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Diffusional Analysis during Air Drying of a Starch Food System.

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Dev.Chem. Eng. Mineral Process., 5(1L2),pp.61-77, 1997.
Diffusional Analysis during Air Drying of a
Starch Food System
W.A.M. McMinn and T.RA. Magee”
Dept. of Chemical Engneering, The Queen’s University of Be&zst,
Stranmillis R o d , Belfast Bl’9 5AG, NORTHERN IRELAAD
Starch, as a major component of several food products ofplant origin, was used as a
simulant for investigation of the basic physical and engineering properties of
particulate and porous foods. An experimental tunnel @er was used to investigate
the drying-rate and temperature projles developed within potato starch gel
cylinders during convective dryng. The experimental diflusional data were
characterised using Fick’s second law and an empirical model was developed to
predict the effective moisture dfisivity as ajknction of air temperature, air velocity
and sample radius. The experimental and predicted results were in good agreement.
The temperature distribution developed within the sample were measured and
presented as a jknction of both drying time and dimensionless distance.
Keywords: Effective moisture diffusivity; potato starch gel cylinders; radial
diffusion; temperature distribution.
Introduction
Drylng with hot air is of part~cularinterest in a number of applications in
biotechnology as a method for preservation of biological products. One of the
primary objectives of food procasing is the conversion of perishable foodstuffs into
stablized products. Several preservation technologies have been employed on an
industrial scale, with the most notable among them being canning, freezing and
drymg. However, a growing resistance to the use of chemicals for food preservation,
and the demand to provide a comprehensiverange of products, has lead to a renewed
interest in drymg operations. The techque of drymg is probably the oldest method
of food preservation practised by mankind Nevertheless, it still remains one of the
most effectve and widely mked unit operations within industry. The removal of
moisture from solids represents an integral part of food engineering and, with few
e x m o n s , most food products from today’s industry undergo dqmg at some
processing stage.[l] The theoretical prediction of drymg of biological material is
fundamentally a problem of simultaneous heat and mass transfer in a multiphase
system. Starch, a complex carbohydrate, is one of the most prevalent constituents
found in foods involved in water transport processes. Model systems of starch gel
prepared at controlled composition, shape and sttucture allow basic information
* Author of correspondence.
61
W.A.M. McMinn and T.R.A. Magee
characterizingthe drymg behaviour of more complex biological materials [11. Potato
starch, as a preferred functional ingredient over other ~ t u t apolymers,
l
e.g. corn,
wheat and rice, improves and increases the rigidity and firmness of gels [2].Previous
studies indicate that potato starch has a large granular strumre, with the adJacent
amylose molecules and outer branches of the amylopectm molecules associating
through hydrogen bonding in a parallel fashion to give radically oriented crystallites,
containing about 100 molecules [3].
Starch gelatinization is an important phenomenon Occurring in various
processing operations of starch-based foods. On heating starch granules in excess
water, the gelatinization transformation results in a 'pseudo' polymerization, or
<Ilsrupbon of molecular order, manifested in irreversible changes in properties, such
as granular swelling, native crystahe melting and starch solubilization [4].
Gels are generalty considered as homogeneous materials [5]. During dqmg
starch gels develop a porous structure, forming a two-phase (solid-gas)
heterogeneous system. The gas phase consists of water vapour and air, while the
homogeneous solid phase constitutes an amorphous material, in which the starch
molecules form a three-dimensional network,or close-knit matrix, encapsulating the
water molecules in small cavities and restricting the diffusion process [6].
Diffusion within a food system during dqmg is a complex process, which may
involve molecular diffusion, capdlary flow, Knudsen flow, hydrodymmc flow, or
surface diffusion;with the physical structure of the food also playmg an important
role. However, it is assumed that during the falling-rate period of drymg, moisture is
transfered mainly by molecular diffusion [q.
