Chemical Engineering and Processing 50 (2011) 687–693
Contents lists available at ScienceDirect
Chemical Engineering and Processing:
Process Intensification
journal homepage: www.elsevier.com/locate/cep
Flow pattern and heat transfer in agitated thin film dryer
Sanjay B. Pawar a , A.S. Mujumdar b , B.N. Thorat a,∗
a
b
Department of Chemical Engineering, Institute of Chemical Technology (ICT), Nathalal Parekh Marg, Matunga (E), Mumbai 400019, India
Department of Mechanical Engineering, National University of Singapore, Singapore 117576, Singapore
a r t i c l e
i n f o
Article history:
Received 24 July 2010
Received in revised form 6 April 2011
Accepted 9 April 2011
Available online 28 April 2011
Keywords:
Scraped surface geometry
SSHE
Bow wave
Conduction drying
a b s t r a c t
The design of agitated thin film dryer (ATFD) is difficult both mechanically and process engineering
point of view. The present work describes the basic flow pattern in ATFD in terms of bow wave and its
transformation along the dryer height. The effect of flow rate, jacket side heating medium temperature
and speed of the rotor has been studied for a pilot scale ATFD. The effect of rotor speed was found less
significant for water as a feed material than for sugar and ammonium sulfate solutions over the studied
range of speed. The scraped side heat transfer coefficient was obtained using the penetration theory and
its value was found in the range of 3000–7000 W/m2 ◦ C.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
Agitated thin film dryers (ATFDs) are widely used in chemical,
pharmaceuticals and food industries to produce dry free flowing
powder. The combination of short residence time, high turbulence
and rapid surface renewal permits the agitated thin-film dryer to
handle the heat-sensitive, viscous and fouling feed streams successfully. ATFD consists of two major assemblies: a heated body
(stator) and a close clearance rotor as shown in Fig. 1. The process
fluid enters in the unit tangentially above the heated zone and distributes evenly over the inner surface of wall by rotating action of
the rotor. The rotor blades spread the feed over the entire heated
wall and generate highly turbulent flow conditions in the thin layer
of liquid. The feed progressively passes through the phases like
slurry, paste, wet powder and finally powder of desired dryness
as shown in Fig. 2.
ATFD can be used as multi-utility equipment. ATFD is sometimes
inadvertently referred to as ATFE, agitated thin film evaporator,
when the desired product is a concentrated liquid. The major difference in the design of ATFD and ATFE lies in the respective
hydrodynamic conditions which occur as a result of speed of the
agitator, the clearance between the blade and inside body surface
and so on. ATFD involves three phases which makes difficult to
model the flow phenomena. ATFD consists of scraper/agitator with
fixed or spring loaded blades. The design of ATFD is a strong function
of process fluid and operating constraints of the process. Never-
∗ Corresponding author. Tel.: +91 22 24145616x2022.
E-mail address: bn.thorat@ictmumbai.edu.in (B.N. Thorat).
0255-2701/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.cep.2011.04.005
theless, the greatest advantage is constant renewal of layer/film
near the wall which helps in reducing the fouling and enhances the
heat transfer coefficient. The heat transfer in such devices can be
modeled using the penetration theory of heat transfer [1–3].
2. Flow pattern in ATFD
As discussed earlier, ATFD is a wiped surface assembly with the
rotor having three or four rows of the blades. The shaft rotates with
a given angular velocity and the blades lay out a thin film on the
inner wall of the dryer. If the volumetric feed flow rate is relatively high enough, the film formed on the inner wall would be
thicker than the clearance between the wiper blade and inner wall
which results in a fillet/bow wave of liquid on blades front edge [4].
The flow can be either laminar or turbulent depending on the fluid
properties and operating conditions.
