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8with the progress and keep in mind the need to reduce the amount of resources used.
REFERENCES:
1. https://vash.market / House-And-Cottage / building-and-repair / plumbing-and-water/select-touch-mixer.html
2. http ://220blog.ru/pro -raschet/realnaya-okupaemost-svetodiodnyx-lamp.html
3. http://proverilnasebe.com/index.php/goods-reviews/equipment/242-induction-cooker.html
4. https://cosmo-frost.ru/svch/chto-takoe-inver-tornaya-mikrovolnovaya-pech-princip-raboty-modeli-
otzyvy/
5. http://klivent.biz/otopleniye/dlina-infrakras-noj -volny. html#i
6. https://sistema-otopleniya.ru/infrakrasnoe-otoplenie/jenergosberegajushhee-infrakrasnoe-otople-nie.html
CALCULATION OF CORRECTIONS ON THE VARIABILITY OF THERMOPHYSICAL CHARACTERISTICS OF LIQUIDS AND GASES IN THE INVESTIGATION IN THE REGULAR
HEAT MODE OF THE FIRST KIND
Naziyev J.
doctor of technical sciences, professor of «Physics» department of Azerbaijan State University of Oil and Industry (Baku, Azerbaijan)
Abstract
Simple correction formulas are obtained for calculating the thermal conductivity and isobaric heat capacity of liquids and gases using the regular cooling (heating) method. These corrections take into account inconsistencies in the cooling rate, thermal diffusivity and thermal conductivity coefficients when measurements are going by the regular mode method of the first kind.
Keywords: liquids and gases, thermophysical properties, regular mode method of the first kind, thermal conductivity, calorimeter.
Taking into account the corrections for the variability of the thermophysical characteristics of substances in precision measurements of the thermophysi-cal properties of liquids and gases is of great practical importance. However, expressions that can be used to calculate corrections due to the influence of the variability of the cooling rate (heating m), thermal diffusiv-ity a and thermal conductivity I when measured using the regular condition of the first kind are not known. Temperature field solutions obtained by E.S. Platunov used by many researchers [1, p. 750-760], [2, p. 12-22] for thermal conditions of the first kind are for a solid cylinder and therefore they cannot be used for calculating calorimeter equations for measuring the thermal conductivity of liquids and gases, as they are based on solving the problem of temperature distribution in a thin cylindrical layer of the test substance. A similar solution was made for the case of periodic heating [3, p. 856-859].
The purpose of this article is to derive simple equations for calculating these corrections for the method of a cylindrical bicalorimeter, the error of which is evaluated as 1 - 1.5%.
The calculation equation to determine the thermal conductivity of liquids and gases with constant m, a, I was derived
cR m ln s
A =-Ax
2 S
(1)
or A = KqmS
1 +
2 C_ 3(s +1) C1
(2)
where C1, C is the total heat capacity of the core material and the liquid under study; s=R2/R1 is the ratio of the outer and inner radii of the investigated annular layer; 5 = R2-R1 is the layer thickness; K= R1/ ô ln s -form coefficient; y= C1/F ; F is the surface area of the core; ; c1, c - volumetric heat capacities of the core and liquid.
Taking into account corrections for the variability of m, a, 1, the equation (1) takes the form
A =
cR m ln s 2
AS(1 + s)
(3)
where £=£m +Sa + £ A , £ m , £a , £ A - cor-
rection terms on the cooling rate and coefficients of thermal diffusivity and thermal conductivity.
Let's determine s for which we use the equation of temperature difference of the cylindrical layer under study, taking into account
0 = 0O+A0 , (4)
where 0O is the temperature difference when the values of m, a, X are constant;
A0 - correction term for the variability of ther-mophysical characteristics;
0 = goR ln5 - 1v02g0R[R2 -R2)- 2R2 ln iv02glR3 ln
>2h5I+ -V02glRf ln25
2
1 2
A0 =-k,g02R2 ln2 5 -—kvlg02R2R2(ln5 -1) -Tkvlg2R2R2
Xr\
1 4
a
3
ln2 5 -2ln5 + 3 Iv 2 _
1 1 3
— k V02 g02 R14 (ln 5 + 1) + - k V02 g02 R14 (ln 5 + -) 2xn 4 2
(5)
(6)
where is the temperature gradient in the zero approximation; v2 = —-; k = k— r — ka; k— r, ka, k^
a„
are relative coefficients of cooling (heating) rate, thermal diffusivity, and thermal conductivity; x0 - the first root of the equation J 0
(*')= 0 •
Let's simplify equations (5) and (6). For a thin layer with a small error
S = RI ln 5 + -ln2 5 + -ln3 5 + ••• I .