Hence, the mass-transfer phenomenon
occurring within the system may be characterizd in terms of an effective moisture
diffusivity. The ef€&e moisture difhiviiy, as an intrinsic property of the sample,
represents the interaction of all parameters influencing the process rate and is an
essential physical transport property for engineering analysis of basic food
processing operations,such as drying, rehydration and extrusion [l]. The objective of
this research is to evaluate the d i f b M t y of moisture and the temperature profiles
developed during the dqmg of potato starch gel under variable operating conditions.
Materials and Methods
Drying Eqrtipment
The experimental tunnel dryer system used in this work is shown schematically in
Figure 1. The equipmeni consists principally of a fan, heating section and drying
chamber. Ambient air is circulated through the dryer by a centrifugal fan located at
one end After passing through a 1kW electric heater, the air passes through a series
of wire mesh distributors giving a uniform flow regime prior to entering the drying
chamber. The centrifugal fan is powered by a variable speed motor (Zenith Electric
Co. Ltd.,London, UK), which controls the air velocity between 0.5 and 1.5ms-'
(M.OSms-'), being restricted due to Ean capacity. The air velocity and humidity are
measured using a hot wire anemometer and humidity probe (Solomat IWM SOOe,
Solomat
UK) respechvely. The air dry bulb temperature is regulated in the
range 30 to 6OoC(set-point of resolution I t l O C ) by a proportional-integralderivative
La
62
Diffusional analysis during air drying of a starchfood system
(PID) temperature controller (West 3510, West Instruments Ltd, UK) and monitored
using a type T thermocouple.
The dtylng chamber contains a Qylng plate (40mm diameter) made of glass
positioned on a weighmg system.The weighmg system consists of an electronic
balance, (Mettler Toledo PJ3602, Wishart Scientific L a UK) with maximum
capacity 610g and precision H.O5g, placed under the dryer to monitor weight loss
continuouslyand accurately without removing the samples from the drylng chamber.
The weight r&g
is carried out by means of a serial data transfer system. The
balance is connected to a computer and the weighmg signals are transferred to the
computer via a LocalCAN universal interface card (Mettler Toledo LC-RS25,
Wishart Scienhtic Ltd,UK).
procedure
Commercial potato starch, containing 80% amylopechn @DH, Poole, UK), was used
for preparation of the gelatinized samples. The high-amylopechn starch powder[7]
was mixed with W e d water to give an initial moisture content of 4.5H.lkg
waterkg dry solid, representing a typ~calinitial moisture content of a high moisture
food. (The required amount of water was measured in a volumetric flask assuming
) . starcwwater mixture was then
the approximate density of water to be i g ~ m - ~The
poured into a cylindrical mould and gelatinized by heating the hydrated sample for
10 min at 100°C in a water-bath. The hot homogeneous fluid colloid was then
removed from the water-bath and allowed to cool to room temperature forming a
solidified gel. To prevent bubbles being introduced into the sample, the water had
previously been boiled under reduced pressure.
On cooling, the sample was removed from the die and a cylindrical sample was
formed of the required radial (between7.5 and 13.5mm) and length-to-radial (4:l)
dmensions. Several measurements of the cylindncal dunensions were made using
sliding vernier calipers and only samples within a 5% tolerance of the average
dunensions were used To restrict the direction of moisture transport to
unidimensional h a l diffusion, the flat ends of the sample were coated with a
moisture-proof material (&sseal@, Borer Chemie, Swimrland).
The experimental dryer was set to the required drymg conditions of air
temperature and air velocity and allowed to stabilize for about one hour to ensure
steady-state con&tions. The prepared sample was then positioned vertically on the
glass drymg plate within the drymg chamber. However, airflow past the sample
induces drag forces. To determine the magnitude of these forces on the gel, the
i n i d weight of the sample was determined outside the system and also within the
system while the air was flowing. The difference between the two readings was
assumed to account for the drag force on the sample, for whch compensation was
made to all subsequent weight readings.