Several authors have studied the flow behavior of various feeds
in the scraped surface geometry. Bott and Romero [5] observed a
continuous fillet in front of the blade along the height of vertical
scraped surface heat exchanger for water as well as water–glycerol
mixtures. Similarly, Abichandani et al. [6] have observed the fillet in
front of the blade tip for horizontal geometry. Zeboudj et al. [7] have
reported that the hydrodynamic conditions of the flow affects the
film thickness and residence time of fluid elements in wiped film
evaporator. McKelvey and Sharps [8] examined the velocity profile and flow structure of the bow wave in wiped blade evaporator
and studied the dependence of blade clearance, film thickness and
throughput. Komari et al. [9] studied the flow structure and mixing
mechanism in the bow wave both theoretically and experimentally
in a wiped film evaporator. The authors examined the effect of fluid
688
S.B. Pawar et al. / Chemical Engineering and Processing 50 (2011) 687–693
Bow wave (recirculating loop)
for flow rate F1
Vapor
Feed
Shell
Hot water
out
F1 < F2
Jacket
Thin film
formation on
inner wall
Blade
Bow wave (recirculating loop) for
flow rate F2
Hot water
in
Dry powder
Fig. 1. Schematic representation of agitated thin film dryer.
Fig. 3. Schematic representation of flow pattern in ATFD showing different fractions
of bow wave at different flow rates.
dimensions of bow wave depend on the feed flow rate and its physical properties. When the thin film flow is of concern in a scraped
geometry, the flow can be distinguished in two sections: one is the
bow wave which constitutes the major portion of feed and other is
the thin film adhering to the inner wall (see Fig. 3).
The concept of Reynolds number (Re) is well defined for a
straight pipe to characterize the flow behavior of Newtonian fluid.
Subsequently, it is also defined for other geometry configurations
such as a stirred tank or an annulus based on the impeller tip speed
and equivalent diameter concept. The rotational Reynolds number
for an annular flow can be given by
ReR =
De (Rr ˝)
(1)
where De is the equivalent diameter which is given by
De = 4 × rh = 4 ×
De = 4 ×
Fig. 2. Schematic representation of zone transformation in ATFD.
(Ds2 − Dr2 )/4
= Ds − Dr
Ds + Dr
(2)
(3)
In the case of thin film flow, only the outer wall (stator) remains
in contact with the fluid and the equivalent diameter can be written
as
De = 4 ×
viscosities up to 13 Pa s and found that from 70 to 90% of fluid flow in
the device lies in the bow wave when the evaporator was equipped
with vertically aligned blades. McKenna [10] presented a model for
the design of a wiped film evaporator. The model considered the
fluid transport and mass transfer aspects of devolatisation of polymer solution. The author observed a limiting rotational speed for
mixing in WFE above which significant gain in the mass transfer
was obtained at the expense of very large power consumption.
From the above literature, it can be said that the flow pattern
in ATFD is a combination of the rotational film flow induced by
mechanical action of blades and an axial flow. The pitched blades
move the fluid in the bow wave both tangentially and axially. The
cross-sectional area of channel
perimeter of channel in contact with fluid
(Ds2 − Dr2 )/4
D2 − Dr2
= s
Ds
Ds
(4)
Thus, the rotational Reynolds number derived in the case of thin
film would be higher as compared to that obtained for conventional
annulus.
3. Heat transfer in ATFD
3.1. Penetration theory
The penetration theory is the key to the analysis of heat transfer
in a scraped surface geometry. Several authors have used the penetration theory in its original form or with some modification (use
S.B. Pawar et al. / Chemical Engineering and Processing 50 (2011) 687–693
of correction factor) to model the scraped-side heat transfer coefficient [11–16]. The correlations based on the Nusselt number have
been also developed considering the laminar and turbulent flow in
such devices [17–19]. The heat transfer is controlled by conduction
into a thin layer at the heat transfer surface and by the speed of
mixing of this layer into the bulk of the fluid. The basic approach of
heat transfer from hot wall which is scraped by a blade is provided
by the penetration theory. The theory is based on conductive heat
transfer. The mass flow rate and viscosity of the process medium
have no influence on the heat transfer coefficient. The heat transfer
process can be divided into following two steps
Hence, the heat transfer coefficient can be expressed as
h(t) =
Each blade scrapes a certain amount of fluid and accelerates
it along the inner hot wall surface. At any given instant, the fluid
pushed by the blade is partly in the form of film behind the blade
and partly in the form of fillet in front of the blade. The penetration
theory assumes the temperature equalization in bow wave/fillet
after the film is scraped off. Hence it has been found that the penetration theory works well for low viscosity fluids. Goede et al.
