M. ^ARNOGURSKÁ et al.: DETERMINING THE HEAT-TRANSFER COEFFICIENT IN AN ISOTHERMAL MODEL ...
339–344
DETERMINING THE HEAT-TRANSFER COEFFICIENT IN
AN ISOTHERMAL MODEL OF A SHAFT FURNACE
DOLO^ITEV KOEFICIENTA PRENOSA TOPLOTE
V IZOTERMNEM MODELU JA[KOVNE PE^I
Mária ^arnogurská1, Romana Dobáková1, Tomá{ Brestovi~1, Miroslav Pøíhoda2
1Technical University of Ko{ice, Faculty of Mechanical Engineering, Vysoko{kolská 4, 042 00 Ko{ice, Slovakia
2V[B – Technical University of Ostrava, Faculty of Metallurgy and Materials Engineering, Ostrava-Poruba, Czech Republic
maria.carnogurska@tuke.sk
Prejem rokopisa – received: 2016-03-03; sprejem za objavo – accepted for publication: 2016-04-01
doi:10.17222/mit.2016.042
The paper addresses an analysis of the influence of the batch grain size and air flow through a shaft furnace on the transfer
coefficient from the air to the batch and the time for heating the batch to the required temperature. The stated influence was
experimentally investigated on a reduced shaft-furnace model at three air-flow amounts, 48.8 m3 h–1, 56.3 m3 h–1 and 72 m3 h–1,
and three varying grain sizes of the used batch: 4–8 mm, 8–10 mm and 10–12 mm. The influence of the stated parameters upon
the evenness of the velocity field of the air along the cross-section of the furnace was also monitored in two selected horizontal
planes in order to obtain information about the air velocity in the vicinity of the wall of the model furnace and at distances of
1.5 cm, 3.5 cm and 5.0 cm from it.
Keywords: batch grain size, heat-transfer coefficient, velocity field
^lanek obravnava analizo vpliva zrnatosti vlo`ka in pretoka zraka skozi ja{kasto pe~ na koeficient prenosa iz zraka na vlo`ek in
na ~as segrevanja vlo`ka na potrebno temperaturo. Navedeni vpliv je bil eksperimentalno preiskovan na pomanj{anem modelu
ja{kaste pe~i, pri treh pretokih zraka 48,8 m3 h–1, 56,3 m3 h–1 in 72 m3 h–1 ter pri treh razli~nih zrnatostih vlo`ka: med 4–8 mm,
med 8–10 mm in med 10-12 mm. Opazovan je bil tudi vpliv omenjenih parametrov na enakomernost hitrostnega polja zraka po
preseku pe~i v dveh izbranih horizontalnih ravninah z namenom, da bi dobili informacijo o hitrosti zraka blizu stene modelne
pe~i in na razdaljah: 1,5 cm, 3,5 cm in 5,0 cm od nje.
Klju~ne besede: zrnatost vsipa, koeficient prenosa toplote, hitrostno polje
1 INTRODUCTION
Using various technical devices, it is necessary to
examine the intensity of the heat exchange between two
substances – most often between a gas and a solid sub-
stance. The heat-exchange intensity is represented by a
heat-transfer coefficient and it takes place via conduc-
tion, convection, flow and radiation.1–2
Metallurgical furnaces currently represent a compli-
cated mechanised and automated equipment and equally
complicated procedures taking place within. The thermal
regime of such industrial aggregates is very complicated
and it therefore requires appropriate attention.
Several authors focus upon the heat transfer in vary-
ing metallurgical furnaces and compare their results
obtained experimentally with the results from numeric
simulations.3–5
2 EXPERIMENTAL PART
2.1 Description of the heat exchange in a layer of a
shaft-furnace batch
The heat exchange in a batch layer of shaft furnaces
and similar furnace aggregates is provided by direct
contact between the gas medium and the batch. The heat
in the batch layer is mainly transferred via radiation and
convection.6–8 The radiation component is present to a
lesser extent than the convection component. When
heating a batch, gas radiation is influenced by the small
dimensions of the channels created between individual
grains of the batch material and the low concentration of
heteropolar gases. In practice, heat exchange via radi-
ation only takes place at high batch temperatures.
