different relative humidity levels. In other cases, preliminary
evaluation is carried out by visually comparing the simulated values against the exper-
imental data as illustrated in Figure 4.7.
When a model (i.e. particularly one based on fundamental physics) is properly val-
idated, one can extrapolate the behaviour of a system to a range of parameters not
tested in the experiment. A parametric sensitivity study can be undertaken to further
Modelling of drying processes for food materials 115
investigate the effects of the uncertainties of various input parameters on the model’s
predictions and to demonstrate the usefulness of the predictive tool in identifying crit-
ical operational factors affecting the drying process. The model can then be used to
test a number of scenarios (i.e. different operating conditions and material properties)
to study the interactions between the factors in the system and to examine the critical
parameters affecting the drying process. For instance, Figure 4.8 depicts the effect of
uncertainties in the drying air temperature measurement on the model predictions in
plum drying. It indicates that the uncertainties in the measurement of this parameter
are likely to represent a greater contribution to the accuracy in the model predictions,
and it also demonstrates that accurate measurement of the drying air temperature and
its sensing location are important in plum drying operations.
4.5 Case study
This section presents a characteristic case study for the convective drying of plums to
illustrate the application of the modelling approach in determining the optimal design
and operating conditions in industrial-scale tunnel drying systems. In industrial tunnel
dehydrators (as in any large-scale industrial drying systems), the materials being dried
are typically exposed to the dynamically changing conditions of the drying air (e.g.
temperature) at any time and position, as illustrated in Figure 4.9(a). This requires
a model of the drying system that comprises both material and equipment models,
in which the material model describes the drying kinetics and the equipment model
determines the changes of the condition of the drying medium with time and space
during drying. Together, these models constitute a complete modelling tool capable
of predicting the dynamic behaviour of the drying system. Thus, the prediction of the
drying air stream conditions flowing across the product surface, which would affect
T = 82 �C
T = 80 �C
T = 78 �C
010
20
30
40
50
60
70
80
2 4 6 8 10Drying time (h)
Moi
stur
e co
nten
t (%
w.b
.)
12 14 16 18
Figure 4.8 Predicted effect of air temperature uncertainties on the drying kinetics of prunes
(RH¼15%; u¼5 m/s) (Sabarez, 2012).
1.5
1
Air outlet
Exhaust
(a)
(b)
Fresh air
Burner
Recirculation
Fan
Motor
Fresh fruit
Air inlet
Temp (�C)
86
84
82
80
78
76
74
0.5
10.8
0.60.4
0.2 01
2 Length (m)Width (m)
Hei
ght (
m)
34
5
Figure 4.9 Schematic diagram of a typical tunnel dehydrator for (a) the commercial drying of
prunes and (b) the measured temperature profile across the drying tunnel (Sabarez, 2010).
116 Modeling Food Processing Operations
the drying behaviour of the solid product, at any time and position in the dryer is of
particular importance in simulating the drying process of industrial drying systems for
which a systematic dynamic variation in drying conditions is typical (Sabarez, 2012).
A 2D axis-symmetric model was developed to describe the simultaneous transfer of
momentum (air only), heat and mass (air and food) occurring in convective air drying
of fruits (e.g. plums). The governing PDEs describing the simultaneous transfer of
heat, mass and momentum in two distinct subdomains (air and food) during the drying
of plums were presented in previous studies (Sabarez, 2010, 2012). The nonisothermal
Modelling of drying processes for food materials 117
turbulent flow of air in the drying chamber is described according to the standard k-emodel (C.O.M.S.O.L. Multiphysics, 2007). The resulting systems of highly coupled
nonlinear PDEs in the space-time domain, together with the set of initial and boundary
conditions, were numerically solved by the finite element method (FEM) coupled to
the ALE procedure to account for the shrinkage phenomenon, using a commercial
software package (C.O.M.S.O.L. Multiphysics, 2007). The details of the numerical
solution are presented in previous studies (Sabarez, 2010, 2012). Also, the solution
of the governing PDEs requires knowledge of the thermophysical and transport prop-
erties of the product and air. The model parameters used in this work are given in pre-
vious studies (Sabarez, 2012, 2014).