[19] modeled the heat transfer considering the regular turbulent
model for pipe flow and the penetration theory for two different
time periods. It is well known that the heat transfer depends on
the flow regime. The values of heat transfer coefficient are usually
low in the case of laminar flow because of low radial mixing and
high in turbulent flow because of high radial mixing. Generally, the
axial and rotational Reynolds numbers decide the flow regime in a
scraped surface geometry and hence several authors have reported
the heat transfer coefficient as a function of axial and rotational
Reynolds number for laminar as well as transition regime [1].
Previously, the studies of heat transfer in scraped surface heat
exchangers were based on the application of the penetration theory to calculate the overall heat transfer coefficient. It has been
assumed that the scraper only removes the boundary layer, bulk
mixing is ideal and the flow pattern is completely rotational. In
order to describe the total heat transfer process with this relation,
the time between two scraper passages should be smaller or at least
equal to the time needed for full penetration of heat into the boundary layer/film. The temperature profile across the boundary layer
can be given by Fourier equation as follows:
∂2 T
∂T
=˛ 2
∂t
∂z
(5)
with boundary conditions z = 0, T = Tw ; z → ∞ , T = TB and initial condition t = 0, T = TB for all z.
Eq. (5) can be solved with given boundary conditions which
results
2
T − Tw
= √
TB − Tw
√
z/(2 ˛t)
2
e−z dz
(6)
0
The steady state conductive transport of heat can be described by
Qw = −k
dT
dz
(7)
Combining Eq. (6) with Eq. (7), the heat flux can be expressed as
dT
Qw = −k
= (TB − Tw )
dz atz=0
kCp
t
0.5
kCp
t
(9)
When the heat transfer mechanism between two scraper actions
is described by the penetration theory, the time mean value of the
heat transfer coefficient can be calculated from following equation
h=
1
ts
ts
h(t) dt
Combining Eqs. (9) and (10) results in
kCp
tsc
h̄ = 2
(11)
Expressing the time between two scraper actions in terms of number of blades (B) and the rotational frequency (n), tsc can be written
as
tsc =
1
nB
(12)
Combining Eq. (11) with Eq. (12), the scraped side heat transfer
coefficient can be given by following equation
hpen = 2
kCp nB
(13)
The complete derivation of Eq. (13) can also be found elsewhere
[20,21].
The fluid passes through the ATFD in several forms such as liquid
feed, paste, wet powder and dry powder at the dryer outlet. The
scraped side heat transfer coefficient can be obtained by assuming
the average properties throughout the dryer which are the function
of moisture content. It can be assumed that the wet powder formed
in the dryer lies in the form of thin layer adhering to the wall until
the outlet of the dryer. The scraped side heat transfer coefficient
decreases from top to bottom as the solid content tends to increase
in the processing fluid along the height of the dryer. The ATFD is
used to produce the powder from some specific type of feeds which
generally have 10–30% solid content with viscosity in the range of
10–100 times that of water. Particularly ATFD is used for the drying
of organic and inorganic salt solutions, pharmaceuticals and bulk
drugs, dyes and pigments, etc.
3.2. Process-side heat transfer coefficient
The heat transfer coefficient on the scraped side in ATFD can
be estimated using the penetration theory. As the penetration theory does not depend on the viscosity, it can be used to calculate
the heat transfer coefficient for slurry and paste type feed materials. The scraped side heat transfer coefficient depends on thermal
conductivity, density and specific heat of the material. Now the
question is how to model the physical properties with respect to
solid content along the height of the dryer. The average values of
thermal conductivity, density and specific heat are considered at
saturation temperature for the given pressure (vacuum) condition.
These properties can be written as
kprocess = XL kLavg + (1 − XL )kSavg
(14)
process = XL Lavg + (1 − XL )Savg
(15)
Cp process = XL Cp Lavg + (1 − XL )Cp Savg
(16)
The heat transfer coefficient by the penetration theory is then calculated as follows,
(8)
(10)
0
(A) Only molecular conduction transfers the heat at the surface
during the time between two scrapings.
(B) At the end of scraping, the film at the surface gets perfectly
mixed with the bulk flow.
689
hprocess-side = 2
kprocess process Cp nB
(17)
690
S.B. Pawar et al. / Chemical Engineering and Processing 50 (2011) 687–693
Table 2
Dimensions of the agitated thin film dryer.
