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Heat Transfer in a Rotary Dryer
Margono, Ali Altway, Kuswandi, Susianto
Department of Chemical Engineering, Sepuluh Nopember Institute of Technology, Indonesia
Heat & Mass Transfer Laboratory, Kampus ITS Surabaya 60111, Indonesia
Telp: (031) 91171516
Email: [email protected], [email protected]
Received July 03th, 2008; correction received October 06th, 2008; approved December 19th, 2008
Abstract
Drying in rotary dryer has been used widely in industries, because it produced good heat and
mass transfer properties. A Rotary dryer consist of rotating cylinder that has an angle to the
horizontal where input material from one end and output product from the other end. Dry air is
used as a drying media. One of the important factors which will govern the size of the rotary dryer
is the feed rate of materials where heat is transferred to those particles. Simulation methods are
used in this work. Generally, mathematical model based on temperature in the solid or gas phase of
the drying process were applied in this paper. The aim of this work was to analyze the heat transfer
phenomena, using steady-state plug flow with back mixing and without back mixing modelling.
Partial differential equations describing heat transfer in the rotary dryer were derived from a shell
balance. Analytical methods were used to solve these partial differential equations. Some
dimensionless groups were used, and it would arrive in dimensionless equations. The computation
results were compared with the numerical method of the previous workers and it was validated to
the pilot plant data. Constant drum rotation of dryer is used in this pilot plant experiment. The
solution of steady-state plug flow equations could be presented as temperature of solid or gas
versus rotary dryer length. The graphical presentation was also developed for steady-state plug
flow modelling with back mixing for heat transfer. Solid temperatures along the dryer length were
measured permitting the evaluation of a true average temperature difference.Then heat transfer at
any point through dryer length could be calculated; since the inside wall temperature could be
found from the outside wall temperature and by solid conduction heat transfer calculations. Heat
transfer along the dryer length could be used as data to design the size of rotary dryer. It could be
concluded that comparison of analytical and numerical results of the gas and solid temperature was
favorable. Decreasing gas temperature is calculated from backmixing because the effects of
dispersion number or inverse of Peclet number. It would be better using rotary dryer length more
than 3 m to get solid temperature lower than 370 K or 97 o C.
Keywords: Solid and gas temperature, rotary dryer, plug flow modelling, heat transfer.
Solid’s water is removed in rotary dryer
because of flowing hot gas into the drying
space. Mass transfer is occured when solid and
air dryer are contacted. The process is mass
transfer from surface of the particles to the
flow of air dryer. The other simultaneous
process is heat transfer from drying air as a
hotter medium to the solid particles falling
through the stream. Heat also transferred to the
solid particles at the bottom of the rotary dryer.
Heat could be transferred also from hotter to
the lower temperature particles.
There are three periodes in drying
processes, these are (1) preheating period or
initial drying period, (2) constant drying rate
period and (3) falling-rate drying period.
During the preheating period, the temperature
of the solid and its surface are lower than
equilibrium temperature. In the first period, the
temperature of the solid and rate of drying rise
1
2 Jurnal Teknik Mesin, Volume 9, Nomor 1, Januari 2009
rapidly in a short time. In the second stage, the
process is evaporation from the surface of the
particles by constant drying rate. Critical
moisture content is found at transition period
between constant rate and falling rate periodes.
Moisture content will decrease linearly starting
from this critical point.
Usually materials in rotary dryer are
flied to the higher part of the rotary dryer by
the effects of the flights and then fall to the
lower parts, and back mixing of the solid is
occurred. There are three flows in a rotary
dryer. Particles plug flow in the bottom of the
dryer, falling particles by gravity force and
particles back mixing flows.
Heat transfer phenomena in the rotary
dryer should be studied well in order to analyze
and to design rotary dryer. To determine the
heat transfer along the dryer length would be
necessary obtaining temperature distribution
through the dryer. Heat transfer at any point
through the dryer are calculated between the
gas temperature along the dryer length and the
inside wall temperature. For the inside wall
temperature could be found from the outside
wall temperature by heat conduction
calculations. The heat transfer process in the
rotary dryer could be expressed in a differential
length of rotary dryer, dz. Calcite and hot air
are used as feed inlet and dryer air. Developing
mathematical model and simulation in rotary
dryer is the concern of this research. Drying
phenomena will be useful in design process
and determining optimum rotary dryer
conditions.
Previous workers, Friedman and Marshal
[1], have used experiment to get heat transfer
coefficient and operation variables effects in
drying process where the results were the same
with the heat transfer test. Wang [2] had
studied the modelling of drying process in a
rotary dryer for a certain material. Fan [3]
found a special solid axial dispersion in rotary
dryer but heat transfer and mass transfer with
axial solid dispersion simulation research are
not available. Pan et al [4] concluded that
granule could be transported at steady-state
processing in a rotary dryer, in this research
they used horizontal rotary drum with inclined
flights.
The aim of this work was to analyze the
heat transfer phenomena, using steady-state
plug flow with back mixing and without back
mixing modelling.
METHOD
Simulation is used in this work, and
presented schematically in Fig. 1. Drying of
solid particle is solved by a method of analytic
and Matlab facilities. This rate of drying results
is used to calculate β constant, in solid
temperature.
While, the result of rotary dryer’s model
developing is a system differential equation
which could be solved analytically by
integration.
Volumetric heat transfer coefficient and
residence time in this work are estimated from
correlation which is based on Friedman and
Marshal [5] and Lisboa et al [6] as presented in
equation (1) and (2)
.
k G 0.67
(1)
Uv  1
D