Throughout the experimental run the sample was rotated to ensure that the entire
circumferential surface was equally exposed to the same awflow pattern resulting in
uniform dryrng conditions. The sample weights were continuously recorded at
predetermined time intervals, set to ensure sufficient data points were collected
When no discernible difference bemeen subsequent readings was observed, it was
63
W.A.M. McMinn and T.R.A. Magee
assumed that the sample had attained equhbrium moisture content. The moisture
content of the potato starch gel cylinders at the beginning and end of each
experiment was determined by drying representative duplicate samples in a
convection oven at 105-110°C for 8-10 hours [8]. The ambient air humidity and drybulb temperature were periodically monitored throughout each experimental run.
The average room air conditions were 22e°C and 5of3% relative humidity.
Sorption isotherms for potato starch gel were experimentally determined by the
standardized static method, based on the use of saturated salt solutions to maintain a
fixed relative humidity (recommendedby the COST 90 project) [9].
1
I
llcl
EXre 1. Experimental air drylng tunnel shaving variable speed motor (I),
centnfigal fan (2), IkW heater (3), PID controller (4), wire mesh distn'butors (5),
anemometer (6), dry bulb thermocouple (7). electronic balance (s), computer (9),
cylindncal gel sample (lo), drying tray (ll), humidity probe (12).
Temperature fiople
The internal temperature profiles developed within the sample during drylng were
monitored using five line wire Chromel"/ Alumel" thermocouples (K-type). Each
thermocouple (0.04mm diameter) were inserted into a stainless steel needle (0.5mm
diameter, 25 gauge), with the junction of the thermocouple located at the tip of the
needle. The arrangement of thermocouples from the surface to the centre of the
sample is shown in Figure 2, with each being linked to a micro-processor
thermometer (Comark Auto-Scanning Thermometer, h e x Systems Ltd., UK) in
which the analogue signals generated were converted to temperatures and recorded
The temperature distribution was experimentally obtained under air conditions of
45OC and 1.5ms-' in a sample of initial radius 13.5mm, length-to-radial ratio 4:l and
vertical orientation.
In order to confirm the existence of only one dimensional heat transfer in the
radial direction, two supplementary experiments were performed under the same
operating conditions (air temperature 45OC and air velocity ISms-'). Fust, the
temperatures in the sample in one horizontal plane 27mm from the top (flat end) of
the sample and at four arbitrary positions around the circumferential surface were
64
Di$fiuional analysis during air drying of a starch food system
monitored (see Figure 3) and second, the temperatures in the Sample in a single
vertical plane 5mm below the circumferential surface (see Figure 4).
Plan View
top
b27mm-----I
+-
--I
I
I
bottom
Sectional View
thermocouples 1 , 2 . 3
equally spaced ot 6.75mm
I
I
I
I
1
I
I
1
I
4
I-
thermocouples 3. 4. 5
equally spoced at 4.5mm
figure 2. Arrangement of thermocouples in the sample to determine the interior
temperature profile during d?ying.
thermocouples at
5 m m from surface
il!,
Plan View
F i e 3. Arrangement of thermocouples in a horizontal plane 27mmPom the top
flat end) of the sample.
65
W.A.M. McMinn and T.R.A. Magee
Sectional View
27mm+
thermocouples equally
spaced at 9mm
I- f- -
E i r e 4. Arrangement of thermocouples in a horizontal plane 5mm from the
circumferential suvace of the sample.
Experimental Design
The technique of drymg is a complex unit operation of coupled heat and mass
transfer. It involves the application of heat, most commonly by convection from a
current of air, followed by movement of water through the food structure and
removal of water vapour from the surface of the food by the air. optimum operation
of a drying process is dependent on factors which control the rate of internal/external
mass transfer, e.g. physical properties of the drying medium and sample
characteristics. Hence, for the purpose of this study the diffusional characteristics of
the starch gel samples were investigated with regard to the three operating
parameters of air temperature, air velocity and sample radius.