Heat exchange via conduction also takes place bet-
ween individual pieces of the batch. However, this heat
exchange is negligible.
The gas-flow velocity has a decisive effect during the
heat exchange between a flowing medium and a batch.9
An analysis of convection during the heat transfer from
the heated air to the batch was carried out on a "cold
model". This means that a simulated batch formed of
crushed chamotte at an ambient temperature was ex-
posed to a flow of heated air with a known temperature
and known volume. The influence of the grain size of the
batch and the air flow upon the intensity of the heat
exchange between the air and the batch was monitored
and represented by the heat-transfer coefficient from the
air to the batch.10
Materiali in tehnologije / Materials and technology 51 (2017) 2, 339–344 339
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
UDK 621.1.016.4:621.18.06:669-5 ISSN 1580-2949
Professional article/Strokovni ~lanek MTAEC9, 51(2)339(2017)
2.2 Experimental model furnace
An experiment focusing upon obtaining the informa-
tion necessary to determine the heat-transfer coefficient
was carried out on an equipment representing an iso-
thermal model of a shaft furnace. A diagram of the
model is on Figure 1 and an image of the experimental
equipment during the measurement is on Figure 2. The
basic parameters of the model are given in Table 1. The
model has a double insulation in the lower part con-
sisting of perlite and chamotte flour. The insulation in
the upper part of the model consists of just chamotte
flour. The brickwork comes into direct contact with the
batch and the flowing air. The bottom of the model is
formed of a graduated grid, on which the batch is placed.
Below the grid, there is pipework, through which the air,
heated in a recuperator, is transported to the furnace
model.
Table 1: Basic parameters of the model
Tabela 1: Osnovni parametri modela pe~i
Height of the model furnace (mm) 856
Inner diameter of the model
furnace (mm) 110
Height of filling (mm) 488
Gas medium air
Batch crushed chamotte
Batch density (kg m–3) 1900
Batch grain size (mm) 4–8 8–10 10–12
Void fraction of the batch (1) 0.55 0.61 0.623
Air flow (m3 h–1) 48.8 56.3 72
The air flow was measured using a gas meter and its
pressure using a U-tube manometer. The measurement of
the temperature of the batch and air was carried out
using K-type (NiCr-Ni) contact thermocouples. The ther-
mocouples were led to terminal boards from where an
electric signal was transported to the data logger.
Recording and storing the data was provided by com-
puter software.
Before starting the measurement itself, air at an
ambient temperature was blown into the furnace using a
fan in order to stabilise the temperature in the batch. The
air flow and grain size changed during the experiment.
The temperature of the batch material and the tempera-
ture of the flowing air were measured along the height of
the model during the experiment.
A scheme of the furnace model with the appropriate
equipment and measurement devices is shown on Fig-
ure 3.
3 DETERMINATION OF THE HEAT-TRANSFER
COEFFICIENT
Balance equations were used for determining the
heat-transfer coefficient. The amount of delivered heat Q
was stated using Equation (1):
Q Q c t t m c t tV= ⋅ − ⋅ = ⋅ −( ) ( )
’ ’’ ’’ ’
vz vz m m m (1)
The heat-transfer coefficient related to the total vol-
ume of the model furnace can be determined from
Equation (2):
Q V t= ⋅ ⋅ ⋅ V LSΔ (2)
M. ^ARNOGURSKÁ et al.: DETERMINING THE HEAT-TRANSFER COEFFICIENT IN AN ISOTHERMAL MODEL ...
340 Materiali in tehnologije / Materials and technology 51 (2017) 2, 339–344
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 3: Scheme of a model furnace
Slika 3: Shema modela pe~i
Figure 1: Furnace model with the thermocouple distribution
Slika 1: Model pe~i z razporeditvijo termoelementov
Figure 2: Image of the experiment equipment during the measurement
Slika 2: Pogled na eksperimentalno napravo med merjenjem
For the logarithmic mean temperature difference
tLS, Equation (3) is used:
Δ
Δ Δ
Δ
Δ
t
t t
t
t
LS =
−’ ’’
’
’’ln
(3)
whilst t t tvz m
’ ’’ ’− = Δ is the temperature difference of the
air and the batch at the inlet to the model and
t t tvz m
’’ ’ ’’− = Δ is the temperature difference of the air and
the batch at the outlet of the model.