A computer-controlled experimental drying system (Figure 4.3) was specifically
developed to study the drying kinetics of various food materials under controlled con-
ditions over a wide range of operating conditions for use inmodel validation. The exper-
imental set-up was designed to allow simulation of a typical commercial dehydration
system. The purpose-built test drying facility incorporated a number of special features,
including a fully programmable cyclic control of process conditions (i.e. temperature,
humidity, and air flow), ultrasonic unit and a dedicated weighing system. It was
equipped with controllers to control the process variables. A number of additional
sensors (i.e. thermocouples, infrared noncontact temperature sensors, air velocity
sensors, relative humidity probes, etc.) were interfaced to a computer-based data
acquisition and control system for further online monitoring and recording of the var-
ious processing conditions. Further details of the experimental drying setup can be
found in previous studies (Sabarez, 2012, 2014; Sabarez et al., 2012; Beck et al., 2014).
Figure 4.10 shows the measured surface and centre temperatures of the product
together with the predicted values. It can be seen from this figure that there is a good
agreement between the experimental data and predicted values. These results confirm
the suitability of the model for describing the heat transfer process during the drying of
Drying time (h)
Surface (expt)
Centre (expt)
Surface (pred)
Centre (pred)
020
25
30
35
40
Frui
t tem
pera
ture
(�C
)
45
50
55
60
65
70
75
2 4 6 8 10 12 14 16 18 20
Figure 4.10 Predicted versus experimental fruit temperature profile at different locations in the
fruit (T¼70 °C; RH¼35%; u¼5.7 m/s) (Sabarez, 2012).
118 Modeling Food Processing Operations
plums, and they demonstrate that the thermophysical parameters used in the model are
reasonable. Similar trends were also found for other drying conditions investigated
(Sabarez, 2010). This validates the dependency of the product’s thermal properties
on both temperature and moisture content.
Figure 4.11 shows the drying curves of plums predicted by the model for the two
experimental drying tests performed at different air temperatures and relative humid-
ity levels under the same air velocity (5.7 m/s). In the moderate drying conditions, the
air temperature was maintained at 70 °Cwith a relative humidity of 35%, while, in the
more intense conditions, the air temperature was 80 °C with a relative humidity of
15%. These conditions were selected to simulate the extreme drying conditions
typically found in industrial tunnel drying operations. As can be seen from this figure,
the simulated results agree well with the experimental data. Also, Sabarez (2012)
presented further validations to verify the predictive capability of the model over a
range of conditions. The results confirm the validity of the model and demonstrate
that the parameters used in the model are reasonable, indicating the suitability of
the model for describing the drying process of plums under various conditions.
A number of numerical scenarios were also tested for different operating condi-
tions andmaterial properties to study the interactions between the factors in the system
and to identify critical operational factors that offer significant and measurable oppor-
tunities for improvement in the drying process. The conditions of the drying air (i.e.
airflow, temperature and relative humidity) are considered to be the main factors
influencing the drying performance in tunnel dehydrators. In particular, the effect
of different air velocity levels was taken as an example to demonstrate the impact
of this parameter on the drying kinetics (Figure 4.12). In this instance, an increase
in air velocity leads to a pronounced decrease of the drying time but only to a certain
level. Beyond this level the air velocity plays a proportionally decreasing role in
Expt (T = 70 �C; RH = 35%)
Expt (T = 80 �C; RH = 15%)
Pred (T = 70 �C; RH = 35%)
Pred (T = 80 �C; RH = 15%)
10
20
30
40
50
60
70
80
0 2 4 6 8 10Drying time (h)
Moi
stur
e co
nten
t(%
w.b
.)
12 14 16 18 22 2420
Figure 4.11 Predicted versus experimental drying kinetics of plums (u¼5.7 m/s) (Sabarez,
2012).
Drying time (h)
Moi
stur
e co
nten
t (%
w.b
.)
0 2 4 6 8 10 12
u = 1.0 m/s
u = 3.0 m/s
u = 5.0 m/s
u = 7.0 m/s
14 16 18 2010
20
30
40
50
60
70
80
Figure 4.12 Predicted effect of air velocity on the drying kinetics of prunes (T¼80 °C;RH¼15%) (Sabarez, 2012).