Th
TW
Parameters
Value
Unit
Diameter of shell
Diameter of rotor
Diameter of scraper
Effective height
Shell wall thickness
Heat transfer area (HTA)
Rotor speed range
Gap clearance
Number of blades
0.112
0.09
0.110
0.18
0.004
0.05
1–10
0.001
3
m
m
m
m
m
m2
rps
m
–
TB
Jacket
Side
Process
Side
Z
Wall
Fig. 4. Schematic representation of conductive heat transfer across the wall.
(corresponding to vacuum in the system) and averaged over the
height of the dryer. For example, the density of ammonium sulfate is 1260 kg/m3 at 45 ◦ C and that of water is 990 kg/m3 . So,
the density of 20% (by weight) ammonium sulfate solution would
be (0.2 × 1260 + 0.8 × 990 = 1044) 1044 kg/m3 . As the water evaporates down the dryer height, its content in solution decreases
relatively to ammonium sulfate. Further, for 20% water loss, the
density would be (0.4 × 1260 + 0.6 × 990 = 1098) 1098 kg/m3 . As the
whole process is operated at constant saturation temperature of
45 ◦ C, the dependence of physical properties over the temperature
range is not considered here.
3.3. Overall heat transfer coefficient
4.2. Agitated thin film drying (ATFD)
The thermal design of ATFD is similar to the conventional heat
exchanger wherein the first step is to obtain the overall heat transfer coefficient (U) and then calculate the desired heat transfer area
for a given capacity. In the present experimental setup the heat
transfer area is fixed (0.05 m2 ) and it is required to calculate the
overall heat transfer coefficient. The process side heat transfer coefficient is calculated using the penetration theory. The schematic
representation of conductive heat transfer through the wall is
shown in Fig. 4. The overall heat transfer coefficient in the ATFD
can be represented by Eq. (18),
The dimensions of the lab scale ATFD (Techno Force Solution
Pvt. Ltd., Nasik, India) are as shown in Table 2. The experiments
were performed to determine the evaporation rate in the lab scale
ATFD. The experiments were performed according to 33 factorial
designs with 27 numbers of runs by varying speed of the rotor,
jacket-side heating temperature and flow rate of feed. The experimental conditions are reported in Table 3. The feed was supplied
by reciprocating type feed pump (V.K. Pumps, Nasik, India) with
a flow range of 0.5–3 kg/h. The whole system was operated under
vacuum created by the rotary vane type vacuum pump (Model:
vkc 6, Precise Vacuum System Pvt. Ltd., Nasik, India). The temperature of feed inlet, hot water inlet and outlet were determined by
K-type thermocouple with 1 ◦ C accuracy. The temperature of vapor
was determined using K-type thermocouple located in vapor line of
ATFD. The vapor was condensed in the vertical condenser (Techno
Force Solution Pvt. Ltd., Nasik, India) of 0.5 m2 heat transfer area.
The chilled water of temperature 10 ◦ C was used to condensate the
vapor to be then collected at the base of the condenser. The quantity of condensed water was measured and thus the evaporation
rate was determined.
The formation of bow wave in front of the blade was confirmed
by measuring the hold-up using conventional start/stop method.
Here, the hold-up is defined as the ratio of occupied volume of the
solution to the annular volume available to flow. The hold-up for
the studied flow rate was found to be greater than the actual volume
between the gap of blades and the outer wall.
1
1
=
U
hprocess-side
D so
Dsi
+
1
Dso ln(Dso /Dsi )
+
hjacket-side
2kw
(18)
The metal wall resistance can be neglected because of the high
thermal conductivity of wall material and small thickness.
4. Materials and methods
4.1. Materials
Generally, the ATFD is used for the low viscosity solution and
mostly the evaporating solvent is water, hence, water was preferred
as a primary test material for the experimental runs. The experimental runs were carried out to determine the maximum/optimum
evaporation capacity of the dryer for the system maintained at
pressure of 133.34 Pa. After fixing the optimum flow rate and the
jacket-side temperature, further experiments were carried out for
sugar solution and ammonium sulfate solution (20%, w/w). The
physical properties of all above mentioned solutions are given in
Table 1. The properties of sugar solution and 20% (w/w) ammonium solution were derived at saturation temperature of 45 ◦ C
5. Results and discussion
As previously described, the agitated thin film drying involves
three phases (feed: liquid, product: solid, evaporated vapor-gas).
Table 1
The physical properties of different feeds at saturation temperature (45 ◦ C).