By comparing Equations (1) and (2), we obtain the
formula for the heat-transfer coefficient related to the
volume of the furnace model:

V
mm c t t
V t
=
⋅ −
⋅ ⋅
( )’’ ’m m
LSΔ
(4)
3.1 Conditions for calculating the heat-transfer coeffi-
cient
For a batch grain size of 10–12 mm and the lowest air
flow of 48.8 m3 h–1 logarithmic mean temperature diffe-
rence tLS was determined from Equation (3) under the
following conditions:
t vz
’ .= 2721 °C tm
’’ .= 2615 °C
t vz
’’ .=160 9 °C tm
’ .=1014 °C
The volume of the shaft furnace model with a filling
height of h = 0.488 m and an area of S = 0.0095 m2
represents value V = 0.0046 m3.
The weight of the batch for the monitored volume
was determined using Equation (5)4:
m V= ⋅ ⋅ − (1 (5)
The calculated weight is 3.32 kg.
The value of the volume heat-transfer coefficient is
38 963 W m–3 K–1.
Figures 4 and 5 show the development of the heat-
transfer coefficient depending upon the time with three
different flows and batch grain sizes of 10–12 mm and
4–8 mm.
The air-flow velocity is related to the flow. With three
different air flows (48.8 m3 h–1, 56.3 m3 h–1 and
78 m3 h–1), it can be seen that the heat-transfer coefficient
V grows with the growing flow (Figure 5). The higher
the air flow, the higher is the value of the heat-transfer
coefficient and the time necessary for heating the batch
shortens.
Figure 6 shows the development of the heat-transfer
coefficient for the batch grain size of 10–12 mm in
relation to time, with the air flow of 48.8 m3 h–1 in three
places along the horizontal plane of the furnace. The
distances of the places from the furnace wall were
1.5 cm, 3.5 cm and 5.5 cm. The horizontal plane was
fictitiously placed at a height of 288 mm on the furnace.
Figure 7 shows the development of this coefficient along
the same plane and in the same places but with a smaller
batch grain size (4–8 mm). The most marked difference
in the heat-transfer-coefficient value is at the distance of
the measured place of 1.5 cm from the wall where, for
M. ^ARNOGURSKÁ et al.: DETERMINING THE HEAT-TRANSFER COEFFICIENT IN AN ISOTHERMAL MODEL ...
Materiali in tehnologije / Materials and technology 51 (2017) 2, 339–344 341
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 6: Development of the heat-transfer coefficient in relation to
time with a grain size of 10–12 mm and air flow of 48.8 m3 h–1
Slika 6: Spreminjanje koeficienta prenosa toplote glede na ~as za
zrnatost vsipa 10–12 mm in pri pretoku zraka 48,8 m3 h–1
Figure 4: Development of the heat-transfer coefficient in relation to
time with three varying flows and a grain size of 10–12 mm
Slika 4: Spreminjanje koeficienta prenosa toplote glede na ~as, pri
treh razli~nih pretokih zraka in zrnatosti 10–12 mm
Figure 5: Development of the heat-transfer coefficient in relation to
time with three varying flows and a grain size of 4–8 mm
Slika 5: Spreminjanje koeficienta prenosa toplote glede na ~as, pri
treh razli~nih pretokih in zrnatosti 4–8 mm
example, with the flow of 48.8 m3 h–1 and the batch grain
size of 4–8 mm (Figure 7), the heat-transfer coefficient
is 17000 W m–3 K–1. With the same flow and the same
distance from the wall, this coefficient increases with an
increase of the batch grain size to 10–12 mm (Figure 6),
by about 62 %. At the distance of 5.5 cm from the wall
and under the same conditions (the grain size of 4–8 mm,
the flow of 48.8 m3 h–1) the coefficient is 4200 W m–3 K–1
and with the grain size of 10–12 mm, it is almost 46000
W m–3 K–1. This represents an approximately 9-fold in-
crease in the value of this coefficient.
