Chemistry & Chemical Technology, Vol.9, No.4, Lviv Polytechnic National University, 2015, P.497-501.
unsteady heat transfer during encapsulation of dispersed materials in quasi-liquefied state
Oleg Nagursky, Yaroslav Gumnitsky and Victoria Vaschuk
Lviv National Polytechnic
University
12, Bandera str., 79013 Lviv, Ukraine; nahurskyy@mail.ru
12, Bandera str., 79013 Lviv, Ukraine; nahurskyy@mail.ru
Received: July 04,
2014 / Revised: August
28, 2014 / Accepted: December
18,
2014
ã Nagursky O., Gumnitsky Ya., 2015
Abstract. Experimental and analytical investigations of the heat
transfer process during encapsulation of dispersed materials in quasi-liquefied
state are presented. The heat-transfer coefficients for different types of materials
have been determined during their heating depending on air rate.
Keywords: unsteady heat transfer, kinetics, quasi-liquefaction,
dispersed material.
1. Introduction
During encapsulation of dispersed materials in quasi-liquefied
state using film-forming solutions it is necessary to heat the particles till
operating temperature. In the batch apparatus such heating is a separate
technological stage [1]. In the continuous apparatus the heating may proceed in
the separate area or directly in the area of coating growing in parallel with
film-forming agent plating depending on design [2].
Irrespective of apparatus type in the certain periods
of time the dispersed material is in the state of unsteady heat transfer. The
intensity of this stage depends on heat carrier rate and temperature, as well
as on material physical properties [3, 4]. Therefore to produce and use the
encapsulated materials the investigations of heat transfer kinetics during
encapsulation of dispersed materials in pseudo-liquefied state are urgent. It
is the possibility to take a scientific approach to the choice of encapsulation
technological parameters, provide the high productivity of the equipment and
obtain the materials with predicted properties.
2. Experimental
The heat transfer between the air and material layer
during heating occurs at the moment of dispersed material loading into an
apparatus and ends as particles are heated till the operating temperature. The
experiments were carried out in the batch cylindrical apparatus of
quasi-liquefied state. During the experiments the working part of the apparatus
was insulated to avoid heat losses throughout the walls. Before the material
loading the apparatus was heated to the operating temperature, hence there was
no heat exchange between the air and apparatus walls. At the beginning the
dispersed material temperature was 293 K. The temperature of heat carrier
was 348 K and it was measured using chromel-copel thermocouple and 7-channels
smart convertor PVI-0298 with computer recording. The change of heat carrier
temperature was fixed from the moment of loading and till approaching of the
air temperature at the apparatus outlet to the initial values.
The used solid materials were: polydispersed layer – granulated
mineral fertilizers (ammonium nitrate, calcium nitrate, carbamide and
nitroamophose) and layer of particles with irregular geometry – seeds which may
undergo the presowing encapsulation by chemical protectants for plants and
chemical elements of additional fertilizing (fodder beet, spinach).
3. Results and Discussion
The dependencies of heat carrier temperature on time at
different values of liquefying air rates within the range between first and
second critical values are represented in Fig. 1.
quasi-liquefied
state
The analysis of the experimental results shows that
the increase in air rate decreases the time necessary for the layer to be in
temperature equilibrium with the heat carrier. The reason is that the higher
air rate decreases the layer thickness at the boundary air–particle surface and
increases the amount of heat transferred from the particle at the same space of
time. These observations are in an agreement with the results of heat-and-mass
transfer in the quasi-liquefied state obtained by other authors [3, 7, 8].
The heat-transfer coefficient a which determines the amount of heat donated or
accepted by the surface unit for time unit is an important thermal
characteristic of the heat transfer processes. The coefficient is determined
experimentally and the theory of generalized variables is used for its
generalization. According to the theory the criterial dependencies between dimensionless
numbers are obtained.
The coefficient a is determined on the basis of heat transfer equation
[3] which includes the surface temperature of the solid matter. To measure the
surface temperature of the particle in quasi-liquefied state is problematic,
therefore to determine the coefficient a we used the method based on the theory of unsteady
heat conductivity.
where λ – the heat conductivity factor of the liquefying air, W/m∙K; c
– heat
capacity
of
the
liquefying
air,
J/kg∙K; ρ – density of
the liquefying air, kg/m3.
Using the value of Bi number, calculated
according to Eq. (4) we calculate the values of the coefficient a. The obtained results are averaged relative to
the layer height and represented in Fig. 2.
Fig. 2. Dependence of the heat-transfer coefficients on dummy rate of the
liquefying air for the dispersed materials heating
One can see from Fig. 2 that the coefficient a increases with the increase in air rate according to
the linear law. It is explained by greater heat application with the increase
of liquefying air amount and decrease of boundary heat layer around the
particle due to the gas flow turbulization. The obtained results (Fig. 2) are
in the agreement with the data of other authors [6].
The experimental results are generalized in accordance
with Eq. (7) [5]:
Fig. 3. Generalization of the experimental results concerning the heat-transfer
coefficients during the dispersed material heating by liquefying air
One can see from Fig. 3 that the experimental points
for all materials are approximated by practically parallel lines. Thus, the exponents
near Reynolds number are equal for different materials. The difference in
vertical placement of the lines is explained by the influence of particles size
on the heat-transfer coefficient. The same as for the heat-transfer
coefficient, the dependence of Nusselt number on the rate of heat agent flowed
around the particles is correlated with the data from Ref. [8, 9] for different
by size balls made from glass and plastics.
The determined coefficients A and n are given in the
Table. The value of the coefficient A
is a function of particle size and exponent n
is the same for all materials and equals approximately to 0.9.
Table
The
experimental data are approximated in the best way by two curves (Fig. 4). The
first curve is drawn through the points that correspond to the coefficient A obtained for the seeds and model
particles, the second – for granulated fertilizers. The points on the graph are
situated from the left to the right in ascending order of particles size. The
exponent in Eq. (8) is the same for both curves and equals to 0.67. A’ for the first curve is 0.418; for the
second – 0.253.
4. Conclusions
The obtained generalized dependencies allow to
determine the heat-transfer coefficients of the dispersed materials heating
till the operating temperature. The difference between different dispersed
materials may be explained by the different form of particles. Thus, the seeds
are characterized by complex geometry having the essential influence on the streamline
conditions of heat agent. Thus, for the seeds the difference between
theoretically calculated Nusselt number and experimental data is approximately
26 %.
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Принцип работы пиролизных котлов, основан на сжигании древесного газа выделяемого в процессе тления дров.