where
Fig. 1. Counter current flows of a rotary dryer
k2 H *
W
G = air mass rate (kg/h.s2)
D = rotary dryer diameter (m)
k1 = a constan, 0.3 – 0.5
k2 =a constant, 0.8 – 0.9
H* = holdup (kg)
 = average time of passage [h]
W = feed rate (kg/h)
(2)
3
Margono, Heat Transfer in a Rotary Dryer
z
∆z
z
Fig. 2. Experimental apparatus: a tray dryer
Fig. 4. A shell balance in a rotary dryer
In a tray dryer, it could be found: 1.fan,
2.electric heating, 3.upstream and down stream
air sensor for wet and dry bulb temperatures,
4.indicator temperatures, and 5.a balance. A
weighted sample is put on the balance, and
drying air is passed over it with a certain
conditions. After a fixed time, the sample is
weighted again, then rate of drying (Rw) could
be found from this data. This data is used in
energy of evaporation rate (equation 6).
The steady-state plug flow modelling
could be developed from a shell balance of
system described in Fig. 4. Steady-state heat
transfer modelling in solid can be developed
through the heat balance described as follows,
Input rate of axial convection energy
1   R 2V s  s C s Ts | z
Output rate of axial convection energy
1   R 2Vs  s C sTs | z z
Drying of
solid particles.
(Experiment &
Simulation)
Models of
residence time
(From previous
work)
Energy of generation rate
UV
1   R 2 z s v v Tgo  Ts
Fs

 Input rate   Output rate 

 

 of axial
  of axial

 convection    convection ...

 

 energy int o   energy from 
 the system   the system 

 

 Energy of 

evaporation   Energy of

   accumulation 

 from the  


  in the system 
 system

(3)
(4)
where
Cs
Fig. 3. Schematic diagram of research work
(6)
(7)
When these five equations are substituted
into equation (8) and divided by (1-ε) πR2∆Z
we have equation (9).
Heat transfer modelling in a rotary dryer
Validation
(5)
Energy of accumulation rate
T
1   R 2 Z  s C s s
t
 Vs C s
Analitical
solution

