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STUDYING THE THERMAL CONDUCTIVITY OF MATERIALS
Lyamin Andrey Vladimirovich,
Xadjibayev Akbarjon Shavkatovich,
Erkinov Ahliyor Komiljon ugli
Tashkent institute of chemical technology, Tashkent, Uzbekistan
E-mail:
lyamin_2020_tkti@mail.ru a.khadjiboev@tkti.uz
Abstract:
The article is devoted to the determination of the coefficient of thermal conductivity
of materials by the method of continuous heat flow. Two types of materials were tested in the
experiment: textolite and fluoroplast, which are both heat-insulating and antifriction. The
experiment was conducted at the department of "Fundamentals of mechanics and engineering
graphics" of the Tashkent institute of chemical technology on a standard laboratory stand. The
results of the experiment are presented in the form of summary tables and a graph.
Keywords:
thermal conductivity, coefficient of thermal conductivity, heat flow, temperature
gradient
.
1.
Introduction.
The thermal conductivity of materials in the construction of modern structures is essential
and important, since comfort and warmth in the living room will depend on which materials
were chosen as construction materials. Currently, basalt fiber slabs produced in Uzbekistan,
among others, are beginning to be used everywhere in Tashkent during the construction and
reconstruction of residential premises [1–9].
In this regard, we consider it necessary and expedient to conduct a comprehensive study
to determine their thermal conductivity in laboratory or production conditions before
manufacturing and installing such building insulation materials.
2.
Methods of research.
To conduct experiments to determine the thermal conductivity coefficient of various
materials, the department of "Fundamentals of mechanics and engineering graphics" has a
corresponding experimental installation. On this type of equipment, studies can be carried out
to determine the temperature gradient of various solid materials of round shape and limited
thickness. This experimental equipment in the fields of science: thermal engineering and
hydraulics, is manufactured by "Zarnitsa" in the Russian Federation (Kazan). Similar laboratory
equipment in this area is manufactured in Germany (Hamburg) by GUNT[10–14].
This article provides a methodology for conducting a study on the thermal conductivity of
samples made of textolite and fluoroplast. These materials are widely used both in general
mechanical engineering and in the construction of various structures.
Recall that the thermal conductivity of materials is the ability of a material div to
transfer heat from its more heated parts to less heated ones through the chaotic movement of
particles. Consider a layer of a solid substance with a temperature of T
0
enclosed between two
parallel plates located at a distance of ∆h from each other. Let the temperature of the lower
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plate rise instantly from T
0
to T
1
at time
=0, which does not change at subsequent times. As a
result, the temperature profile inside the layer begins to change over time and, at sufficiently
high temperatures, a stationary linear temperature distribution is established. In stationary
conditions, to maintain the temperature difference (temperature gradient) ∆T=T
1
–T
0
, a constant
heat flow Q is required. For sufficiently small values of ∆T, the ratio is valid:
Q
F = λ ∙
ΔT
∆h
(1)
According to expression (1), the rate of heat transfer through a unit surface area of the
layer F is proportional to the temperature difference at a distance of ∆h. The coefficient of
proportionality is called the coefficient of thermal conductivity of the material[15–18].
Equation (1) is also valid in cases where the space between the plates is filled not only
with a solid, but also with a liquid or gas, provided that there is no convection and radiation.
Thus, this ratio describes the process of thermal conductivity in solids, liquids and gases.
If the local rate of heat transfer through a unit of the layer surface (heat flux density) in
the positive direction of the "y" axis is denoted by q
y
, then at ∆h
0 the ratio (1) takes the
form:
q
y
=− λ ∙
dT
dy
(2)
This equation is a one-dimensional formulation of Fourier's law of thermal conductivity.
It is valid if the temperature depends on only one "y" coordinate. Thus, the following
formulation can be given to the law of thermal conductivity: the density of the heat flux due to
thermal conductivity is proportional to the temperature gradient. The minus sign in equation (2)
means that heat is spreading in the direction of decreasing temperature.
When experimentally determining the coefficient of thermal conductivity, as a rule, they
strive to create a one-dimensional temperature field. So, in relation to the one-dimensional
temperature field of flat, cylindrical and spherical layers under boundary conditions of the first
kind, the equation for determining the thermal conductivity coefficient looks like this:
λ =
K ∙ Q
t
1
− t
2
(3)
where: Q is the heat flux (in W); t
1
& t
2
are the temperatures of the outer and inner
surface of the layer (ºC); K is a coefficient depending on the shape and size of the test
sample (m
-1
) [19–23].
It follows from formula (3) that in order to determine the thermal conductivity coefficient
of the material under study, it is necessary to measure in stationary mode the heat flux Q
passing through the sample under study and the temperatures of its isothermal surfaces.