It can be seen from Figures 6 and 7 that the smaller
the batch grain size, the greater is the hydraulic resist-
ance of the batch, and the air in the direction of the flow
only partially passes through the centre of the model. For
this reason, the flow is more intensive in the very close
vicinity of the wall of the furnace model. The flowing air
therefore delivers less heat to the batch than in the case
of a lower hydraulic resistance, where the air passes
through the cross-section of the furnace more evenly –
this is the case with a larger batch grain size.
With a greater air flow and the largest batch grain
size used in the experiment (10–12 mm), there was a
more even distribution of the air flow along the cross-
section of the model furnace (Figure 8). With the grain
size of 4–8 mm, the air flow was again more intensive
close to the wall (Figure 9).
In order to verify the air-flow conditions along the
cross-section of the batch in the model furnace, a
calculation was carried out using the numeric method in
the ANSYS_CFX program. The solution was expected to
confirm or deny the nature of the flow and the distribu-
tion of the air-velocity field along the cross-section of
the furnace. The used edge conditions of the solution
were identical to the conditions in the real experiment.
Figure 10 shows the distribution of the velocity
along the cross-section of the model furnace with the air
flow of 48.8 m3 h–1, grain sizes of 4–8 mm and
10–12 mm, and with the batch height of 280 mm. Fig-
ure 11 shows the distribution of the velocity along the
M. ^ARNOGURSKÁ et al.: DETERMINING THE HEAT-TRANSFER COEFFICIENT IN AN ISOTHERMAL MODEL ...
342 Materiali in tehnologije / Materials and technology 51 (2017) 2, 339–344
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 9: Development of the heat-transfer coefficient in relation to
time with a grain size of 4–8 mm and air flow of 72 m3 h–1
Slika 9: Gibanje koeficienta prenosa toplote glede na ~asa pri zrnatost
vsipa 4–8 mm in pretoku zraka 72 m3 h–1
Figure 7: Development of the heat-transfer coefficient in relation to
time with a grain size of 4–8 mm and air flow of 48.8 m3 h–1
Slika 7: Spreminjanje koeficienta prenosa toplote glede na ~as pri
zrnatosti vsipa 4–8 mm in pretoku zraka 48,8 m3 h–1
Figure 10: Air-velocity profile along the cross-section at a height of
batch of 280 mm and air flow of 48.8 m3 h–1
Slika 10: Hitrostni profil zraka po pre~nem prerezu pe~i, pri vi{ini
vsipa 280 mm in pretoku zraka 48,8 m3 h–1
Figure 8: Development of the heat-transfer coefficient in relation to
time with a grain size of 10–12 mm and air flow of 72 m3 h–1
Slika 8: Spreminjanje koeficienta prenosa toplote glede na ~as pri
zrnatosti vsipa 10–12 mm in pretoku zraka 72 m3 h–1
cross-section of the furnace, at the same batch height, the
selected grain sizes and at the higher air flow (78 m3 h–1).
At the air flow of 72 m3·h-1 and the batch grain size
of 4–8 mm, the air-velocity field is displayed in the
vector shape on Figure 12a. Figure 12b shows the
velocity field at the same flow and the grain size of
10–12 mm. Figure 12b documents a more even distri-
bution of the air-velocity field than in the case of using a
smaller batch grain size.
4 RESULTS AND DISCUSSION
The influence of the flow upon the heat-exchange
intensity is shown on Figures 4 and 5. With the grain
size of 10–12 mm and air flow of 78 m3 h–1, the heat-
transfer coefficient was about 50 % higher compared to
the flow of 48.8 m3 h–1. With the grain size decreased to
4–8 mm and the same flow of 78 m3 h–1, this coefficient
decreased by about 63 %. The maximum value of the
heat-transfer coefficient for both flows was reached in
approximately the same time of heating the batch which
was about 4 min.