1 v 2 6 I
Then equality (5) takes the form
00 = g 0 R- ln 5 1 + -V02 R-2 ln2 51 = 0(
\ 2 Sc ^ 1 +
v
3 R1C1
where vn = ■
2 c
R2 ln 5 c1 Similarly, we get
2
3x „
12
From here we get the relation
0 = 1 + IS+0»
00 3 R1c1
__^ _c _it Sc ^
k ^ , k k
2 3x0 c1 6 R1c1
Then corrections
0°
If we consider that km r =km T - ka, we get
2 c 1 Sc ^
k o , k k
2 3x 0 c 6 Rc1
(7)
A0 =1 kgR2 ln22 5 —^ kvlg2R4 ln3 5 -—kvlglR4 ln4 5 . (8)
(9)
(10)
£ =
0C
k,--4, (lka - kmt T)~ - 1 (lka - kMt T)
c 1
3x n
c 3
Sc Rq
Approximately
£ =
01 2
k,-^- (lka - r)
3x,
'1I
(11)
(12)
Since c«ci in the particular case for gases from equation (12) we have
-Q\
(13)
Here, the parameters of the layer under investigation refer to the temperature of the base section, i.e. to autoclave temperature. Therefore, if in (3) X is the arithmetic mean temperature
, = c1 R1mln5 Ag^ + £.) , ' 20 V. . \c
where £ = — (2ka - km,J-3xA c
(14)
2
c
because A = AJ 1H— k, d°
(16)
For the case £ = 0, A = 1 and
— c R m ln s
A -
2
(17)
That means no corrections to the basic equation are needed. As follows from relations (14) - (15), for liquids, these arguments are right.
If there is no coefficient ka for the liquid under study, the expression ka = kx — kc can be used. The difficulty is to find the value kmT . It is advisable to replace it with other factors. Differentiating equation (1), you can get
2 Sc
k = k — 2 k — k km,T = kX ~ n kc kc .
3 Rc
But because the second term of the right-hand side of (18) is relatively small,
km,T ~ kZ — kc ,
(18)
(19)
where kc is the relative temperature coefficient of heat capacity of the core material.
Let us determine the effect of the variability of thermophysical characteristics for the triplecalorimeter. From the work [5], the calculated equation of the triplecalorimeter for calculating X is known:
cRl m ln s
A = ■
2
1 AOA
1 + —3 At1
(20)
where Ar = 1 +
V "-1
2 Sc A . —,-^ —— ; Atr, At3 - temperature changes of the inner and outer cylin-
1 At3
1 + —3
AO
R2Ï Rc
R
1 y
ders.
At inconstancy of m, a, X equation (20) takes the form
cR2 m ln s . / n.
A = -yJ-^ AT (1 + £T )
2
1 +
At., At1
(21)
where
Atj - At3
(22)
Atx + At3
As can be seen from (22), since sT < s the effect of the corrections sT on the thermal conductivity is relatively small in relation to the case of a bicalorimeter.
For equilibrium triplecalorimeter Atx = At3, therefore sT = 0 and
A =
cRl m ln s
4
1+2
3
R2 -1
R
^
(23)
Equations (3) and (6) are valid only for the case of the constancy of the thermophysical characteristics of the core material. This is permissible in the case when the core is made of a well-conductive material - metal. However, in practice there is a case when the core consists of the liquid under study (an ampoule with a liquid), for example, in the relative version of a regular cooling bicalorimeter. Then there is a need for corrections to the variability of the thermophysical coefficients of the core material.
First of all, it is necessary to have the temperature field equation of a continuous cylinder (core) under the condition of a bicalorimeter. The solution of the temperature field of a cylinder in the regular conditions of the first kind is known from [2]; it is possible to obtain the temperature difference from it
2
3
c
c
+-
A0
4k + 3ka - 3km,r )4 + (k'a - km,r ) X ~p pR2 - PRÏ \ + (k'a - ^r )p2R 0' tf)
(24)
A0
where approximation J0 (a0 R ) = 1 - pR\ is used, and solutions of zero approximation
00 =0(r)(l - pr2 ) , J0 (a0 R ) - Bessel function of the first kind and zero order. In (24) it is necessary to use the boundary conditions:
0, =0, (4 - pRi2 ) ,
„ ( d0„ 4
(25)
(26)
dr
=4 0
\ dr J R
where 6X (r) is the temperature in the center of the cylinder; 9"n - the same on the surface
2 m
A2 = — =
24
a 4 R\ in s
From (26) and (27) we get p =
4
R2 (24 ln s + 4)'
From equation (24) we find the magnitude of the corrections for the variability of the characteristics of the material of the core.
a
= 0, tf
Here 0, (t) =
4(k4 + 3ka - 3km,r )4 + (k'a - k'm,r ) A0
02
pRi2
p
A0
2 - 1 I + (ka - km,r )+ p 2 R4\ •
1 - pRi2 '
For the case of Xi « X we get
00 4(24iln s + 4) k + 4k- 4k )
'= 2 444 ln 2 s [k4+ 4ka 4kmr ) -
and for the case of Xi = X we get
a =
2 ln s
(k4 + 4k'a - 4kmr ) •
(28)
(29)
In the calculation equations of heat conductivity (3) and (21) instead of s it is necessary to substitute
eo6 = ^ + a •
Thus, from equations (13), (22), (28) and (29), it is easy and fairly accurate determine the corrections for the variability of the cooling rate and thermal properties to calculate the thermal conductivity of liquids and gases using the method of a bicalorimeter and a triplecalorimeter.
REFERENCES:
1. Burovoi S.E., Kurenin V.V., Platunov E.S. Thermophysical measurements under monotonic conditions. - Journal of Engineering Physics and Thermo-physics. Russia. v. 21, #4, 761p.
2. Express methods for determination of thermo -physical properties of different types of materials within a temperature range of -1500C to +18000C. -
Proceedings of 31-th Int. Thermal conductivity conference and 19-th Thermal Expansion Symposium. Canada. 2011, 325p.
3. Naziyev Y.M. The effect of variability of characteristics of substances during determination of their thermophysical properties by the method of periodic heating. - High Temperature. Russia. 2001. v. 39, #6, 1005p.
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