Formula (3) describes the temperature distribution in solids, as well as in liquids and gases in
the absence of heat transfer methods other than thermal conductivity. In the case of a
temperature dependence of the thermal conductivity coefficient, formula (3) can be used
provided that a small temperature difference occurs in the sample under study.
Despite its methodological simplicity, the practical application of stationary thermal
conductivity methods to determine the appropriate coefficients is associated with difficulties in
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creating a one-dimensional temperature field in the studied samples and taking into account
heat losses.
In addition, stationary methods require considerable time for conducting experiments due
to the duration of the installation's transition to a stationary thermal regime.
In the study of thermal insulation materials with low thermal conductivity (
≤2,3 W/m∙K),
the method of an unlimited flat layer has become widespread, when a sample of the material
under study is given the shape of a thin plate. To create a temperature difference, one surface of
the plate is heated, and the other is cooled using devices between which the test sample is
clamped.
When choosing the geometric dimensions of the studied samples of materials with low
thermal conductivity, it is necessary to fulfill the condition:
δ ≤
1
7
…
1
10
∙ D
(where D is the
diameter of a round plate or the side of a square), which ensures the one–dimensionality of the
temperature field. Thermal insulation is used to eliminate heat losses from the side surfaces of
the sample.
The disadvantages of the method include the difficulties associated with the elimination
of thermal resistances that occur at the points of contact of the sample with the surfaces of the
heater and refrigerator. The error in determining the thermal conductivity coefficient due to the
contact resistance can reach 10-20% with a sample thickness of 1,5-3,0 mm and becomes even
greater with an increase in the thermal conductivity of the material under study. To reduce the
contact thermal resistance of the surface of the sample and heat exchangers, they are subjected
to careful processing, and significant compressive forces are created to ensure good contact.
The experimental stand "Study of thermal conductivity of materials" is made in the form
of a desktop stand equipped with a horizontal work surface for the arrangement of the studied
laboratory modules and a vertical work surface on which the control and control unit is located
(Fig.1). The measuring system of the experimental installation has the ability to output the
temperature regime to a personal computer in the form of graphs.
The main module consists of two laboratory samples "4", which are placed between the
heater "1" and two refrigerators "2" (Fig.2). The necessary density of contact of the studied
samples with hot and cold surfaces is provided by the use of the device "5". To reduce heat
losses, the heater has a casing "3".
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Figure 1. General view of the experimental installation:
1 – control and display module; 2 – centrifugal pump; 3 – set of laboratory samples; 4 – air-
water heat exchanger; 5 – water tank; 6 – module "determination of thermal conductivity
coefficient".
А
B
Figure 2. Image of the main module (position #6, Fig.1):
A – exterior view; B – sectional view; 1 – heater; 2 – refrigerator; 3 – thermal insulation casing;
4 – test sample; 5 – clamping screw.
The main module consists of two refrigerators and one heater (see Fig.2-B). Refrigerators
are placed at the bottom and top, and the heater is in the middle of the prefabricated structure. A
sample of the test material (specially treated disc) is placed between each refrigerator and the
corresponding side of the heater. For a tight fit of the samples to the walls of the refrigerator
and heater, the module is equipped with a screw clamp. For temperature measurement, the
module is equipped with 7-point temperature sensors with Pt100 calibration.
The stages of the experiment can be represented as the following algorithm:
1. Determination of the average temperature values of the inner hot t
ht
and outer cold t
cd
surface of the samples according to the formulas:
t
ht
=
t
1
+ t
2
+ t
3
+ t
4
4
– the average surface temperature of the samples from the
heater side;
t
cd
=
t
5
+ t
6
2
– the average surface temperature of the samples from the
refrigerator side.
t
av
=
t
ht
+ t
cd
2
– the average temperature between the hot and cold side of
the test sample.
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2. Determination of the heat flux Q passing through the samples: Q=Q
ht
– Q
hf
, where
Q
ht
=U
2
/R is the heat flux from the heater;
Q
hf
=
5π
cs
2
d
ht
+d
cs
d
cs
−d
ht
δ
ht
+ δ
cs
(t
ht
− t
cs
)
- heat
losses on the casing.
3. Determination of the coefficient of thermal conductivity according to the formula:
=
K∙Q
t
ht
−t
cd
=
Q∙δ
2F∙(t
ht
−t
cd
)
, where: K=
δ
2F
– a coefficient that takes into account the shape of the
sample;
- sample thickness;
F =
πd
2
4
– the surface area of the sample. The installation
parameters required for calculations are shown in Table 1.
4. After determining the value of "
" for two different materials, it is necessary to plot
the dependence of the thermal conductivity coefficient on the average temperature.