The heat exchange in the batch along the cross-
section of the model furnace has a varying intensity. This
is related to the structure of the batch and the amount of
the air flow. For example, at the distance of 1.5 cm from
the wall, the flow of 48.8 m3 h–1 and the batch grain size
of 4–8 mm (Figure 7), the heat-transfer coefficient is
about 17000 W m–3 K–1. At the same flow and the same
distance from the wall, this coefficient increases with an
increased batch grain size of 10–12 mm (Figure 6) to a
value of 60000 W m–3 K–1, i.e., by about 2.5 times.
Higher air flows influence heat exchange more in-
tensively. With the same distance from the wall (1.5 mm),
the air flow of 72 m3 h–1 and batch grain size of 4–8 cm
(Figure 9), the heat-transfer coefficient is circa
58000 W m–3 K–1. With the same air flow and at the same
distance from the wall, the heat-transfer coefficient
increases more than threefold with the batch grain size
increased to 10–12 mm (Figure 8), i.e., to a value of
192000 W m–3 K–1.
The influence of the distance of the investigated
location of the batch upon the heat-transfer coefficient is
more pronounced with a lower batch grain size. For
example, for the air flow of 72 m3 h–1 and grain size of
4–8 mm, the heat-transfer coefficient has a value of
21000 W m–3 K–1 if the distance from the furnace wall is
5.5 cm. At the same distance from the wall and the grain
size of 10–12 mm, the value of the coefficient remains
the same as for the distance of 1.5 cm, i.e., 192000
W m–3 K–1. It is clear from the above that the air velocity
along the cross-section of the furnace is distributed more
evenly with a greater batch grain size. The same result
was confirmed by calculating the flow conditions using
the numeric simulation.
5 CONCLUSION
The value of the coefficient of the heat transferred
from the flowing air into a batch depends upon several
factors. Important roles are played by the batch grain
size, the fact of how evenly it is distributed, the input
temperature of the flowing air and the amount of the air
flowing through the batch layer. Most of the heat
transferred to the batch at a given temperature of the
flowing air was reached with the largest grain size. In
order to achieve an intensive heat transfer with a lower
M. ^ARNOGURSKÁ et al.: DETERMINING THE HEAT-TRANSFER COEFFICIENT IN AN ISOTHERMAL MODEL ...
Materiali in tehnologije / Materials and technology 51 (2017) 2, 339–344 343
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 12: Air flow along the whole cross-section of the furnace with
an air flow of 72 m3 h–1
Slika 12: Kro`enje zraka po celotnem pre~nem prerezu pe~i, pri
pretoku zraka 72 m3 h–1
Figure 11: Air-velocity profile along the cross-section at a height of
batch of 280 mm and air flow of 72 m3 h–1
Slika 11: Hitrostni profil zraka po pre~nem prerezu pe~i, pri vi{ini
vsipa 280 mm in pretoku zraka 72 m3 h–1
batch grain size, it is necessary to ensure a higher flow of
the heated air and an even distribution of the batch. With
a smaller grain size, it is very complicated, or even
impossible, to ensure that the hydraulic resistance of the
batch does not increase. This always results in the
changes in the direction of the input air flow to the batch
layer and the flow is directed towards the furnace wall,
where it leaves the model furnace without any significant
transfer of heat to the batch. This is documented with the
outputs of the numeric simulation.
Acknowledgments
This paper was written with the financial support of
project KEGA ~. 003TUKE-4/2016, project EU opera-
tional programme ITMS 26220220044 and
SP2017/37-FMMI V[B TUO.
Nomenclature
V heat-transfer coefficient related to the
volume of the model W m–3 K–1
c specific heat capacity of the air J m–3 K–1
cm specific heat capacity of the batch J kg–1 K–1
 void fraction 1
tLS logarithmic mean temperature
difference °C
m batch weight kg
Q amount of heat delivered J
QV air flow m3 s–1
 chamotte density kg m–3
tvz’ air temperature at the inlet to
the furnace °C
tvz’ air temperature at the outlet from
the furnace °C
tm’ batch temperature at input °C
tm’’ batch temperature at output °C
 time s
V volume of the model shaft furnace m3
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M. ^ARNOGURSKÁ et al.: DETERMINING THE HEAT-TRANSFER COEFFICIENT IN AN ISOTHERMAL MODEL ...
344 Materiali in tehnologije / Materials and technology 51 (2017) 2, 339–344
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS