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METHODOLOGY OF TEACHING AND OBTAINING CRITERIA
DEPENDENCIES IN THE COURSE OF SPECIAL DISCIPLINES OF
THERMAL ENGINEERING PROFILE
NABIEV ABDULO ABDUVOKHIDOVICH
Assistant of the Department of «Physics, biophysics and medical physics» of the
Samarkand State Medical University
ANNOTATION
:
In the context of integration of science, education and
technology, in order to prepare specialists in the heat and power engineering
profile, information is needed on theoretical and experimental research methods,
on methods of processing results used in this field of science. It is necessary to
emphasize that the main attention should be paid to the disclosure of the theory,
tasks, types and forms and the basics of planning the experiment. This work
proposes a methodology for teaching the above-mentioned topic and obtaining
criteria, as well as dependencies characterizing heat and mass transfer processes
in industrial heat exchangers.
Key words: education, technology, differentiation and integration, heat and
mass transfer , industrial power engineering, machine tools, film condensation,
gaseous state, Nusselt criteria, Peclet criterion, Stanton criterion
In the context of the integration of science, education and technology, in
order to prepare specialists in the heat and power engineering profile, information
is needed on theoretical and experimental research methods, on the methods of
processing the results used in this field of science. As shown by many years of
experience in teaching special disciplines in the heat engineering profile and
practice, the solution of many scientific and technical problems is simplified by
applying the theory of dimensionality, similarity and modeling. [1,2]. It should be
Ilm fan taraqqiyotida raqamli iqtisodiyot va zamonaviy
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emphasized that the main attention should be paid to the disclosure of the theory,
tasks, types and forms and the basics of planning the experiment. The processing
of the results of the experimental study is carried out on the basis of the methods
of graphical processing of experimental data, graphical differentiation and
integration. Then, mathematical descriptions of the process under study are
performed, empirical formulas are selected, conclusions and proposals are
formulated.
This paper proposes a methodology for teaching the above-mentioned topic
and obtaining criteria, as well as dependencies characterizing heat and mass
transfer processes in industrial heat exchange devices.
The educational and training task is to explain the physical nature of thermal
conductivity , convective heat and mass transfer and teach students to conduct
experiments , measure thermophysical parameters, and perform calculations in
heat and mass exchange devices of power plants. Of greatest practical interest is
film condensation, which is mainly encountered in various types of industrial heat
exchange devices, where there is forced movement of steam along rough wetted
cooling surfaces . The study of the heat transfer process during film condensation
is actually reduced to the study of the process of heat exchange of a liquid film
with the wall surface, i.e. heat exchange between a solid and a single-phase
medium. However, the peculiarity of the process under study is that the process
of film formation itself is caused by the transition of the medium from a gaseous
state to a liquid one. The essence of the theory of film condensation of steam is as
follows [3,4]. When steam comes into contact with a wall, the temperature of
which is below the saturation temperature t
n
, the steam condenses, a film is
formed on the surface of the wall, and if its movement mode is laminar, then the
heat released during steam condensation is distributed by thermal conductivity
through the thickness. In this case,
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Where α
x
is the heat transfer coefficient during steam condensation on the surface
of the cooled wall in section
X; λ is
the thermal conductivity coefficient of the
condensate; δ
x
is the thickness of the condensate film in section
x.
From the first three equations we obtain the criteria known to us
and from the heat balance equation
rdM = с M
1
dt ,
where rdM = dQ is the elementary amount of heat transferred from the vapor to
the liquid during condensation of the amount of vapor dM ; dQ = cM
1
dt is the
elementary amount of heat received by the mass of liquid M
1
and causing an
increase in its temperature by dt . If we process the heat balance equation using
the methods of similarity theory, we obtain the Kutateladze criterion K = r /
c
∆ t
-phase transition where r is the heat of evaporation;
c is
the heat capacity of the
condensate,
a ∆
t
= t
n
- t
cm
. Since in the laminar regime the nature of the fluid motion does
not depend on the speed, the Re criterion drops out and the criterion the equation
for heat transfer during condensation of steam takes the form
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Nu= ʄ( Ga; Pr ; K)= φ ( Ko ),
Where Ko= Ga Pr K is called the condensation criterion.
As a result of generalization of experimental data conducted with various
liquids, the following calculation formulas were obtained for determining the
average heat transfer coefficient during steam condensation:
A vertical wall or pipe of height H,
The determining dimension in these equations for vertical walls and pipes is their
height, and for horizontal pipes – their diameter. The determining temperature is
the saturation temperature t
н
.
Similarity criteria can be modified by considering them together in order to bring
them to a form most convenient for describing specific problems. Thus, when
studying the motion caused by different densities of individual particles of a liquid
without moving its entire volume by an external source of motion, the flow
velocity cannot be measured. In this case, it is more convenient to combine them
in such a way as to isolate a new criterion that would include the difference in
densities of individual particles (layers) of the liquid, which is the cause of the
motion, and the flow velocity would be excluded. To do this, Fr is multiplied by
Re
2
and by the relative difference in flow densities (р-р
0
)/р
0 ,
where
р
and
р
0
are
the densities of different particles (layers) of the liquid:
It is called the Archimedes criterion.
Finally, if the difference in densities of different layers of liquid is determined by
the difference in their temperatures
∆ t
, as is the case with natural convection, the
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expression
(р-р
0
)/р
0
can be replaced by the product β∆ t , in accordance with the
equation р=р
0
[1-β
( t - t
0
)
] , where β is the coefficient of volumetric expansion
of the liquid; i.e.
(р-р
0
)/р
0
= β∆ t . Substituting this value into equation (14) we
obtain the Grashof criterion :
Gr = g l
3
β∆ t / v
2
(15 ) r Criterion Gr characterizes the ratio of inertial forces and gravity of the
lifting force in the absence of forced fluid movement and is most convenient for
describing free movement (natural convection).
It is known that the complex ω l / a is called the Peclet criterion:
ω l/a= Pe
(16)
If we expand the value of the thermal conductivity coefficient a = λ/(cp) and
multiply the numerator and denominator of the expression of the Pe criterion by
the temperature difference ∆ t between some points of the flow, then the criterion
can be presented in the following form:
From which follows the physical meaning of the Peclet criterion, i.e. the Pe
number is the ratio of the density of the heat flow transferred by convection from
one point in space to another to the density of the heat flow transferred between
these same points by conduction. As is known, convective heat transfer, the
characteristic of which is the Pe criterion, is precisely the combined action of the
two specified heat transfer mechanisms. It is advisable to transform the Pe
criterion in order to exclude from it the flow velocity ω as quantities that have
already been included in other similarity criteria ( for example Re ). To do this,
we divide Re by Re :
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(18)
The resulting dimensionless complex is called the Prandtl criterion: v / a = Pr .(19)
The Prandtl criterion, which contains only thermophysical parameters ,
characterizes the influence of the physical properties of liquids on convective heat
exchange. Substituting the value of the factors of such a transformation, we
obtain.
α
/
l
/
/ λ
/
= αl / λ =
idem .
This dimensionless complex is called the Nusselt criterion:
Α l/λ=
Nu.
Note that the Nu criterion includes the heat transfer coefficient α, which is usually
the desired value when studying convective heat exchange processes. Thus, with
thermal similarity of two or more systems, the equality criterion Pe (or Pr ), Nu
takes place .
In some problems of convective heat transfer, the complex Stanton criterion
is used :
It should be recalled that a necessary condition for thermal similarity is also
hydrodynamic similarity, i.e. with thermal similarity, Re (or Gr ), Eu are also
equal . Thus, heat and mass transfer are widely used in practice, the significance
of their laws is of primary importance for thermal and nuclear power engineering,
industrial thermal power engineering, power engineering, aviation, astronautics,
rocket engineering, etc.
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Literature:
1.
Lebedev A.N. "Modeling in scientific and technical research ." - M.: Radio
and Communications, 1989. 224 p.
2.
Kutateladze S.S. "Similarity analysis and physical models ". - Novosibirsk:
Nauka, 1986. - 290 p.
3.
Tsvetkov F.F., Grigoriev B.A. " Heat and Mass Transfer ": Textbook for
Universities. - M.: MEI Publishing House, 2001 - 550 p.
4.
Heat engineering: Ed. by V.N. Lukanin . - M.: Higher School, 2003, 671 p.