Air temperatures of 30,45 and 60°C were considered. Temperatures above 60°C
and below 30°C were not used due to loss of desirable fresh food qual~ty
characteristicsand difficulties in control due to the closeness to ambient temperature,
respectively. Air velocities of 0.5, 1.0 and 1.5m.s-' were used which, although
restricted by equipment performance, ensured that internal and not external
resistance to mass transfer was the limiting factor. This was theoretically verified by
calculation of a mass transfer Biot number greater than 10 [lo] and experimentally
corned as no measurable difference in drymg-rates was found in Qylng tests
carried out at 0.5 and 1.5m.s". Samples of cylindrical conf&p'ation were considered,
allowing both one dimensional and two dimensional diffusional analysis; sample
radii of 7.5mm, 9.25mm and 13.5mm were tested,being restricted due to practical
considerationsof sample preparation.
The experimental design used for the investigation was a modified 23 factorial
design of the three variables of air temperature, air velocity and sample radius [111.
66
Dijkional analysis during air drying of a starch food system
Fourteen experimental runs were performed in triplicate in a random manner, such
as to reduce the effects of systematic experimental errors with time. The first 8
design points were a standard factorial design, however, the final 6 points included
medium values of the variables for greater precision. To give vedication of
experimental variability an additional experiment was performed at the centroid
point, i.e. all three variables set at the medium values.
Theory
Fick's second law, based on an intemal moisture transport mechanism governed by
the gradient of moisture content, is mathematically expressed for a cylinder by the
classical mass balanceconservation equation [121:
-
dt
I
{-
(rD,z)
r Br
+;(?%)
+g(rDzz)}
,..(l)
with the dif€usivities D,, Do and D, accounting for the possible anisotropic nature
and hence, directionally dependent diffusion properties of the material. Considering
one dimensional diffusion in the radial direction,equation (1) may be reduced to:
Utilizing several simpl@mg assumptions, applied in most research in the area of
drying, namely: (i) uniform initial moisture content; (ii) constant directio~l
diffumity; (iii) constant solid geometq, i.e. no shnnkage or deformation observed,
(iv) neghgible external resistance to heat and mass transfer, so the surface of the
solid is at equil~briumwith the surrounding air; and (v) constant Qylog conditions
throughout the process; and with the following appropriate initial and boundary
conditions:
t=O
t>O
OlrSR
r=R
X
=
X, (cylinder)
X = X,
(suface)
equation (2) was solved by the method of variable separation to give the well
established expression [131:
...(3)
Equation (3) describes diffusion in a solid cyhder of infinite length (as the
cylinder is sufficiently long, L:R ratio 4:1, with the flats ends of the cylinder sealed
so that diffusion is essentially radial) in an infiniteatmosphere (as the volume of the
67
W.A.M. McMinn and T.R.A. Magee
surrounding atmosphere is large and circulating) with an infinite rate of evaporation
(i.e. rate of evaporation so high €hat the moisture concentration on the evaporating
surface falls to zero as soon as the process starts). For large values o f t (> 10 min),
equation (3) can be reduced to the first term of the series.
Results and Discussion
Within this study, moisture transfer solely in the radial direction was considered.
Drymg-rate data for potato starch gel samples under specified conditions were
obtained following a statistical (factorial) design of experhem (see Table 1). The
e e e n t a l data were represented in terms of dimensionless moisture content
(ln[X-XfirXJ)versus timeplots, as shown in Figures 6,s and 9, with this form of
data representation being basedon the solution of Fick’s second law.
Within a typical m e , the data appeared to fall into two straight lines of
differing slopes, indicating the existence of two stages during the falling-rate period
drymg. A linear regression analysis was employed to calculate the characteristic
effective moisture difbivity from the slopes of the 1nX-Xfl&Ye versus time curves.