Modelling of drying processes for food materials 119
reducing the drying time. This has significant implications for the energy consumption
of the drying process, as shown later.
The advantage of the proposed numerical model is that the temperature and
moisture distributions across the solid food domain, as well the changes of the con-
dition of the drying air with location, can be established at any time during drying
(Figure 4.13(b)). This is important for simulating the drying process that will take into
account the dynamic changes in the drying conditions, allowing simulations that
mimic the industrial-scale tunnel drying of plums in both parallel-flow and
counter-flow modes of operation (Figure 4.14). It should be noted that the mode of
operation in a tunnel drying system is one of the key factors that significantly influ-
enced the drying performance (Sabarez, 2010).
A number of computer simulations were further carried out to study the drying per-
formance under various drying conditions in an industrial tunnel drying operation. It is
well known that the air velocity field greatly influences the heat and mass transfer
rates at the food–air interfaces. Therefore, the temperature and concentration of mois-
ture in the product and the drying air are basically controlled by the level of air veloc-
ity and its distribution. So, the effect of different air velocity levels in the drying tunnel
operated in parallel-flow mode was used to demonstrate the impact of this parameter
on the drying kinetics and energy consumption. The other selected conditions are rep-
resentative for the current commercial tunnel drying operation for plums (Sabarez,
2010). Figure 4.15 depicts the simulated effect of different levels of air velocity on
both drying time and energy consumption in an industrial tunnel drying operation.
As can be observed from this plot, there appears to be an optimum level of air velocity
required to achieve better drying performance, which can be found at the intersection
of the plots. Under these conditions, the optimum air velocity level appears to be
around 4–5 m/s. As the air velocity increases the energy consumption also appears
to increase. This is obvious because increases in air volume would result in increased
energy requirements for heating the large volume of air to the desired temperature
0(a) (b)
−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0.04
0.01 0.02
x (m)
y (m
)
y (m
)
x (m)
0.03 0−0.01
−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0.04
0.01 0.02 0.03 0.04 0.0435 63
80
100
120
140
160
180
200
220
240
260
278
0.0436
0.0438
0.044
0.0449Air Food
Time=64300[s]; Food: concentration, c [kg/m^3]; Air: concentration, c2 [kg/m^3]; Arrow: Velocity field [m/s]
0.0448
0.0446
0.0444
0.0442
Figure 4.13 Predicted product moisture concentration, moisture concentration and velocity
profiles of the drying air during the drying of plums (T¼80 °C; RH¼15%; u¼5.7 m/s)
(Sabarez, 2012).
Drying time (h)0 2 4 6 8 10 12
Parallel-flow (predicted)
Counter-flow (predicted)
Parallel-flow (measured)
Counter-flow (measured)
14 16 18 2010
20
30
40
Moi
stur
e co
nten
t (%
w.b
.)
50
60
70
80
Figure 4.14 Simulated and measured drying kinetics of prunes in industrial-scale drying for
both modes of operation (u¼5 m/s) (Sabarez, 2010).
120 Modeling Food Processing Operations
15
14
13
12
11
10
9
80
01
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9 10Velocity (m/s)
Dry
ing
time
(h)
Drying time Energy use
Ene
rgy
use
(GJ)
Figure 4.15 Effect of air velocity on drying time and energy consumption in an industrial-scale
drying operation (inlet: T¼85 °C, RH¼15%; recycle: T¼70 °C, RH¼30%, ratio¼90%;
ambient: T¼25 °C, RH¼65%) (Sabarez, 2010).
Modelling of drying processes for food materials 121
level. On the other hand, the drying time seems to significantly decrease as the air
velocity increases but only to a certain point. Beyond this point, the air velocity plays
a proportionally decreasing role in reducing the drying time.
