HUNGAR~JOURNAL 
OF INDUSTRIAL CHEMISTRY 

VESZPREM 
Vol. 30. pp. 155 -160 (2002) 

KINETICS AND CHARACTERISTIC CURVE FOR CONVECTIVE AND INFRA-
RED CONDITIONS DURING DRYING OF CLAY 

F. ZAGROUBA, D. MIHOUBI, A BELLAGI1 and A SZALAY2 

(INRST, B.P. 95, 2050 Hammam-Lif, TUNISIA 
1
ENIM, Av. Ibn Eljazzar, 5000 Monastir, TUNISIA 

2RICV, B.P. 459, 8200 Veszprem, IfUNGARY) 

Received: April 30, 2002 

In this work, we present the experimental drying curves obtained by two heating modes, namely: convection and Infra 
Red. We examined the influence on the drying kinetics of the infrared flux density and of the aerothermic air condition: 
temperature, velocity and humidity. A comparison of the results obtained by the two heating modes are compared 
Finally, a polynomial equation was fitted to the experimental characteristic drying curve. 
From the experimental drying kinetics the moisture diffusivity and the heat transfer coefficient values were identified. 

Keywords: internal diffusion, heat transfer 

Introduction 

In many industrial processes, drying treatment 
generally, uses some conventional techniques of energy 
supply as convection and conduction. Nevertheless, 
these heat transfer modes have .limit heat transfer 
capacities which can be inadequate for same 
separations. 

Some "new" sources are found in radiative like Infra 
Red (IR.), microwave, as the high frequencies 
technologies. The energy transfer to the product is direct 
and permits therefore to attain rapidly suitable levels 
temperature, which activates the fundamental drying 
mechanisms of the operation. Because of their 
performances, these techniques present currently a 
strong development. 

The drying by Infra-Red radiation has been applied 
to several products like the agro-food products: [1-21. 
paint: [3] and pure and homogeneous materials: [4]. 
However, it is difficult to study the IR drying of 
foodstuff materials. They possess a complicated 
structure and, the knowledge of their optic properties is 
limited. 

The effect of the emissivity of a deformable 
~anu1ated bed during IR drying was investigated only 
In the constant rate period: [5-8]. Though for the drying 
of paper, the optic characteristics are better known. the 
problems bound to the effect of the geometry were not 
discussed in detail: [9]. However, it has been shown that 
geometric dimensions have a large influence on the. 
functioning of tlre process: [ 10-llJ. 

The IR drying rate depends essentially on the 
radiation absorption, on the density of IR flux and on 
some optic characteristics which vary with geometry, 
structure and water content. So, the main objective of 
our work was, to study the experimental IR drying 
curves and to compare these data the corresponding 
obtained with the convective drying. 

Infra-Red Radiation 

Before approaching the drying by IR, it is important to 
remind some useful essential properties as well as the 
principal advantages of IR radiation. 

In fact, the IR radiation differs only from other 
electromagnetic vibrations: X rays, Ultra~ Violet rays, 
visible light and hertzian waves, by its wave length 
which is included between 0.8J1m and l5J.Im (Table 1). 
This physical characteristic distinguish lR from other 
radiations. However, the essential laws remain identical 
such as the phenomena of propagation, absorption and 
transmission. 

In practice, one could not separate the IR and the 
visible radiation which are too near: one often detects 
some visible light in an IR drier. 

TheIR radiation in the range from 0.76j.lm to 15!J.m 
can be subdivided normally into three types: 

- the short lR from 0.76~J.m to 2j.tm, 
- the middle lR from 2pm to 4J1m, 
• the long IR from 4;.un to lSf.lm. 

Contact information: E-mail: zagrouba.fathi@inrst.rnrt.tn; Fax: +216 71 430 934 



156 

Table 1 Limits of wave of the Radiations 

Type of y Rays X Rays UV Rays 
radiation 

Wave 3.IO"'A 0.1A at 200A at 
length at O.lA 200 A 0.4 "m 
limits ,.. 

visible lR Rays Hertzian 
light Waves 

0.4f.1m at O.Sf.Im at 15f.lm at 
0.8f.lm 15f.1m some km 

If the processes of convective drying have already 
been the object of many studies, it is not the same for 
the mixed processes associating the convection and the 
IR heating, for which exists only very little literature in 
particular for the case of strong radiation densities, IR 
heating presents the following advantages: 

very high flux densities (up to lOOkW/rnZ) and 
compact equipments, 
no direct contact with the product (dusts), 
possibility offocalising the energy, 

- very response time which leads to easy control 
procedure. 

