PAPER BY A.V. BULYGS ON "STUDY OF HEAT TRANSFER FROM HEAT DEPENDENT SEMICONDUCTOR ELEMENTS IN RAFIFIED GASES FOR CONTROLLING LOW PRESSURES"

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00247A004300220001-8
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 28
• Document Creation Date: December 27, 2016
• Document Release Date: April 24, 2014
• Sequence Number: 1
• Publication Date: December 30, 1964
• Content Type: REPORT

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STUDY OF HEAT TRANSFER FROM HEAT DEPENDENT SEMICONDUCTOR
ELEMENTS IN RAREFIED GASES FOR CONTROLLING LOW PRESSURES
A.V.Bulygag Heat and Mass Transfer Institute,
Aca,.'.emy of Sciences of the B.S.S.R,Minsk,U.S.S.R
Abstract - The study is carried out to reveal the regulari-
ties of heat transfer inside heat-dependent semiconductor
elements ( thermistors ) and on their interface with the
surrounding rarefied gas. Peculiarities of thermodynamics
of thermistor operation in superraref action are discussed.
Being the basis for the design of thermoelectrical va-
cuum gauges, the results obtained are used for the analysis
of the sensitivity of the sensing element over a wide pres-
sure range - from the values corresponding to a free mole-
cular flow to the atmospheric pressure which is peculiar
of a viscous gas flow.
Nomenclature
c� - heat-transfer coefficient;
- mean volume ac and surface temperatures of thermistor,res-
pectively;
temperature of the surroundings; 17 =Ts- 19 T- 9;
A,8- constants of the material of thermistor;
- current of thermistor,the surface area of which is S and
diameter d;
Nu,Gr,Pr,Kr- Nusselt,Grashof,Prandt1 1Knudsen numbers ,respectively;
i) - diameter of envelope around the heat transfer cylindrical
element or the enternal diameter of a boundary layer;
heat conductivity of gas at reference temperature 7,�4r+60i
R - gas constant in p-f4Rr ,where p is density
C, C,,- specific heat of gas at constant pressure and constant volu-
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mf-,respectively;
4- e;ravity acceleration;
moment-un transfer coefficient.
The high temperature resistance coefficient of ther-
mistors is the main precondition of their use as gauges
which are sensitive to the change of the heat transfer condi-
:Lonsj3,6,I31 .
The latter follows from the consideration of sensitivi-
ty of the gauge D which is determined as a ratio of the
change of some output value .9 to the change of the input
value A , i.e. S: =ct3/GLX .
.Thermistor, as a primary transformer of a nonelectrical
quantity into electrical one, may be represented as a series
of links each of which represents transformation of one non-
electrical quantity into another one. If thermistor is used
as a pressure transmitter of vacuum gauge, its resistance R,
ts connected with a pressure p ( input value of the trans-
former) by a series of relations:
-1(-7") T=Y)(01) (P), (I)
aad the sensitivity of this transformer may be determined
by The, expression [12]
R dRr a04 aT a Pr
=
P p a p ad a 7' (2)
or
= is; seer s:,
where in accordance with the data of 6, 13 , the sensitivi-
ty of the third link will be
ST =firRy � (3)
The influence of the heat transfer conditions of ther-
mistors_n their electrical parameters is expressed
the coefficient of the dissipated power k .
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Comparing the Newton formula [6, 13]
P=ocsg,
( 4 )
which expresses the regularities of heat transfer and the for-
mula
k= P/g,
which determines this parameter, gives
A- =ctS.
(5)
(6)
It is supposed that the mean-volume temperature T and the
surface temperature of the thermistor Ts are equal.
To select gauge and regime of its operationtit is necessary
to reveal the physical significance of the parameter It. Having
the grounded analytical expression for this parameter,an invisti-
gator may save tedious experiments and thier treatment at numeri-
cal determination of k and also it will Permit to control its
value in certain ranges.
The physical significance.of.the parameter k is qualitative-
ly clear from the definition. However for the determination of
the quantitative relations,it is necessary to consider the compo-
nents of the dissipated power P .