Energy of evaporation rate
1   R 2 Z  s Rw hs
Volumetric heat
transfer coefficient
modelling.
(From previous work)
Numerical solution
in a rotary dryer
(Yliniemi, 1999)
z+∆z
Ts U vVv
Ts  Tso   Rw hs  0 (9)

z
Fs
= solid heat capacity [kJ /kg.K]
z = differential length [m]
 t = differential time [s]
Fs
∆hs
L
Rw
(8)
= solid linear density [kg /m]
= solid specific latent heat [kJ /kg]
= dryer length [m]
= drying rate [1/s]
4 Jurnal Teknik Mesin, Volume 9, Nomor 1, Januari 2009
R
Ts
Tso
Uv
Vv
Vs
Table 1. Some of variables and parameters values of
Yliniemi works [7]
= radius of drum dryer [m]
= solid temperature [K]
= initial solid temperature [K]
=heat transfer volumetric
coefficient [kJ /m3.K.h]
= cylindrical volume per unit
length(air flow free) [m3/m]
= axial solid linear velocity [m/h]
The following dimensionless groups are
defined

F
z
L
 L  z
Ts  Tg 0
(10)

Equations (10) and (11) are substituted
into equation (9), and then we arrived to
equation (12)
Vs C s

(Tso  Tgo )F
L
 ...
(12)
U vV v
Tso  Tgo F  Rw hs
Fs
U V
F
  v v

 Fs
 R h
 w s
T T
go
 so
 L

 C sVs
 L

 C V
 s s
 U V  L 

1   v v 
 Fs  C sVs 

 F ...

(13)



1

) exp(  )  1
1
1
(16)
The steady-state plug flow modelling of heat
tarnsfer in drying air could be found as in the
solids modelling, and we have
2

) exp(  2 )  2
2
2
(17)
where
 L

 C V
 g g
 R h 
(14)






equation is
1 F0  1 exp( 1 )  1
1
where
Cg
Fg
∆h
Vg
= gas heat capacity [kJ/kg.K]
= gas linear density [kg /m]
= specific latent heat [kJ /kg]
= axial gas linear velocity [m/h]
In steady-state plug flow modelling of
heat transfer with back mixing in solids, we
have the same equation as the equation of
steady-state plug flow modelling, except the
back mixing form is added to them.

1
 F  1,
w
g
 L  Fs 
 2  

 
T

T
go  C g V g  Fg 
 so
;
F
   , solution of this
(

F


)
1
1
F0
0
1
F  (1 
 U vVv
 F
 g
F
 1 F  1

F
Steady state
values
1,01 kJ/kg K
0,84 kJ/kg K
0,27 kJ/s.m3
K
0,19 m3/m
and we have F0 = 1, the equation (15) become
2  
 R h  L 
F
At   0  Ts  Tso
F  (1 

 1   w s 
 Tso  Tgo  C sVs 

Steady staste Paravalues
meters
1,0 r/min
cg
0,7 m/s
cs
4,78 x10-3 m/s
Uv
0,12 kg/m
Vv
8,77 kg/m
472 K
421 K
293 K
360 K
Boundary condition 1

 Ts0  Tg 0 F  Ts (11)
Ts0  Tg 0
Variables
ndrum
Vg
Vs
Fg
Fs
Tg,in
Tg,out
Ts,in
Ts,out
(15)
Margono, Heat Transfer in a Rotary Dryer
 Vs C s

Ts
k  2Ts

...
z  s z 2

Simulation methods
(18)

U vVv
Tg 0  Ts  Rw hs  0
Fs
For solid temperature modelling, first α1
and β1 are calculated from data (Table 1).
These constants are substituted into equation
(16),
where
k = solid heat conductivity [kJ/h.m.K]
 s = solid density [kg/m3]
Tgo = initial gas temperature [K]
F  (1 
1

) exp(  1 )  1
1
1
where ξ = z/3 and
The same dimensionless forms as in the
steady state plug flow modelling without back
mixing are used in this solution. Some
boundary conditions are used in this solution
B C 1 at z  0    0  F 
Ts  Tg 0
Ts 0  Tg 0
 1;
B C 2 at z  L    1  F  0
(19)
exp .m2   exp .m1    3
3
where
 U V  L 
;
 R h  L 