Basis Concepts of Drying 

Basic principles of convective drying are well known. 
Starting from a very wet capillary product, the moisture 
is moved to the surface under the form of a continuous 
liqujd flux (capillary flow). The surface temperat~e of 
the product is constant (wet bulb temperature), so 1s the 
air temperature, hence the flux of evaporation remains 
constant. After a certain time, the capillary forces 
become inoperant to move liquid water from inside to 
the surface. New mechanisms of water displacement are 
found in surface diffusion, and evaporation-
condensation cycles. The front between very wet 
material and almost dry material receeds towards the 
core of the product. IR radiation provokes an 
instantaneous drying of a thin superficial layer its 
temperature raising well above any wet bulb 
temperature. The results is then ambiguous: quick 
drying of a thin layer which in turn will slow down any 
water movement from inside. Thence the IR is reserved 
for thin materials or superficial drying. 

Material and Method Infra-Red Drying 

Experimental apparatus 

Our drying experiences IR radiation is conducted by 
means of a device composed principally of: 

some emitters ofiR energy, 
a sample placed at the bottom of the air tunnel, 
an electronic scale, 
excess air and steam exhaust. 

Overall kinetics 

The material was placed inside an aluminium 
cylindrical support. The mass and thermal exchanges 

Tests 
N 
1 
2 
3 
4 
5 

Table 2 Some tests of drying by IR 

Air Temperature 
(oC) 

Initial Moisture Content 
(kg/kg) 

Ll 

"" 
0.5 

,.. 
0.3 

0.2 

0.1 

0 

0 

0 

160 
120 
70 
120 
160 

. . 
* 

0.969 
1.018 
1.087 

0.5843 
0.72 

0 . 
0 . 
0 

* . * \ 
o 10 2.0 ao 4D so 60 70 eo 90 too 

Time(mn) 

... .. 

a n u ~ ~ m ® u 1 -
Fig.l Influence of IRradiation on the kinetics of drying (Tests 

1,2 and3) 

were supposed unidirectional. The cont~nuous weighting 
of the sample allowed to determine the drying kinetics. 
Several tests were achieved for different values of 
moisture and temperature (Table 2). Globally, 
experimental data presented on the following figures 
show distinctly: 

at constant drying rate: period is sufficiently long 
and covers a large part of drying time. During this 
period, quite aU the energy provided to the material 
was used for water evaporation, 
a decreasing rate period: it is very short and begins 
with the complete drying up of the surface of the 
material ; the temperature of the material increases 
noticeably. One supposes that the drying front 
receeds into the material. 

Influence of Infra-Red Radiation 

Under IR heating, the drying rate and therefore the 
water loss, depend directly on the incidental infrared 
flux. 

In order to study the quantitative effect of the IR 
energy on the drying process, we applied different IR 



Table 3 Some tests of drying by convection. 

Tests Air Temperature Air Humidity Air Velocity fuitial Moisture 
N (°C) (%) (rnls) Content (kg/kg) 
I 37.5 22.1 2.3 0.49 
2 50.8 50.8 1.5 0.538 
3 55.7 16.9 2.3 0.69 
4 48 20.8 2.2 0.433 
5 54.9 13.9 1.6 0.76 

flux densities to the clay and we recorded the sample 
mass versus time. As already noticed [10,13-16], we 
observed that the drying rate is proportional to the IR 
emitted flux (Fig.l) e.g.: the flux of matter is doubled 
when the power is doubled. 

Convective Drying 

Experimental apparatus 

The experimental apparatus in which we conducted our 
tests of convective drying allowed to control the 
velocity, the temperature and the humidity of the drying 
air. It was made principally of: 

a simple aspiration ventilator with adjustable speed 
of rotation, 
some electric resistances for the heating of the air, 
of a humidifier/dehumidifier, allowing to maintain a 
constant humidity of air, 
of a sample holder into the vein of measurement on 
a balance, precision 0.1 mg. Data acquisition and 
treatment is insured:-

Several tests were achieved for different values of 
moisture, temperature and air velocity (Table 3). · 

Influence of Air Temperature 

The Fig.2 shows that the drying kinetics increase with 
air temperature because of the increase of heat flux 
brought by the air to the product, and because the 
acceleration of the internal water migration bound to the 
coefficient of diffusion. One notes that the moisture 
content corresponding to the change of regime is so 
much more elevated when the temperature increases, 
whereas the equilibrium moisture content evolves in the 
opposite sense. 