The power P which is supplied to the thermistor in sta-
tionary conditions dissipates by convection and heat conduction
F),, through a gas layer and by radiation Fc., and also by heat
conductivity along the supply wires )?, ,i.e.P--13v#P,.+Pfl
E�x pressing this relation through the heat transfer coeffi-
cients yields
a = cer # cvn
(7)
The component of the heat transfer coefficient ocean be
determined according to the well4suoun Stafau-Boltssam formula
fAl Igemmoiror thm malution of this =Chian is aft= difficult as smii
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the trustworthy data on the thermistor emissivity eTare absent.
The available data on this problem in the special literature
main4 reffer to metals and some non-conducting materials.The da-
ta for the semiconductors are almost absent.It is difficult to
determine the thermistor emissivity by usual methods which are
based on comparison of measurements with the data for the refe-
rence standards because of their small sizes.
The above reasons caused the necessity to determine the
thermistor emissivity E7. atsuch experimental conditions when
convection is completely absent and heat losses by heat-conduc-
tion are more than two order lower than the losses by radiation.
Such conditionslallowing us to consider the relative error of
determination of 6T to be not higher than I5,set in vacuum at
the pressure of the order 10-2 - 10-3 M.m-2. In this case the
heat transfe- coefficient d. will be expressed as:
a)
b)
C) c,,, = R/S
(8)
The total heat losses I, through the supply wires are deter-
mined as a sum of losses by heat conduction through two semiinfi-
nite rods of an infinite length [6,8]
where 2,- the heat-conduction coefficient of the wire,with a
cross-sectional area of fc, ; m'(/j,,;
oe... heat transfer coefficient between the supply wire the perimeter
of which is qmand the surroundings.
After substitution of the value 1 from equation (9) into (8-c)
(9)
we V shall obtain for wires of circular cross�section
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�5-.
9474ince
_ V., ff n � (10)
According to the expirement conditions CC0r .Therefore,
the values of 04 are easily calculated by equaition (8-b) if E,,
is substituted for 6. and 7n/ for where
= (7+O)/2.)
The combined solution of equations (8a),(8-b) and(I0)with
account of equation (II) with respect to ergives:
Er =4. � I/6�E, An ct,7'),
(I2)
- -
where 6 ce 0- 8 7:�3, 6 4 Co >08 ( 3.
The rename component of the be3at transfer coefficient �ex,
which is caused by a joint action of convection and heat conduc-
tion is the mainland special expirements are carried out for its
determination. For oarying out a test,the unit is constructed
of which schcmetic drawing is shown in Fig.I. The main assembles
of the eXpiremental unit are two shifted working chambers I and
16,which are placed into thermostate bath 4,vacuum pumps II and
13 and a system of the operating and controlling vacuum guages.
Different sizes of working chambers, in the form of cylind-
rical glass bulbs 9 ard 3 cm in diametertallow simulation of heat
transfer processes of thermistors in conditions of a limited
and non-limited space.
The expiremental design allows us to obtain the primary
characteristics of thermistors: temperature characteristics and
current-voltage ones in the operation temperature range and at
the pressures of working medium.from atmospheric pressure to
1,33 10-2 M.m-2. These characteristics are the initial material
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6
listcr and on its interface with the surrounding medium in
3tationary operating conditions.On this unit which laig.a loop
oscillograph, the experimental data are obtained for calculati-
n of dynamic thermistor parameters.
Before proceeding to the description of the experimental
investigation of the regularities of heat transfer of thermis-
tors in yacuumoit is necessary to dwell on some pecularities of
their operation at .the pressures in superrarefaction when the spe-
cial size of a system becomes small in comparison with the free
path length . The neccessity of such an analysis is caused
by appearing disturbances of the gas temperature conditions in
superrarefaction that at increased sensitivity of thermistors
to the temperature changes can essentialy influence their physi-
cal and electrical parameters.
In f21 the relations are obtained which take account of.
pecularities of the temperature regime of the superrarefied gas.
The Measurements of :.hermistor resistances are carriei out for
the experimental verification of these relations.
The diagrams plotted according to the experimental and pre-
dicted data (Fig.2,3),from which it is seen that in the pressure
raage,from the atmospheric pressure to 13,3 , the change
of presSuredossnot practically influeme, the quantity of ther-
mistor resistance Rroand the material constant 13, which i deter-
mined from equation 1-,I1
= A exp (B/7") .