Properties
Water
Sugar solution (40%)
20% ammonium sulfate
Density (kg/m3 )
Viscosity (kg/m s)
Specific heat (J/kg ◦ C)
Thermal conductivity (W/m ◦ C)
990
0.0006
4180
0.6
1060
0.00283
3800
0.51
1040
0.001
3500
0.35
S.B. Pawar et al. / Chemical Engineering and Processing 50 (2011) 687–693
691
Table 3
The operating conditions in ATFD for various systems.
Feed
Speed of rotor (rps)
Water
40% sugar solution
20% aqueous ammonium sulfate
1–10
1–10
1–10
Rotational Reynolds number (ReR )
22,544–184,020
4000–15,160
14,250–114,020
It is well known that the dealing with the three phase flow phenomena is a very complex problem. So preliminary, it was decided
to go with the two phase flow phenomena using water as a feed
instead of slurry or solution to determine the optimum parameters
for the present dryer. Here, the processing unit can be termed as
ATFE. Actually, there is no significant difference in ATFD and ATFE
except for the speed of the rotor and the heat input. For the high
viscosity solutions, ATFE can be operated at higher speed of the
rotor (typically 25–30 rps) to overcome the laminar flow regime.
For ATFD working with typically low viscosity solutions such a high
speed of the rotor is not necessary, however, higher heat flux will
be required.
The experiments were carried out for the feed flow rate of
1–3 kg/h at different heating temperatures Twj (jacket side) and
speed of the rotor. The hot water was used as a heating medium
at the jacket side. The feed of 40 ◦ C was supplied by the feed pump
at the top of the dryer over the feed ring. The vapor formed in the
dryer was sucked by the vacuum pump through the vapor line. After
several trials, it was found that the speed of the rotor did not make
any significant increment in the evaporation rate. The evaporation
rates are as shown in Fig. 5 for various operating parameters. It can
be seen that the evaporation rate is below the 50% for the flow rate
of 3 kg/h and Twj at 70 and 80 ◦ C as shown in Fig. 5A. The evaporation rate was found to be increased up to 70% for Twj at 90 ◦ C;
whereas for the flow rate of 2 kg/h, the evaporation rate was found
to be greater than 70% for Twj at 80 and 90 ◦ C as shown in Fig. 5B.
The above results could be due to the incomplete mixing of thin
film and bow wave in the case of relatively high flow rate and it is
possible that there could be relatively high hold-up of the water in
the form of bow wave in the evaporator at high flow rate. Further,
for the flow rate of 1 kg/h, the evaporation rate was found to be
greater than 90% at Twj of 80 and 90 ◦ C as shown in Fig. 5C. Based
on this, it can be said that the Twj of 90 ◦ C is sufficient to evaporate
the feed of 1 kg/h for given operating conditions of the system.
After optimizing the system for water as a feed, further
runs were carried out for sugar solution of viscosity 40◦ Brix
(0.00325 Pa s). Slightly different results were obtained for this case
as compared to the earlier system of water as a feed. The effect of
speed of the rotor was found significant in this case and the evaporation rate was found to be increased from 40% for 1 rps to 56%
for 5 rps at Twj of 90 ◦ C. For the case of ammonium sulfate solution,
the results of the thin film drying were similar to that obtained for
the earlier system of water as a feed and hence they are not shown
here.
When applying the penetration theory, the process of heat
transfer from wall to liquid layer can be considered as molecular
conduction to the semi-infinite solid. Those who were suspicious
of applicability of the penetration theory for highly viscous liquid, they have developed the Nusselt type correlations which
are based on rotational Reynolds number and/or Prandtl number
[1,22]. Latinen [21] and Trommelen et al. [12] have well described
the penetration theory. The theory is independent of the velocity
(mass flow rate) and the viscosity of the liquid. It has been reported
that the penetration theory works well for low viscosity liquid such
as water in turbulent regime (ReR > 6000). Actually the theory is
based on the assumption of temperature equalization in bow wave
immediately after scraping which might not happen in the case of
high viscosity liquid. In contrast, the assumptions are quite realistic
Axial Reynolds number (Rea )
1.5–4.5
0.335–0.88
1.02–3.12
Prandtl number (Pr)
4.12
90.5
10
Fig. 5. % water evaporation at different wall temperatures: A: flow rate 3 kg/h, B:
flow rate 2 kg/h and C: flow rate 1 kg/h.