Influence of Air Moisture 

An increase of the relative moisture entrains a reduction 
of the isenthalpic flux. The moisture content 
corresponding to the change of regime evolves in the 
same way as the isenthalpic flux. The equilibrium 
moisture content increases naturally with an increase of 
the relative moisture content (Fig.3). 

157 

. 
M .. 
~ .. . 
0.7 +. .. 

ln5 ++ ... .. .. . · .. 
'• ... .... 

.,1 0~;;:;;--#~;;_~+tt~-~~li~IJI~lll~ll!~l!I~JIH~ ;- l!Ili1COXJ&lll}KOl\UlXJ11ml _, 

~.~,~~~~U~M~M~.~.-,7,~ .. ~ .. ~, ..... , 
Fig.2 Effect of the temperature of the air on the drying 

kinetics (Tests 1 and 4) 

Characteristic Curves of Drying 

The method adopted for the determination of a master-
curve, called characteristic curve of drying (CCD), it. 
near in its principle to the one reconnnended by [11, 12-
18], only used in the case of the products presenting a 
period of constant rate drying. 

The purpose of CCD consists in establishing a law 
of drying based on some experimentation ; it derives 
from some basic knowledge acquired in the domain of 
drying but remains without complete theoretical 
justification. Consequently, only its aptitude to foresee 
some drying curves attests of its validity (heuristic 
approach). 

A CCD results from the transform of the abscissa 
and of the ordinate in order to reassemble all the 
experimental curves (Fig.4) on a unique curve: 

m [- ~:)-7 f= -[d;) 
dt I 

(1) 

(2) 

The determination of a reduced variable curve after 
the transformation appears here very delicate because of 

the impossibility of reaching the values of ;;u and of 

[-d;) . We propose a new transformation, derived dt 1 
from the previous one: 



158 

t . 
t . 
'• 
•' . 

t •• 
t • . .. 

t •• 
t •• 

t + •••• .. 
; 

i 

+++t ••• ••• 

t t 

.. 
: 

+ t 

. . . . 

.. . .... 

t .. 

a m m u ~ ~ M m M ~ 1 -
Fig.3 Effect of the moisture of the air on the kinetics of drying 

(Tests 2 and 5) 

w -HP == w-w,q 0:::; lf>:::; 1 (3) 
wo -w,q 

·m 
(- ~)->/" ~( ~l 0~/~1 (4) 

The application of this new transformation to the 
whole set of experimental curves of drying by IR 
radiation led the global Fig.5. 

A polynomial interpolation of the experimental 
points led us to the following relation: 

f = F(if> )= 2.79211> 3 -4.5175if>z + 2.7556<P + 4.096910-2 {5) 

Coefticient of Diffusion 

The resolution of the model necessitates the knowledge 
of various physical properties of the day among which 
the coefficient of diffusion is important 

In a general way, the coefficient of diffusion D 
intervenes in the expression of the temporal evolution of 
fields of the moisture (Eq.(6} and (7}): 

If the product is not deformable, the equation reads: 

aw =~(D aw) (6) 
dt iJx iJx 

If the product is submitted to a unidirectional 
shrinkage it becol!les: 

Fig.4 Comparison between convective and Infra-Red drying 

0,20 0.40 0.110 

Fig.5 Characteristic Curve of drying of the clay 

(7) 

Extracting diffusion coefficients as a function of 
moisture content from drying curves is very difficultand 
does not produce satisfactory results. KETELAARS 
attributes this difficulty to the fact that drying curves are 
sensitive to the moisture concentration dependency of 
the diffusion coefficient in a limited range. 

Outside this region, the diffusion coefficient has 
little to no value. Only diffusion coefficient derived 
from internal moisture profiles are valuable. 

Our clay sample G is very similar to clay A used by 
[24], as their shrinkage curves are similar. With both Wr 
shrinkage limits are in the vicinity of 0.25. 

Nevertheless, we have tried to identify a coefficient 
of diffusion from drying curves for values of w<O.l. 
Our two results fit in rather well with KETELAARS, 
values near 10·9 m2s·1 (Fig.6). A possible expression for 
the coefficient of diffusion is: 

. D(w,T)== n{ exp( b:Vw) }x{-; J (8) 
with D0 , a, b and c parameters for adjustment (Table 4). 

Heat and Mass Transfer Coefficients 

The CHR..TON-COLBURN analogy is largely used in 
drying studies. Indeed, if one admits that the 
temperature and vapour cc·~centration boundary layer 
are very similar, the convective coefficients heat he and 
mass km are related by the LEWIS relation of: 



Table 4 Values of parameters of diffusion 

a b c 
4.61 1.8019 0.031 16 

__ c -= f(Le) = __!!_ h (s )213 
kmpCP Pr 

(9) 

So, the mass transfer coefficient value km can by 
derived from he, values which are generally calculated 
from some classical empirical heat transfer correlation. 