_2 ,2 � (13)
In the pressure range from 13,3 to 1,33-10 Nm the valu-
es of )3 calculated by formula (13) decrease with the drop in
pressure and expose their dependence on temperature.
Nevertheless the thermistors resistance does not depend on
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pressure in the conditions of the equality of temperatures
of all assemblies of the vacuum system ( at the values of
0= 3,413 IC -3).With the results obtained,the change of
thermistor resistances at drop in pressure should be explained
not by the change in the parameterB but by the temperature
difference between two connecting vessels.in One of which
the thermistors investigated are placed and into another one
the control vacuum guage is inserted.For confirmation of this
conclusion the construction of the experimental uLit was
changed so that the controlling vacuum gauge and the bulb
with the.thermitors together with connecting bulbs by tube
was placed into a thermostate bath. In such conditions the
value of B calculated by resistances of thermistors measured
did not change its quantity at all pressures.
� The results o-.....tairied of the experimental investigation
confirmed the truth of the analytical relations obtained and
showed that the cLange of environment pressure does not in-
fluence the physical parameters of a semiconductor material
of the investigated thermistors.
Besides the electronic nature of the conductivity in
thermistors of the type KMT -I and KMT -II is confirmed.
Expiremental Study of Heat Transfer of Thermistors.
Carried lilt is the series of experiments on study of heat .
transfer from thermistors in dense and rarefied gas [3] to
obtain the initial data at development of the sensitive ele-
ment of vacuum gauge on. the base of the thetmistor and deter-
mine the interfaces of applicability of criteria' equations
2
Nu � 9' 3 7
e" [1 � (Gr.Pr)o'25
d
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(14)
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i)
2
- 2
- D (15 )
To fulfil the problem, the static current-voltage characte-
ristics of thermistors of the Lype KMT-I and KMT-II are expe-
rimentally obtained at an ambient temperature of 0=293,2�K
and different pressures. The curves for thermistors of both
types (Fig.4) are obtained accordirig to the experimental data.
The pressure range in which the current-voltage characte-
ristics are obtained, includes viscous, molecular-viscous and
molecular regimes of free gas flow and allowes us to observe
a smooth change of heat transfer parameters in transition
from one regime to another.
The experimental data on heat transfer in the conditi-.
ons of rarefaction are shown in Fig.5 as diagrams a! =4cIti9iv)
and Cik
These curves are plotted by the coordinates of current-
voltage ,7,haracteristics, which correspond to the same wean
volume tempexature T of the thermistor in the whole pressu--
re range. For the thermistor of the type KMT-I a value- of
327.6c"K was taken for the temperature T 1 that corresponds to
R7.=2I,I5ki1olim;for the thermistor of the type KMT-II the
temperature corresponds to T=328,1�K ( RT= 442,5 kilokam).
At the analytical calculation of o( , the tentative accomoda-
tion coefficients a are taken. . For the surfa-
ces of the thermistors and supply copper wires a=0,9 and
for the nickel wires 0= 0,47. Fig.5 shows that the shape
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of relations a Pt (ey P) and oc = P1 (e9, p) is
approximately the same for the both thermistors. For the
qualitative analysis of the results obtained it is conve-
nient to, divide these curves into four approximately
linear sections.
The first section, to which the molecular regime
corresponds of the free flow, includes the pressure ran-
ge from 1,33 10-2 to I X.m There is a proporkdonal de-
pendence between the parameters 04 and ( eg p ).
The second section (egp =0,0 - 1,6 for the ther-
mistor type 1T -I and esp=0.0 - 2,4 for KMT -II ) corres-
ponds to the molecular - viscous regime. It is characterized
by more strong dependence of the total heat transfer
coefficient 06 and its convect4me component 06� on gy p
than the first section. The higher sensitivity of the
thermiztoro to z...he drop in pressure in this range is caused
by the presence of a temperature jump on the surface of a
solid.