692
S.B. Pawar et al. / Chemical Engineering and Processing 50 (2011) 687–693
Fig. 6. The comparison of heat transfer magnitude derived from the penetration
theory for 20% ammonium sulfate, 40% sugar solution and pure water.
in the case of wiped thin film flow rather than the full liquid flow
such as in a scraped surface heat exchanger. With the hold-up of
15–20% in ATFD/ATFE, the complete mixing is possible even for the
high viscosity liquid because of turbulence created by the rotor.
Moreover, the penetration theory was found to be applicable to
predict the heat transfer coefficients for the drying of sludge and
paste type materials. The drying of sludge and paste type materials in the paddle dryer [23,24], Nara type paddle dryer [25] and
LIST type knead dryer [26] were carried out under vacuum conditions. The authors have used the penetration theory to model the
heat transfer from the wall to the processing material and they
followed the methodology originally developed by Schlunder and
Mollekopf [27] for free flowing particles. Hence, it can be said that
the penetration theory can be used for sludge, paste or granular
materials to predict the heat transfer coefficient under vacuum or
in the presence of inert gas conditions [28,29]. In the case of ATFD,
even if the feed is in the form of solution, rapid evaporation at the
entrance results in deposition of solids along the inner wall which
is immediately scraped off by the scraper and get mixed with the
bow wave. Thus, the processing feed becomes slurry and passes
subsequently into the form of paste and wet powder.
From the above studies, it can be said that the penetration theory
can be used to describe the behavior of slurry in a scraped geometry provided the properties of slurry are averaged. In the case of
ATFD, wherein, the feed is in the form of solution and the product is
powder (which comes from dissolved solid), it is necessary to consider the average properties of process fluid. These properties can
be obtained by solving Eqs. (14)–(16) assuming the linear relationship of moisture content with respect to the height of the dryer.
The heat transfer coefficients are determined by Eq. (17) for sugar
solution and 20% ammonium sulfate. It is then compared with that
obtained for pure water evaporation (Eq. (13)) which is shown in
Fig. 6. It has been observed that the average heat transfer coefficient
for 20% ammonium sulfate solution (80% water) shows lower Nusselt number than that obtained for pure water evaporation at the
same operating conditions. This signifies that the change of phase
(solution to wet powder) lowers the heat transfer along the height.
This variation of the heat transfer coefficient along the height is
the key point to determine the effective heat transfer area for the
thermal design of ATFD.
In the present work, it is assumed that the evaporation occurs
on the interface of thin film only and any bubble formation is
Fig. 7. The prediction of heat transfer magnitude for 20% ammonium sulfate along
the height of the dryer (H/H0 ) by the penetration theory (flow rate 1 kg/h and
Twj = 90 ◦ C).
Table 4
The overall heat transfer coefficients for different types of materials (data adapted
from Perry’s Chemical Engineers’ Handbook).
Process side fluid
Jacket side fluid
Agitation
U (W/m2 ◦ C)
Solution
Slurry
Paste
Lumpy mass
Powder (5% moisture)
Steam
Steam
Steam
Steam
Steam
Double scrapers
Double scrapers
Double scrapers
Double scrapers
Double scrapers
990–1190
910–990
710–850
425–545
230–290
suppressed by scraper. The feed behaves as a paste type material
throughout the dryer. The heat transfer coefficient along the height
of the dryer for 20% ammonium sulfate is shown in Fig. 7. The heat
transfer coefficient was found in the range of 5500–300 W/m2 ◦ C
along the height from top to bottom. The heat transfer coefficient
is likely to change with respect to the percentage of dissolved solids
in the feed. The properties and fraction of the dissolved solids in the
feed solution can greatly affect the heat transfer coefficient along
the height and hence its average value. The overall heat transfer
coefficients (U) for various types of feed are shown in Table 4. The
values reported in Table 4 are taken from Perry’s Chemical Engineers’ Handbook [30] to provide the idea of the range of U for
various types of process fluids.
6. Conclusions
The only way to identify the flow regime in ATFD is the bow
wave in front of the blade which occurs because of the low axial
Reynolds number. The bow wave forms in front of the blade irrespective of the viscosity of fluid and flow regime. Thus it is difficult
to express the flow regimes in the agitated thin film dryer. Hence,
the rotational Reynolds number has been defined to characterize
the thin film flow in ATFE/ATFD.