 3   w s 
 Tso  Tgo  C sVs 
;
 k  L 

   
  s  Vs C s 
m1 
1  1  4
2
and
m2 
Ts  T g 0
Ts0  T g 0
From Table 1 it is found that
F
Ts  472


z
 (1  1 ) exp (  1 ( ))  1
293  472
1
3
1
Ts could be calculated for every z value. Then
a plot of solid temperature versus dryer length
is found. Using the same methods equations
16, 17 and 19 are plotted in the Figs. 5, 6, 7, 8
and 9.
   3 
 exp .m1 ...
F   3
 3 
 3 3


exp .m1   exp .m1  



...
3
 3


exp .m2   exp .m1 




F
where dryer length L = 3 m.
The solution of equation (17) is

 3   v v 
 Fs  C sVs 
5
1  1  4
2
RESULTS AND DISCUSSIONS
The computational results obtained from
this study was presented graphically in Fig. 5
through Fig. 9, showing the rotary dryer
performance under steady-state conditions and
using plug flow and plug flow with back
mixing modelling.
Figure 5 was a plot of gas temperature
(K) and dryer length (m). Analytical method is
used in this work, while numerical method is
used by Yliniemi [7]. Input gas temperature for
analytical and numerical methods were 472 K,
while numerical output temperature almost the
same with analytical data (426 K for numerical
and 424 K for analytical temperatures). Heat is
given up by the air dryer to the solid particles,
and to the dryer wall. The temperature of gas
will decrease and it reached 424 K at the
output product.
Plot of solid temperature (K) versus
rotary dryer length (m) was presented in Fig.6.
Initial solid temperatures in feed rate is 293 K,
and it increased exponentially and then it
became lower on the rest of 2/3 length of the
6 Jurnal Teknik Mesin, Volume 9, Nomor 1, Januari 2009
480
Tg, pilot data
Numeric
460
450
440
430
Analitic
420
0
0,5
1
1,5
2
Rotary dryer length (m)
2,5
3
400
350
Tsolid, analitic
300
Ts, pilot data
250
0
Solid temperature (K)
390
Numeric
350
Analitic
310
0,5
1
1,5
2
2,5
3
Dryer length (m)
Fig. 7 Plot of solid and gas temperatures (K) versus
dryer length (m) in a rotary dryer of co-current flows
between numerical (Yliniemi) and analytical method
(this work) and also pilot plant data.
Figure 8 was a result of simulation under
steady-state plug flow modelling and presented
as a plot of solid and gas temperatures (K)
versus drying length (m) in a rotary dryer of
counter current flows between numerical [7]
and analytical (this work) methods. Input solid
temperature was 293 K, and output solid
temperature was 371 K. Counter current flows
dryer are used for temperature sensitive
particles.
500
Tgas, numeric
Solid and gas temperatures (K)
dryer. Heat is received by the solid particles
from the air dryer, and temperature of the solid
will increased. If heat loss from the dryer is
great, then solid materials may transfer heat to
the dryer wall. Usually, in industries isolators
are needed to protect heat loss from rotary
dryer.
Figure 7 was a plot of solid and gas
temperatures (K) versus dryer length (m) in a
rotary dryer of co-current flows. Solid temperatures for analytical and numerical methods
increased exponentially until it reached 1/3
length of the dryer. While gas temperatures for
both methods decreased in the same way. The
temperature difference between solid and gas
product was 50 K. The analytical values for
solid and gas temperatures are very closed to
those determined experimentally.
330
Tgas, analitic
Tsolid, numeric
Fig.5 Plot of gas temperature (K) versus rotary dryer
length (m) of analitical (this work) and numerical
(Yliniemi) modelling in a rotary dryer.
370
Tgas, numeric
450
Solid and gas temperature (K)
Gas temperature (K)
470
450
Tgas, analitic
400
Tsolid, numeric
350
Tsolid, analitic
300
290
1
2
3
4
5
Rotary dryer length (m)
6
Fig 6 Plot of solid temperature versus dryer length (m)
of analitical (this work) and numerical (Yliniemi)
modeling in a rotary dryer
7
250
0
0,5
1
1,5
2
2,5
Dryer length (m)
Fig.8 Plot of solid and gas temperatures (K) versus dryer
length (m) in a rotary dryer of counter current flows
between numerical (Yliniemi) and
analitical methods (this work)
3
Margono, Heat Transfer in a Rotary Dryer
Solid and gas temperature (K)
500
Tg, PF back mix
450
Heat lost in each incremental length was
added to the heat transfer to the same
increment length to obtain the heat lost of the
drying air in travelling the same distance.
In this work, steady-state plug flow
equation is used. On the other paper, unsteadystate plug flow equation is used, where
temperature in solid was function of time. For
example,
unsteady-state
heat
transfer
modelling of plug flow equation is
Tg, PF
400
Ts, PF
350
Ts, PF back mix
300
250
0
0,5
1
1,5
2
Dryer length (m)
7
2,5
3
Fig.9 Plot of solid and gas temperature (K) versus
rotary dryer length (m) in a rotary dryer of cocurrent
flows between PF and PFwith back mixing in
anaiytical modeling
Figure 9 was a result of simulation under
steady-state plug flow with back mixing and
without back mixing modelling. It was
presented as a plot of solid and gas
temperatures versus dryer length (m) in a
rotary dryer of co-current flows. In 1 m length
of the dryer the solid and gas temperatures
reached at 353 K and 430 K respectively.
In Figures 5, 6, 7, 8 and 9, the
temperature gradient of gas and solid particles
are changed drastically. In this point (1m from
the feed point), the temperature of the solid rise
rapidly in a short time. This stage is called
preheating periode or initial drying period, In
the second stage, the process is evaporation
from the surface of the particles by constant
drying rate.
The solid particles and drying air
temperatures were plotted on Fig. 7, and shell
temperatures was 400 K along the length of the
dryer (as indicated on Fig. 7). Heat balance
between heat gained by the solid particles and
heat lost by the drying air is called the over-all
heat loss.
For accurate calculation, the length of the
dryer was divided into 3 incremental length.
The heat loss was calculated in proportion to
the temperature different between average shell
of the individual incremental length and room
temperatures. Heat transfer to the solid
particles was found from the plot of
distribution solid temperatures along the length
of the dryer.
 VsCs
Ts U vVv
Ts  Tso   Rw hs  Cs Ts