The validity of this pure convection analogy in 
presence of IR radiation and an important flux of matter 
was discussed and checked by [17]. 

Transfer of Heat by Convection 

The film theory allows to express the flux of heat 
through a boundary layer of steam by the relation: 

Q =!i_h L ( 1 CpJTa-Tsurf)) conv C en+ L 
Pv v 

(10) 

In the case of a drying with a weak rate of 
evaporation, the flux of sensible heat is very much 
lower compared to the fluxes of latent heat in such a 
way that one gets: 

Ln(l+ CpJTa-Tsurf) )=C Ta-Tsurf (l 1) 
Lv Pv Lv 

This equation is then equivalent to Eq.(12) of 
common use: 

159 

''"'l 
t!.OOE-9 

* 
* 

t.SOE-9 

iJ 

"' c LOOE-9 

5.00!:·10 

O.!lOE+O ~."~"! w(kg~odoJ~ ().()() 
Fig.6 Evolution of diffusion coefficient with the moisture 

content 

With: N - hcDh . R - VaDh . G - pgfrp-Too)Dh3 u----, e- , r- , 
A. v vz 

v: kinematic viscosity (mis-1), 
{3: air compressibility. 

c. Equivalent Radiative Heat transfer Coefficient 

= rY(Ts:rt + r; )(Tsurt + Ta XT.urt - T. ) = 
= h/Tsurf - Ta ) 

Mass Transfer Coefficient 

(17) 

Qconv =hiT a- Tsurf) (12) According to NAVARRI, the coefficient of transfer is 
independent of the presence variation of the IR flux. In 

Convective Heat Transfer Coefficient 

If the hydrodynamic and aero thermic regime is well 
established, the heat transfer coefficient can be 
estimated from well known relationships: 

a. Forced conv~ction 

Drrros BOELTLER proposed the following relation 
taking into account some secondary side effects: 

Nu = 0.023Re0·8 Pr113(1+6~ J (14) 
where Dh and L are respectively the diameter and the 
length of the duct. 

b. Natural Convection 

From the GRASHOF's work, one may use: 

*3.103 <Gr<108~ Nu=0.27(GrPrr5 (15) 

the case of the humid air, ( ~: J13 :::::I , so it is possible 
to estimate the mass transfer coefficient: 

k = ..5:_ 
m pCp 

(18) 

As checked by [17], this analogy also could be 
applied in the case ofiR drying. 

However, the previous analogy applies only in the 
case of pure convective heat transfer. In this study and 
as a measure of simplification, we supposed that the 
analogy applies to the global coefficient of transfer 
(h=hc+hr) which is a convenient coefficient for the 
experimental reality. 

Conclusion 

In this work, we studied the clay drying kinetics by two 
different heating modes: convection and IR radiation. 

In the case of convective or IR heating, the drying 
kinetics show two drying periods departed by the 
critical moisture content. 

The increase of the drying air relative humidity 
decreases the drying rate in the ease of convection, 



160 

contrary to the case of IR heating for which this 
humidity does not have a significant influence. 

The increase of the air temperature enhances 
appreciably, in as much as it is tolerated by the product, 
the drying rate during the constant rate period. 

The increase of the IR generally flux density implies 
a very height increase of the drying rate, which reduce 
the drying time and preserving the quality of the product 
(Fig.4). 

The concept of characteristic drying curve was 
checked in order to an overall expression of the drying 
kinetics. By using an appropriate change of variable, 
one could determine an empiric expression of the drying 
kinetics suitable to control and predict the drying 
process independently of the chosen parameters. 

In spite of a satisfactory, essentially for small 
moisture content, identification of the material diffusion 
coefficient from the kinetics, we will adopt the 
KETELAARS results in the numeric part. As for the 
coefficients of thermal transfer, we will apply the 
analogies generally admitted. 

SYMBOLS 

C specific heat, Jkg1 K 1 

D diffusion coefficient, m2s·1 

h heat transfer coefficient, wm-2K 1 

k mass transfer coefficient, ms·1 

Le Lewis number, -
Nu Nusselt number,-
Pr Prandtl number,·-
Q heat flux, Wm'2 
T temperature, K 
t time, s 
w moisture content, kgkg-1 

Indexes 

c convective 
cr critical 
eq equivalent 
o initial 

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