The assumptions of the penetration theory are quite realistic in
the case of wiped thin film flow rather than the full liquid flow in a
scraped geometry. The theory can be used to model the conductive
heating from the wall to the wet particles in a scraping geometry
provided the wet particles form thin film over the scraping wall. The
dependence of the penetration theory over the speed of the rotor
(n0.5 ) signifies that the heat transfer coefficient increases with an
increase in the speed of the rotor. However, in actual practice after
some optimum speed of the rotor, no significant increment in the
heat transfer coefficient was found for the studied feed materials.
S.B. Pawar et al. / Chemical Engineering and Processing 50 (2011) 687–693
Appendix A. Nomenclature
B
Cp
Ds
Dso
Dsi
De
Dr
F1 , F2
h
h
H
H0
(H/H0 )
k
kw
L
n
Q
rh
Rr
rps
t
tsc
T
TB
Th
Tw
Twj
XL
U
V
z
Z
number of blades
specific heat capacity of the feed (J/kg K)
diameter of shell (m)
outer diameter of shell (m)
inner diameter of shell (m)
equivalent diameter (m)
diameter of the rotor (m)
mass flow rates (kg/s)
heat transfer coefficient (W/m2 ◦ C)
time mean value of the heat transfer coefficient (W/m2 ◦ C)
varying height of the dryer (m)
constant height of the dryer (m)
dimensionless height of the dryer (m)
thermal conductivity of the feed (W/m ◦ C)
wall thermal conductivity (W/m ◦ C)
effective height of the dryer (m)
speed of the rotor (rev/s)
heat required (W)
hydraulic radius (m)
radius of the rotor (m)
revolutions per second
time (s)
time between two scraper actions (s)
temperature (◦ C)
bulk temperature (◦ C)
average temperature of jacket side (◦ C)
wall temperature (◦ C)
temperature of hot water used in jacket side (◦ C)
mass fraction of solvent (w/w)
overall heat transfer coefficient (W/m2 ◦ C)
axial velocity (m/s)
thickness of boundary layer (m)
co-ordinate axis (as shown in Fig. 4)
Dimensionless numbers
Pr
Prandtl number (Cp /k)
Reynolds number (Dsi V/)
Rea
ReR
rotational Reynolds number (De (Rr )process /)
Nu
Nusselt number ((hprocess-side Dsi )/kprocess )
Greek letters
˛
thermal diffusivity = (k/Cp ) (m2 /s)
density of the feed (kg/m3 )
viscosity of the feed solution (kg/m s)
˝
angular velocity (rad/s)
Subscripts
avg
average
e
equivalent
jacket
jacket side
h
hot water side
liquid
L
process process side
pen
penetration
r
rotor
solid
S
s
sc
w
693
stator
scraper
wall
References
[1] H. Abichandani, S.C. Sarma, D.R. Heldman, Hydrodynamics and heat transfer in
liquid full scraped surface heat exchangers—a review, J. Food Eng. (9) (1986)
121–147.
[2] T.R. Bott, J.J.B. Romero, Heat transfer across a scraped surface, Can. J. Chem. Eng.
41 (1963) 213–219.
[3] M. Harrod, Scraped surface heat exchangers: a literature survey of flow patterns, mixing effects, residence time distribution, heat transfer, and power
requirements, J. Food Proc. Eng. 9 (1986) 1–62.
[4] S. Komari, K. Takata, Y. Murakami, Flow and mixing characteristics in an agitated thin film evaporator with vertically aliened blades, J. Chem. Eng. Jpn. 22
(1989) 346–351.
[5] T.R. Bott, S. Azoory, K.E. Porter, Scraped-surface heat exchangers. I. Hold-up and
residence time studies, Tran. Inst. Chem. Eng. 46 (1968) 33–36.
[6] H. Abichandani, S.C. Sarma, Heat transfer and power requirements in horizontal thin film scraped surface heat exchangers, Chem. Eng. Sci. 43 (1988)
871–881.
[7] S. Zeboudj, N. Belhaneche-Bensemra, R. Belabbes, P. Bourseau, Modeling of flow
in a wiped film evaporator, Chem. Eng. Sci. 61 (2006) 1293–1299.