 z Fs
t
The right hand side of this equation is
accumulation form, where T s is function of
time t. This equation could be plotted as T s
versus drying length z in fixed time t, or it
could be plotted as Ts versus time t in fixed
length of dryer z.
The result of this work is useful for
design a rotary dryer since a good product
conditions are resulted from accurate
modelling of the dryer. For example, this
model could be predicted the exact temperature
of the product. The length of the dryer could be
re-designed for different raw materials.
CONCLUSION
1.
2.
3.
4.
5.
Temperatures
distributions
of
the
simulation results under steady-state plug
flow with back mixing were lower than
without back mixing.
Comparison of analytical and numerical
results of the gas and solid temperature
was favorable.
Heat transfers at any point through the
dryer are calculated from temperature
distribution data along the dryer length.
Heat transfer to the solid particles was
found from the plot of distribution solid
temperatures along the length of the dryer.
Decreasing gas temperature is calculated
from backmixing because the effects of
dispersion number or inverse of Peclet
number as shown in Figs. 7, 8 and 9.
Solid temperatures along the dryer length
were measured permitting the evaluation
of a true average temperature difference as
well as the heat transfer.
8 Jurnal Teknik Mesin, Volume 9, Nomor 1, Januari 2009
6.
7.
8.
9.
It would be better using rotary dryer length
more than 3 m to get solid temperature
lower than 370 K or 97o C.
Rate of drying is found from experimental
data and was depend on temperature of
drying air. This data is used in energy of
evaporation rate (equation 6). If we used
variation temperatus of drying air, then
variation of drying rate were found, or it
could be used average drying air.
If it was used the biggest values in the
range of drying air data , then the lower
surface temperature of the particle was
found.
If we used the biggest or the lowest values
of rate of drying then the result was not
match with the data of previous research.
Average values of drying air were used in
this work.
X
z
s