second Period
Conditions
Br
Temperature
PC)
Airvelocity
(ms-’)
Sample
Radius
(mm)
30
30
30
30
60
0.5
1.5
0.5
1.5
0.5
0.5
1.5
1.5
1.o
1.0
1.o
1.5
0.5
1.o
7.5
7.5
13.5
13.5
7.5
13.5
7.5
13.5
9.25
9.25
9.25
9.25
9.25
7.5
60
60
60
45
30
60
45
45
45
DI
1
I
(1010
m’s-’)
3.73
5.19
5.25
6.83
9.73
11.03
11.51
14.71
8.38
5.18
10.11
9.12
5.67
7.13
1.26
1.20
0.85
1.39
2.12
1.29
1.05
2.02
1.75
1.08
1.80
1.98
2.57
2.28
2.27
3.24
3.68
3.68
6.32
7.35
5.84
8.40
5.18
3.70
6.41
5.43
3.70
4.54
’
2.38
1.32
4.41
3.93
2.37
1.89
1.70
4.69
0.69
3.38
2.83
1.61
4.09
3.65
Table 1. Summary of eflective moisture dimsivities for radial difuaon in potato
starch gel cylinders. Operating conditions: length-to-radial ratio 4: 1 and vertical
sample orientation.
Values for the effective moisture dif€usivities(see Table 1) range from 3 . 7 3lo-’’
~
to 14.71~1O”~m~s~’
and 2.27~1O-’~to
8.40x10~’’m2s~’
for the first and second f w g rate periods respeaively, with the values being comparable with other liteTaaue data
for simila~materials [q.This decrease in effective moisture dif€usivity at lower
moisture content is a result of more strongly bound moisture and hence, a decrease in
availibility of water molecules for diffusion.
68
Di.siona1 analysis during air drying ofa starchfood system
To ascertain the ability of the calculated and cotlstant effective moisture
Wsivity values to prerllct the experimental data, the mean relative percentage
dewation modulus, E, was used, as defined by:
100 N le, -P*l
E%=-CN i=1 ei
..(4)
This parameter is used widely in the literature to evaluate the goodness of fit of
mathematical expressions, and it is generally considered that E values below IOYO
gwe a reasonably good fit for practical purposes [14]. The average mean relative
percentage deviation moduli, E, for the first and SecOIlcl falling-rate periods
r e r n v e l y are 1.61% and 2.66%. Considering the drying process as a whole, the
average E value is 2.14%. Since the overall E value is less than lo%, this indicates
that the calculated constant effective moisture cfiffusivity values adequately predict
the drylng data for the entire process, as shown by Figure 5.
Ergure 5. Compm.son between predicted and experimental moisture content versus
time curve.
As shown in Figure 6 and from the values in Table 1, the effective moisture
W i v i t y increased with increasing temperature. The temperature dependency of
the effective moisture diffusMty may be represented according to an Arrhenius
relation:
69
W.A.M. McMinn and T.R.A. Magee
The activation energy for diffusion for each fallingrate period was calculated from
the slope of the straight lines, In D versus reciprocal of the absolute temperature
(]A‘) (see Figure 7).
Time (min)
0
I
800
4.2
loo0
1m
4.4
4.6
4.8
-1
-1.2
+
-a-
-1.4
-1.6
I
-1.8
Figure 6. Influence of air temperature on eflective moisture a’iflusivity for radial
dfision in potato starch gel cylinders.
1K (K’)
I
0.0031
-1 4
First Period
0.MXn
0.0033
A Second Period
figure 7. Dependence of eflective moisture difisivity on temperature.
70
Diffusional analysis during air drying of a starchfood system
The relationships between the effective moisture dBusivity and temperature for each
period are represented by:
First Period
Dl = 3.71 x
(
exp - 21'6 lo'
RT
D, = 3.60 x 1Od exp
Second Period
R 2 =0.967
...(6 )
R2 =0.999 ...(7)
The activation energy of diffusion for the second period (23.13 Idmol") is higher
than that in the first falling-rate period (21.57 ldmol-I), indicating the presence of
more strongly bound moisture in the latter stages of drymg. The calculated energies,
lymg within the range of physical adsorption, were comparable with reported values
[15], despite the large variation in this parameter due to the innuence of numerous
factors (maturity rate, geometry, initial moisture content,size, etc.).
In order to ascertain whether internal resistance to mass transfer is indeed
controlling,tests were conducted for samples of varying radii. As shown in Figure 8,
sample radius also had an influence on drymg, with a decrease in sample radius
glving an increased drymg-rate.
lime (min)
O
L
I
Kn
loo0
1200
F i r e 8. Free moisture content versus time for dging of potato starch gel cylinders
of v q h g rarhi.