[8] J.M. McKelvey, G.V. Sharps, Fluid transport in thin film polymer processors,
Polym. Eng. Sci. (1979) 652–659.
[9] S. Komari, K. Takata, Y. Murakami, Flow structure and mixing mechanism in an
agitated thin film evaporator, J. Chem. Eng. Jpn. 21 (1988) 639–644.
[10] T.F. McKenna, Design model of a wiped film evaporator: application to the
devolatisation of polymer melts, Chem. Eng. Sci. 50 (1995) 453–467.
[11] A.M. Trommelen, W.J. Beek, Flow phenomenon in a scraped surface heat
exchanger, Chem. Eng. Sci. 26 (1971) 1933–1942.
[12] A.M. Trommelen, W.J. Beek, H.C. Van De Westelaken, The mechanism for heat
transfer in a Votator type scraped surface heat exchanger, Chem. Eng. Sci. 26
(1971) 1987–2001.
[13] A.H. Skelland, D.R. Oliver, S. Tooke, Heat transfer in a water-cooled scrapedsurface heat exchanger, Brit. Chem. Eng. 7 (1962) 346–353.
[14] A.H.P. Skelland, Correlation of scraped film heat transfer in the votator, Chem.
Eng. Sci. 7 (1958) 166–175.
[15] P. Harriot, Heat transfer in scraped surface heat exchangers, Chem. Eng. Prog.
Symp. Ser. 29 (1959) 137–139.
[16] W.R. Penny, K.J. Bell, Close clearance agitators, Part 2: Heat transfer coefficients,
Ind. Eng. Chem. Res. 59 (1967) 47–54.
[17] M. Harrod, Methods to distinguish between laminar and vertical flow in scraped
surface heat exchanger, J. Food Proc. Eng. 13 (1990) 39–57.
[18] H. Abichandani, S.C. Sarma, Heat transfer in horizontal mechanically formed
thin film heat exchangers-application of penetration theory model, Int. J. Heat
Mass Tran. 33 (1988) 61–68.
[19] R. Goede, E.J. Jong, Heat transfer properties of scraped surface heat exchanger
in the turbulent flow regime, Chem. Eng. Sci. 48 (1993) 1393–1404.
[20] J. Kool, Heat transfer in scraped surface vessels and pipes handling viscous
materials, Tran. Inst. Chem. Eng. 36 (1958) 253–258.
[21] G.A. Latinen, Discussion of the paper: correlation of scraped film heat transfer
in the votator, Chem. Eng. Sci. 9 (1958) 263–266.
[22] C.S. Rao, R.W. Hartel, Scraped surface heat exchanger, Crit. Rev. Food Sci. Nutr.
46 (2006) 207–219.
[23] P. Arlabosse, S. Chavez, C. Prevot, Method for thermal design of paddle
dryers: application to municipal sewage sludge, Dry. Technol. 22 (2004)
2375–2393.
[24] J.H. Yan, W.I. Deng, X.D. Li, F. Wang, Y. Chi, S.Y. Lu, K.F. Cen, Experimental and
theoretical study of agitated contact drying of sewage sludge under partial
vacuum conditions, Dry. Technol. 27 (2009) 787–796.
[25] W.Y. Deng, J.H. Yan, X.D. Li, F. Wang, S.Y. Lu, Y. Chi, K.F. Cen, Measurement and
simulation of the contact drying of sewage sludge in a Nara-type paddle dryer,
Chem. Eng. Sci. 64 (2009) 5117–5124.
[26] A. Dittler, T. Bamberger, D. Gehrmann, E.U. Schlunder, Measurements and simulation of vacuum contact drying of pastes in a LIST-type kneader drier, Chem.
Eng. Proc. 36 (1997) 301–308.
[27] E.U. Schlunder, N. Mollekopf, Vacuum contact drying of free flowing mechanically agitated particulate materials, Chem. Eng. Proc. 18 (1984) 93–111.
[28] E. Tsotsas, M. Kwapinska, G. Saage, Modeling of contact dryers, Dry. Technol.
25 (2007) 1377–1391.
[29] E. Tsotsas, U. Schlunder, Contact drying of mechanically agitated particulate
material in presence of inert gas, Chem. Eng. Proc. 20 (1986) 277–285.
[30] R.H. Perry, D.H. Green, Chemical Engineers’ Handbook, 7th edition, McGraw
Hill, New York, 1997.