The third section (egp =1,6 - 3,8 for the thermis-
tor of the type KMT -I and i)yp =2,4 - 4,4 for KMT
corresponding to the viscous regime and partially to the
transient region, i.e. to slip flow which is characterized
by-independence of the convective component di, and a
slight dependeroe on the total heat transfer coefficient
on the pressure. Some negligibale change ()Let the pressure
change of in the range indicated is the result of
change of heat losses throughthe supply wires. In turn these
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�I0�
losses change because the temperature jump on the surface
of supply wires at higher pressures than on the surface of
a 4.mermistor body.
The fourth section (4193,8 for KMT-I and
for KMT-II) completely corresponds to viscous regime and
characterized by the presence of convection in the heat
transfer process. The beginning of this section coincides
with a value of 1.10-3 for GrPr=1C:3
The results of the experimental measurements are
treated in terms of similarity criteria (Fig.6) that gives
possibility to express the results analytically and to compa-
re them with data of other authors L6, 10] .
Theory and Principles of Pressure
Gauge Construction.
The analysis of technical characteristics of real
constructions of heat dependent pressure ganges[I 1 7,9,12,
14-16] shows that the proportional increase of the gauge
sensitivity does not solve the whole problem of its improve-
ment in all range of the controlling parameter. The main
disadvantage of these gauges is as before a pronounced non-
linearity of their static characteristics and, as the result,
nonuniform sensitivity which approaches zero in some ranges.
Thu reduction of inertness. is the essential problem of tie
construction of gauges.
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The investigations carried out an boat transfer of
thersistors and determination of their clynamic paremeters
[2,3] have shown that the above problems can be settled by
adequate choice of the shape and geometrical sizes of the
gauge.
It is not difficult to see this when the static charac-
teristics and sensitivity of a gauge are analysed and de-
fined .
The analytical relation between the convective com-
ponent of the heat transfer coefficient otx and the tempera-
ture T can be exprezsed from the Newton formula Nes fol..-
lows
I2A'r
T=9- �
asg
(I6)
which is a static characteristic of the second link. In
accordance with the difinition of the sensitivity from for.-
mula (2), differentation of relation (I6) over the parameter
c!CK upon substitution 0164/Sir gives
arAc- e2
cit I2Rr (I7)
The analytical relation between the input gauge
parameter p and the heat transfer coefficient otk is
more compliceted and can not be expressed by one
equation in a whole� react of perunter 1D.
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For the case of a viscous gas flow we may use the simpliest
structure of the heat transfer equation of the type [6]
= C(G.Pr.)" cp
(I8)
and solve it with respect to the heat transfer coefficient
C
=L ( P r),r7
(19)
assuming for simplification the gauge to be an ,infinite cylinder
for which 4Pr"=/ . If the values of dimensionless criterion is
expressed through the physical gas parameters [617] we shall have:
where
rl
H 2/i
A1= Tm3 n P
H=
=
(20)
Usually the value 1/4 - 1/8 [6]does not exceed the numerical
values of the exponent n =J (G). Pr)
in equation (20) which
represents the regularities of heat transfer of real constructions
and conditions of the pressure gauge operation. In connection with it,
it is more convenient to consider the static characteristic in a
semilogarithm scale and thus expression (20) can be given as:
H r 2 n (Cyp)
xi f�
cit-3" Tm32
(20a)
Hence the sensitivity of the link S; is given by differentation
of equation (20a). over the variable 11= eyp
04 daS r
,S7 irf = gri
P f a (eyp) - d's" 73" d'I
(21)
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Por the pressure range, corresponding to the molecular-
viscous regime of the gas flow, the static characteristic of the
thIrd.li�ak Gan be obtained in similar manner, expressing the wine
of the heat transfer coefficient from the formula (I5)
2
ci
where ci ; e=q-, 4->)A 2,,,
Ece
(22)
/5 2-j
)3f=',T;;I j4 �
Differenting (22) over the 'parameter = eyp we have the
sensitivity
sac dacg _ 2,1,7e
P2 a (cY)7pL-i-e)2 13 �
(23)
At pressures, corresponding to the nolecular-viscous regime of
the gals flow but approaching the viscous oneti.e. when L *eVp,
the formula for the sensitivity 4 will be
22me
=
P�e� L2 P � (24)
The same is in the other limiting came when 1.