The application of Fick's second law was further verified by dqmg samples at
varying air velocities. On consideration of the drylng curves in Figure 9,it is evident
that air velocity has a limited effect on dqmg behaviour. Thus, it would appear that
the external drylng conditions are relatively unimportant, as compared with the
71
W.A.M. McMinn and T.R.A. Magee
internal conditions. Theoretical verification of the velocity effect was primarily
accomplished by calculation of the corresponding Reynolds numbers. Reynolds
numbers ranged between 4000 and 20,000. This indicates turbulent air flow and,
therefore, the existence of external mass transfer may be considered unlikely. The
relative importance of internal versus external mass transfer resistance on the
dehydration kinetics was further evaluated using the concept of the mass transfer
Sherwood number, Sh. Sherwood n u m b greater than 10 were calcukd, thus
satisfying the proposed criterion for the insigdicance of external mass transfer.
Therefore, the amlyses confirm that, under the prevailing conditions, internal
resistance is the lirmting phenomenon which governs the overall moisture transfer
process.
0
4.2
4.4
4.6
L
4.8
-1
-1.2
-1.4
1
-1.6
-1.8
figure 9. Effect of air velocity on the drying behaviour of potato starch gel
cylinders.
Applying the empirical approach, the experimental effective moisture
difkivities were correlatedby a linear relation with the three independent variables
of air velocity, air temperature and sample radius using multiple linear regression:
D = c , +c,V+c,T+c,R
...(8)
where co, cl, c2 and c3 are the estimated &cients
and V, T and R normalized
values of the independent variables under consideration, each varying linearly with
the ef€eciive moisture diffusiviry. For the first and second falling-rate periods
respectively, the following relationships were developed:
72
Dimional analysis during air drying of a starch food system
Dl= -6.97+3.58V +12.40T+4.70R
D,= -3.17
+ 0.98V + 7.11T + 2.98R
R 2 = 0.963
PA =6.30
...(9)
R2 = 0.931
E% =7.20
...(10)
From analysis of variance, the h
e
a
r functions given by equations (9) and (10)
were shown to be statistically acceptable at the 5% level, with E values less than
10%. This inchcated that the model adequately predicted the effective moisture
diffusivities, with the calculated values being in good accordance with the
experimental results as shown in Figure 10.
I
1
I
-
0
2
0
4
6
8
Predicted k CIOJmin")
1
=First Period
ASecondPeriod
1
figure 10. Comparison behveen predicted and experimental effective moisture
dfisivities.
One underlymg assumpuon of the dLfhsional model is the isothermal nature of
the dqmg process. As a consequence of heat transfer, the temperature at each
position increases progressively with time until thermal equhbrium conditions are
attained. The temperature evolution, as illustrated in Figure 11, is manifested by a
rapid increase dunng the early stages, followed by a levelling-off thereafter to a
constant temperature, below the air dry-bulb temperature[l6] and, hence, thermal
equd~briumconditions.Figure 11 also reveals that the temperature differential only
becomes neghgible when the majority of the moisture initially present w i h the
food matrix has been evaprated. However, with respect to the overall dqmg time,
the duration of this transient period is lirmted. As the d a c e temperature is never
constant, it may be concluded that no measurable constant-rate period exists, with
the entire process taking place during the falling-rate period. This confirms that the
73
W.A.M.McMinn and T.RA. Magee
proms is entirely controlled by internal mass transfer and consequently may be
interpreted using Fick’s ddkion model (i.e. equation 3).
.:
Air Dry-Bulb Temperature
-..----....--~......---.
::
A
of First Falling-Rate Period
I
100
0
200
300
400
500
Time! (rnin)
I
A Centre Temperature
Surface Temperature
1
figure 11. Centre and su$iace temperature profiles during the air-dyng of potato
starch gel.
I
0
100
200
300
400
500
Time (min)
E v e 12. Ecperimental temperature profle in a horizontal plane 27mm fiom the
top (flat end) of the sample.