5. Comparison of the found thermal conductivity coefficients with the corresponding
theoretical values. The values of "
" for some materials are shown in Table 2.
Table 1.
Individual parameters of the experimental
mounting.
Name of the parameter
Numerical
value
Heater resistance, R
280 Om
Diameter of the heater, d
ht
0,17 m
Heater thickness,
δ
ht
0,02 m
Sample diameter, d
0,14 m
Sample thickness,
0,005 m
Thermal conductivity coefficient
of the casing (material is glass-
textolite),
cs
0,3
W/(m∙К)
Outer diameter of the casing,
d
cs
0,19 m
Thickness of the casing,
δ
cs
0,024 m
Table 2.
The
actual
thermal
conductivity
coefficients of some materials.
Material
0
, W/(m∙К)
Asbestos (
=500
kg/m
3
)
0,107
Asbestos cement
0,088
Wool felt
0,047
Textolite
from 0,23 to 0,34
Fluoroplast
0,255
3.
The results of the experiment.
The main results of the experiment are presented in tabular form (see Tab.3 and Tab.4)
and the dependency graph (Fig.3).
Table 3.
The results of measuring the thermocouple readings at the experimental mounting.
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№
U, V
the
voltage
on the
heater
Thermocouple readings, °С
t
ht
,
°С
t
cd
,
°С
t
av
,
°С
Type of
material
T1
heati
ng
T2
heati
ng
T3
heati
ng
T4
heati
ng
T5
cooli
ng
T6
cooli
ng
T7
casi
ng
0
the
room
temperat
ure
18,2 18,1 18,0 18,0 17,8
18,7
20,3 18,
0
18,
2
18,
1
Fluorop
last
1 100
26,0 28,2 23,4 23,4 26,1
26,3
23,4 25,
2
26,
2
25,
7
2 150
36,4 39,5 31,0 31,0 25,8
25,9
25,4 34,
4
25,
8
30,
1
3 200
51,2 59,7 42,2 42,3 25,1
25,1
29,7 48,
8
25,
1
36,
9
4 250
71,6 84,4 58,4 58,7 25,0
25,0
36,6 68,
2
25
46,
6
0
the
room
temperat
ure
28,1 28,0 28,4 28,5 25,6
26,4
25,0 28,
2
26
27,
1
Textolit
e
5 100
31,0 33,0 29,1 29,1 21,9
21,9
24,2 30,
5
21,
9
26,
2
6 150
36,7 41,3 32,2 32,3 21,7
21,8
24,7 35,
6
21,
75
28,
6
7 200
46,0 54,0 38,2 38,3 21,9
22,0
26,5 44,
12
21,
9
33,
0
8 250
61,2 73,3 49,6 49,9 22,5
22,7
30,6 58,
5
22,
6
40,
55
Table 4.
Heat flow measurement results.
№ U, V
the voltage
Q
ht
, W
heating
Q
hf
, W
losses
Q, W
the total
t
ht
,
t
cs
,
t
ht
- t
cs
, W/(m∙К) Type
of
material
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on
the
heater
heat flow °С
°С
Т7
°С
the
coefficient
of thermal
conductivity
0
the
room
temperature
18,075 20,3
Fluoroplast
1
100
35,71429 3,450546 32,26374 25,25
23,4 1,85
-5,739033
2
150
80,35714 16,92633 63,43082 34,475 25,4 9,075
1,2427645
3
200
142,8571 35,71781 107,1393 48,85
29,7 19,15
0,7623121
4
250
223,2143 59,07894 164,1353 68,275 36,6 31,675 0,6409329
0
the
room
temperature
28,25
25,0
Textolite
5
100
35,71429 11,84377 23,87052 30,55
24,2 6,35
0,4516231
6
150
80,35714 20,37687 59,98027 35,625 24,7 10,925 0,7074663
7
200
142,8571 32,87345 109,9837 44,125 26,5 17,625 0,8116991
8
250
223,2143 52,03796 171,1763 58,5
30,6 27,9
0,7803322
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Figure 3. Graph of the dependence of the thermal conductivity coefficient on the average
temperature.
4.
Discussion of the results.
According to the results of the conducted studies, it can be seen that the theoretical values
of the thermal conductivity coefficients of textolite and fluoroplast differ greatly from each
other. So, according to Table 2, for textolite this value ranges from 0,23 to 0,34 W/(m∙K),
which is 2,3 times less than the obtained average experimental values; for fluoroplast, the
reference values range from 0,255 W/(m∙K), which is as much as 3,5 times less than the
obtained average experimental values. Thus, it makes sense to re-conduct studies for different
temperature and time ranges..
