Научная статья на тему 'ACCOUNT FOR THE INFLUENCE OF THE ECCENTRICITY OF SPHERICAL INSALLATIONS FOR MEASURING THERMAL CONDUCTIVITY OF SUBSTANCES'

ACCOUNT FOR THE INFLUENCE OF THE ECCENTRICITY OF SPHERICAL INSALLATIONS FOR MEASURING THERMAL CONDUCTIVITY OF SUBSTANCES Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

CC BY
8
3
i Надоели баннеры? Вы всегда можете отключить рекламу.
Ключевые слова
HEAT TRANSFER / THERMAL CONDUCTIVITY / SPHERICAL CALORIMETER / ECCENTRICITY

Аннотация научной статьи по электротехнике, электронной технике, информационным технологиям, автор научной работы — Naziyev J.

To calculate thermal conductivity using spherical measuring instruments, it is necessary to know the heat flux and temperature difference between symmetrical spherical working surfaces. For the case of symmetric spherical surfaces, the calculation equation is well known. In this work, the influence of the eccentricity of the spherical surfaces of devices in calculating the thermal conductivity is theoretically determined.

i Надоели баннеры? Вы всегда можете отключить рекламу.
iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.
i Надоели баннеры? Вы всегда можете отключить рекламу.

Текст научной работы на тему «ACCOUNT FOR THE INFLUENCE OF THE ECCENTRICITY OF SPHERICAL INSALLATIONS FOR MEASURING THERMAL CONDUCTIVITY OF SUBSTANCES»

TECHNICAL SCIENCES

ACCOUNT FOR THE INFLUENCE OF THE ECCENTRICITY OF SPHERICAL INSALLATIONS FOR MEASURING THERMAL CONDUCTIVITY OF SUBSTANCES

Naziyev J.

doctor of technical sciences, professor of «Physics» department of Azerbaijan State University of Oil and Industry

Baku, Azerbaijan DOI: 10.5281/zenodo.7049648

Abstract

To calculate thermal conductivity using spherical measuring instruments, it is necessary to know the heat flux and temperature difference between symmetrical spherical working surfaces. For the case of symmetric spherical surfaces, the calculation equation is well known. In this work, the influence of the eccentricity of the spherical surfaces of devices in calculating the thermal conductivity is theoretically determined.

Keywords: heat transfer, thermal conductivity, spherical calorimeter, eccentricity.

To increase the efficiency and strength of equipment used in various production processes where heat transfer processes take place, it is necessary to have data on the thermophysical properties of the materials from which the equipment and the working fluid are made. Thermal conductivity is the most important of them.

There are different methods for determining thermal conductivities, both stationary and non-stationary [1, p. 19-72]. Recently, non-stationary methods have been used more [2, p. 347-355; 3, p. 12-22]. According to the shape of the working surfaces, cylindrical, spherical and flat bicalorimeters are distinguished [1, p. 7781].

Let us determine the exact solution of the problem of the influence of eccentricity for eccentric spherical

surfaces. Consider the differential equation of heat conduction [4, p. 30]

d 2t d2t A ■ + —- = 0

dx2 dyz

(1)

We solve this equation using the method of point heat sources, where the resulting temperature field is found by adding the fields from separate symmetrically located sources A and B (Fig. 1).

For the case of point sources, the temperature difference

0 =

Q

1 1

V r r ;

(2)

We compose the following system of equations

Y= 0

1 1 1

1 1

r d — r d + r

m m m m

— r = 2(h — r )

m

r + r = 27n

mm

a — a = a H — h = a

(3)

Here Y = h - a'.

Solving this system of equations with respect to h and H we get

2h = a 2H = a' +

— + r — a r a

R

— + R2 — a" R a

(4)

For the joint solution of the last three equations, we have

R6

(a)2 (a)

R3 r

+ 2

(R5

— + — a a

I —(r 4 — - )— 2(a" R3 + a r3 )+[(a)2 R2 +(a)2 r2 ]—

— 2a 2| —+ — I a a

2a2 (r2 + r2 )+ 2(a R + a r)+ 2Rr(ar + a r)+

(5)

y

+ 2Rr — r2 + — Rz

a

a

— 2R2r2(4 + - | —2Rr I a a )

Under certain assumptions, it is possible to obtain an analytical solution to the problem of the eccentricity of spherical bodies.

For the surfaces temperature difference, we write

At =

Q

4kX

1111

—---r + —---r

V rm rm rM rM y

. (6)

Taking into account the inequality (Fig.)

1 1 1 + — rM 1,

r m r m rM

and taking into account that rm )) rm and rM )) rM

1 1

, and fractions —- , —— have opposite signs, we can

rm rM

make the first assumption:

( R2 r2 -

—— — + a a

V a a y

r — r

n m

rN — rM

— 2 R2 r2 + a 4 = 0.

Where

r — r

n m

rN rM

r

R

(13)

(14)

From (11) and (12)

r„ — r

r„ — r,

r — r

n m

r\T —

rm rM rn rN

rmrM

rnrN

. (15)

'N 'M N 'M

Then the following inequalities can be written:

iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.

........ f "' ' \2 f

-)

V rmrM y

r,

M

V 'm y

V AR2

(

Vry

. (16)

At =

Q

4kX

1 1

V rm

(8)

' M y

Since the temperatures over the entire surface of the first and second spheres are the same

(9)

----- = ----- , (10)

or

1 1 1 1

r r r r

m m n n

1 1 1 1

rM rM rN 'N

r — r = (r — r

n m \ n m )

(r — r )•

nm

rr

mn

rr

mn

rN rM = —

(rN rM^

rMrN

rMrN

It is also seen from the figure that

(11)

(12)

Let's make the following second assumption:

rmrM

rmrM

rnrN

rnrN

( R12

Vr y

(17)

Comparing relations (14), (15) and (17) we obtain

( R13 Vr y

r„ — r

= 1.

rN rM

From figure 1

rm + a = r

rM + a" = R

r — a = r

n

-n— a = R

a —a = a

Using equation (19) from (18) we find

(18)

3

r

y

/

6

r

1

rM

m

rm rM

rm rM

)

'mrM

rn-N

J

a = ■

ar

R - r3

aR

a =

d3 3

R - r

(20)

Taking into account (40), the (8) can be written as

x = -

_Q_

4 nAt

(R - r 1 -

R - r

(21)

Rr

1-

aR1

n ! 3

R - r

1-

ar

iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.

n ! 3

R - r

From (21) for limiting cases we obtain:

At =

At = 0 at a = R - r Q R - r

at a = 0

4nX Rr

The resulting expression (21) is very convenient for calculating the thermal conductivity coefficient, taking into account the eccentricity of the working surfaces of equipment.

.References

1. Назиев Д.Я. Теплопроводность углеводородов и методы ее измерения. Монография. Баку. Азербайджан. 2001. - 357 с.

2. Platunov E.S. Instruments for measuring thermal conductivity, thermal diffusivity, and specific heat under monotonic heating. Compendium of thermo-physical properties measurement methods. Vol. 2. Recommended measurement techniques and practices. Plenum Press New York and London. 1992. - 643 p.

3. Litovsky E., Issoupov V., Horodetsky S., Klei-man J. 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.

4. Цветков Ф. Ф., Григорьев Б. А. Тепломассообмен: учебник для вузов. М.: Издательский дом МЭИ, 2011. - 562 с.

/

a

i Надоели баннеры? Вы всегда можете отключить рекламу.