74
Diffusional analysis during air drying of a starch food system
Figure 12 represents the temperature profiles in a horizontal plane 27mm from
the top of the sample (thermocoupleslocated in positions 6, 7,8 and 9, as specified
in Figure 3). As shown in Figure 12, no s i m c a n t temperature Werence was
observed at the four points. Similar temperature observations were recorded by
thermmuples (9, 10, 11 and 12) positioned in a single vertical plane below the
circumferential surface. These results may indcate that the major extent of heat
transfer occurs in the radial direction, i.e. in a direction concurrent with moisture
transfer.
From the experimental results internal temperature profiles were evaluated as a
function of drying time, as illustrated in Figure 13. The distance is normalized from
the centre of the Sample and further corrected for the presence of radial shrinkage,
i.e. a value of zero represents the distance at the centre of the sample and the
distance at the circumferential surface e q u a b g 1.0. The temperature profiles
exhibit a h e a r temperature distribution between the sample surface and centre.
However, the overall temperature gradients between the innermost and outermost
positions are small. A maximum temperature difference of approximately 3OC is
cfisplayed after about one hour, however, this is observed to decrease with increasing
dqmg time, in accordance with a power law relation.
The results indate that internal heat transfer is much more rapid than internal
mass transfer. Consequently, the drylng phenomena may be regarded as exclusively
controlledby internal mass transfer resistance, and for practical purposes isothermal
conditions are assumed. This hypothesis
was theoretidy validated by calculation of
._
the heat transfer Biot number.
"T
15
I
0
0.25
0.75
0.5
1
RlRo
1
+Ohr
mlhr
r2hr
x3hr
04hr
r6hr
e7hrI
Figure 13. Temperature proJTle within sample as a function of position and d y . n g
time.
75
W.A.M. McMinn and T.R.A. Magee
The thermal Biot number provides a measure of the relative importance of the
internal versus external resistance to heat transfer. Moreover, the internal
temperature may be considered uniform, with little error, when the heat transfer Biot
number is less than 0.2 [lq.The Biot number was determined using heat transfer
coefficients obtained from heat transfer correlations. The calculated low value of 0.8
for the Biot number is consistent with the criterion for small internal resistance to
heat transfer within the sample. This analysis provides further support for the limited
internal temperature gradients observed during the drylng process. Moreover, the
absence of si@cant internal temperature gradients confirms the validity of the
d
o
m in equation (3), and further substantiates the hypothesis of a
assumptions a
liquiddiffusionalmechanism.
Conclusions
0
The experimental results for potato starch gel drying show quahtatke agreement
with drylng data of foodstuffs reported in the literature.
Main factors affecting the diffusional process are air temperature, sample radius,
and to a lesser extent air velocity.
Internal heat transfer is much more rapid than mass transfer indicating a process
controlledby intend mass transfer.
Acknowledgement
The basis of this paper was o r i p d l y presented at the 5* Irish IChemE Research
Symposium in ~~, March 1W6.The authors would like to thank the research
symposium organizers for their assistance with further publication of this research.
Nomenclature
Pn
CO
CI
C2
c3
D
0 0
e
E
E.l
P
N
r
R
R
t
T
V
76
l3essel ftlEcton roots (PI = 2.4048)
Coefficient defined in w o n (8)
Coefk5ent defined in equation (8)
CoelEcient defined in equation (8)
C d c i e n t defined in equation (8)
Effective moisture diffusivity
~onalconstant
Experimentalvalue
Mean relative percentage deviation modulus
Activation energy for diffusion
predicted value
Number ofobservations
Radial coordinate
Cyljnder radius
Gasconstant
Time
Airtemperature
Air velocity
Diffusional analysis during air drying of a sfarchfood system
X
Moisture content (dry basis)
(kgkg dry solids)
Subscripts
e
Equilibrium
r
Radial
9
Tangential
z
Longitudinal
0
Initial
References
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Received 11 September 1996; Accepted afer revision 12 February 1997.
77
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