= mass of moisture per solid mass
[kgm /kgs]
= axial distant [m]
= solid density [kgs /m3]
= fraction of bed void [ - ]
= dimensionless length [ - ]
= a constant [ - ]
ACKNOWLEDGEMENT
The authors wish to acknowledge the
financial support of Fundamental Research
Grant 2009 administered by Department of
Research and Social Service, Directorate of
Higher Education, Indonesian Ministry of
Education.
REFERENCES
NOTATION
Cg
Cs
D
z
t
Fs
Fg
F
G
H*
∆h
k
k1
k2
R
Rw
Ts
Tg
t
Uv
Vg
Vs
Vv
W
= gas heat capacity [kJ/kg.K]
= solid heat capacity [kJ /kg.K]
= rotary dryer diameter [m]
= differential length [m]
= differential time [s]
= solid liniar density
[kg /m]
= gas liniar density [kg/m]
= dimensionless temperatures [ - ]
= air mass rate [kg/h.s2)]
= holdup [kg]
= specific latent heat [kJ /k
= solid heat conductivity
[kJ /h.m.K]
= a constan, 0.3 – 0.5
=a constant, 0.8 – 0.9
= radius of drum dryer [m]
= drying rate [kgm/kgs j]
= solid temperature [K]
= gas temperature [K]
= time [hour]
= heat transfer volumetric
coefficient [kJ /m3.K.h]
= axial gas linear velocity [m/h]
= solid linear rate in axial direction
[m /j]
= cylindrical volume per unit
length (air flow free) [m3 /m]
= feed rate [kg/h]
[1] Friedman, S.J. & Marshall, W.R.Jr., 1949,
“Studies in Rotary Drying - Part 1.
Holdup and Dusting”, Chem
Eng
Progress, vol.45, no. 8, pp. 482-493.
[2] Wang, F.Y., Cameron, I.T., Litster, J.D. &
Douglas, P.L., 1993, “A Distributed
Parameter Approach toThe Dynamics of
Rotary Drying Processes”, Drying
Technolog, vol. 11, no. 7, pp. 1641- 1656.
[3] Fan L.T., Ahn, & Yong-Kee, 1961, “Axial
Dispersion of Solids Flow
Systems”,
Applied Scientific Research, vol. 10, no.1 ,
pp.465-47
[4] Pan, J.P., Wang, T.J., Yao, J.J., & Jin, Y.,
2006, “Granule transport and mean
residence time in horizontal drum with
inclined flights”, Powder Technology, 16,
(2006), 50 – 58.
[5] Friedman, S.J. & Marshall,W.R.Jr., 1949,
”Studies in Rotary Drying- Part 2. Heat
and Mass Transfer”, Chem Eng Progress
,vol.45, no. 9, pp. 573-588.97.
[6] Lisboa, M.H., Alves, A.B., Vitorino, D.S.,
Delaiba,W.B., Finzer, J.R.D. & Barrozo,
M.A.S., 2002, “A study about particle
motion in rotary dryers”, 2nd Mercosur
Congress on Chemical Engineering.
[7] Yliniemi, L.,1999, “Advanced Control of
a Rotary Dryer’, PhD Thesis, Department
of Process Engineering, University of
Oulu, Finland.
Margono, Heat Transfer in a Rotary Dryer
9