Furthermore, the predictions in the distributions of moisture content and temper-
ature across the food materials are important for characterising the quality changes
during drying. The development of mathematical models for improved understanding
of the underpinning heat and mass transfer mechanisms controlling the drying process
and the associated impact on product quality attributes is crucially important for
achieving the optimum design and operating conditions of a drying system that max-
imises the retention of the desired quality attributes of the product. One of the impor-
tant quality attributes that usually accompanies dehydration of food products,
particularly for fruits (e.g. grapes), is the change of product colour due to browning
reactions (i.e. enzymatic and nonenzymatic). The ability to predict changes in product
colour during drying would be useful for optimising the drying process in order to
produce the desired premium colour attributes. For example, a kinetic model was
coupled to the heat and mass transfer calculations to describe the drying kinetics
and the evolution of product colour during the finish drying of trellis-dried sultanas
(Sabarez, 2014). This allows simultaneous predictions of the moisture content, tem-
perature and colour profiles of the product in a space-time domain during the drying
process as a function of various operating conditions, establishing the optimal drying
conditions for producing the desired premium colour attributes of the product. This
approach could be extended to other food products, and it could incorporate other
product quality attributes.
122 Modeling Food Processing Operations
4.6 Future directions
The drying processes that are currently used in the food industry will continue to play a
significant role in food manufacturing as long as they are still viable and have not
reached their limit of performance. As with many other food processes, further rede-
sign and optimisation of these existing drying technologies are crucial in order for the
industry to become more productive and sustainable. In addition, new challenges are
continually emerging as new innovative drying technologies appear to overcome the
limitations of the conventional drying processes. Modelling strategies will be needed
to further assist in developing such incremental improvements of the existing drying
processes and in intensifying innovation of new drying concepts for effective and effi-
cient implementation at an industrial scale.
With advances in computing capabilities, further progress can be made in the devel-
opment of advanced and realistic multiscale drying models that couple the transport
phenomena (heat and mass transfer, fluid dynamics), physical or structural changes,
chemical reactions, phase changes, complex food compositions and other physical phe-
nomena (e.g. acoustic, electric, electromagnetic fields). This is important in understand-
ing the length- and time-scale interactions involved in simulating the drying processes
for scaling-up and optimisation, without excessive trial-and-error and the associated
costs of physical experimentations. In addition, modelling the drying process in a
way that incorporates the prediction of food qualities (i.e. sensorial, functional and nutri-
tional) will also be important in the development of new drying technologies allowing
the manipulation and control of food quality to achieve the desired attributes.
These developments, together with advances in sensing and visualisation tech-
niques, will enable the development of real-time model-based control systems for dry-
ing processes, ensuring an efficient process, safe operation and a higher-quality
product. The development of advanced sensing and instrumentation capabilities
should also improve the availability of experimental data that would otherwise be very
difficult to obtain in some drying systems due to the challenges associated with
measurement-taking (e.g. hostile environment of high temperatures and/or pressures).
Appendix: Nomenclature
c
water concentration in food (mol/m3)c1
ultrasonic propagation velocity in capillary (m/s)c2
water concentration in air (mol/m3)C
colour parameters (L*, a*, b*) (–) Cp specific heat (J/kgK)Cm
model parameter (–)Ce1
model parameter (–)Ce2
model parameter (–)D
effective water diffusivity in food (m2/s)E
electric field (V/m)f
ultrasonic frequency (kHz)g
acceleration of gravity (m/s2)Modelling of drying processes for food materials 123
I
ultrasonic intensity (W/m2)hc
heat transfer coefficient (W/m2K)k
thermal conductivity (W/mK)kc
mass transfer coefficient (m/s)M
moisture content (% wet basis)n
direction normal to surface (–)P
pressure (Pa)rm
average radii of capillary (m)RH
relative humidity (%)T
food temperature (°C) T2 air temperature (°C) TR temperature of the radiator (°C) t time (s)Subscripts
a
air (–)i
initial (–)s
food surface (–)Greek letters
e
dissipation rate (m2/s3)e1
emissivity (–)e0
dielectric constant of vacuum (A s/V m)er00
real part of complex permittivity (–)l
latent heat of evaporation (J/kg)�
dynamic viscosity (N.s/m2)k
turbulence energy (m2/s2)r
density (kg/m3)sk
model parameter (–)s
Stefan-Boltzmann constant (–)u
velocity (m/s)References
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