References:
1. Experimental Measurement of Thermal Conductivity of an Unknown Material A Thesis
Presented for The Master of Science Degree The University of Tennessee, Knoxville.
Aaron
Christopher
Whaley
May
2008.
https://trace.tennessee.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1470&cont
2. Marsha A. Presley NASA Ames Research Center, Moffett Field, California & Philip R.
Christensen Department of Geology, Arizona State University, Tempe. Thermal
conductivity measurements of particulate materials. JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 102, NO. E3, PAGES 6535-6549, MARCH 25, 1997.
https://www.researchgate.net/publication/241391404_Thermal_conductivity_measurement
s_of_particulate_materials_1_A_review
3. Abdullaeva S.Sh., Nurmukhamedov A.M., Abdullaev A.Sh. The Proceedings of the
International Scientific-Practical Conference on “The Fourth industrial revolution and
innovative technologies” dedicated to the 100
th
anniversary of the National Leader Heydar
Alieyv, 3-4 may 2023 y., Ganja. Part 1. p.91 - 93.
4. Bahadirov G.A., Nabiev A.M., Rakhimov F.R., Musirov M.U. Determination of the
parameters of the chain conveying device of the roller machine. Izvestiya Vysshikh
Uchebnykh Zavedenii, Seriya Teknologiya Tekstil'noi Promyshlennosti № 5 (407) 2023. –
p.
168-174.
content/uploads//2023/12//407_24.pdfhttps://doi.org/10.1186/s42825-019-0017-5
5. Amanov A.T., Bahadirov G.A., Nabiev A.M. A Study on the Pressure Mechanism
Improvement of a Roller-Type Machine Working Bodies. J
Materials
. 2023; 16(5):1956.
Switzerland.
https://doi.org/10.3390/ma16051956
6. Nabiev A.M., Tsoy G.N., Bahadirov G.A. Conditions for vertical pulling of semi-finished
leather products under driving rollers. E3S Web of Conf. Volume 376, 2023. International
Scientific and Practical Conference “Environmental Risks and Safety in Mechanical
Engineering” (ERSME-2023)
https://doi.org/10.1051/e3sconf/202337601073
7. Caihong Jia, Min Cao, Tingting Ji, Dawei Jiang and Chunxiao Gao Investigating the
thermal conductivity of materials by analyzing the temperature distribution in diamond
anvils cell under high pressure. 2022 Chinese Physical Society and IOP Publishing Ltd.
DOI
10.1088/1674-1056/ac29aa.
,
.
https://iopscience.iop.org/article/10.1088/1674-1056/ac29aa/meta
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Journal:
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8. M. Ausloos Thermal Conductivity. Université de Liège, Belgium. Available online 1
January 2003.
https://doi.org/10.1016/B0-08-043152-6/01650-8
9. GÖRAN GRIMVALL THERMAL CONDUCTIVITY. The Royal Institute of Technology,
Stockholm, Sweden Available online 2 September 2007.
10. R. Taylor Thermal Conductivity. University of Manchester Institute of Science and
Technology,
Manchester,
UK.
Available
online
2
December
2012.
https://doi.org/10.1016/B978-0-08-034720-2.50130-1
11. A.K. Lahiri Transport phenomena and metals properties. Indian Institute of Science, India
Available online 27 March 2014.
https://doi.org/10.1533/9781845690946.1.178
12. Basic Properties of Building Decorative Materials. Available online 27 March 2014.
https://doi.org/10.1533/9780857092588.10
13. Abhishek Yadav, Shailendra K. Shukla, Jeevan V. Tirkey, Saurabh Pathak Sustainable
Biofuels for Automotive Applications. Indian Institute of Technology (BHU), Varanasi,
India. Available online 20 January 2020, Version of Record 20 January 2020.
https://doi.org/10.1016/B978-0-12-803581-8.11115-4
14. Jean Mulopo, Jibril Abdulsalam. Energy storage properties of graphene nanofillers.
Sustainable Energy and Environment Research Group, School of Chemical and
Metallurgical Engineering, University of the Witwatersrand, Johannesburg, South Africa.
Available online 9 August 2019, Version of Record 9 August 2019.
https://doi.org/10.1016/B978-0-12-815811-1.00009-0
15. Annaev N. A. et al. Compacting solid waste from chemical industries //AIP Conference
Proceedings. – AIP Publishing, 2022. – Т. 2432. – №. 1.
https://doi.org/10.1063/5.0090958
16. Sharipov, K., Abdullaeva, S., Khalilov, S., & Xadjibayev, A. (2025). ANALYSIS OF THE
EFFECTIVENESS OF HYDROCARBON VAPOR CONDENSATION. International
Journal
of
Artificial
Intelligence,
1(2),
1287-1291.
