(SANITIZED)UNCLASSIFIED SOVIET PUBLICATIONS ON SPACE FLIGHT SCIENCE(SANITIZED)

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00247A003100320001-0
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 101
• Document Creation Date: December 23, 2016
• Document Release Date: March 4, 2014
• Sequence Number: 1
• Publication Date: October 20, 1964
• Content Type: REPORT

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VASANOV x/o Y.G.JULEV XX/
OPTIMUM CONTOUR OF HEAT REJECTIiG
TRIANGULAR YIDS WITH MUTUAL I HAADIATIO.N BETWEEN
FINS AND COOLED BASE SUitFACES ? THE SYSTEM OF
PARALLEL STAR SHAPED RADIATORS* EFFECTS OF THE
THERMAL RESISTANCE OF COATINGS
?
A/ Ingeneers Mosoow In?te of Ihysius and Technics.
xx,/ Kandidat of Teonnius, Mosuow In?to of physius ana Teuhnics.
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In the present paper tne result(' of tne tneoretical investigation or
tne star-snaped radiatiors are disoussed.
tne paper consists ox the tare? parts. Tne rirst part aeals witn
one-dimensional problem of tne optimum size and number ox neat rejection
triangular fins radIally arranged at tile apices or tne pelynearai prism WiUn
mutual irradiation oz tne tins aria tne Burrito? or the 000led prism.
Tne numerical solution ox the problem is obtaiaea witn the assumption
that the temperaGure gradient aorosa tne zin is negligible in comparison with:
that ot along tne tin and surroundings are assumed as a black body OX zero
temperature. Tne relationships Of dimensiOnless parameters are given whica
determine the optimum (w214 respect to weight) numuer ox tins anu ;near geo-
metry for any oombivation of tne 000led prism temperature and size, amount
or tile rejected neat, the emissivity of raoiatieng tins ann heat oonduntivity.
ot the tin material.
It is found thrt tne optimum (in tne senoe of'weignt) number ot radia?
ting tins inokeaoes /tom 4 tor blauk emitting surraoe0 to about 10-11 ter
tne emissivity of tnese surfaces .of the order ot 0.5..
In the seoona part tne thermal radiation oftaraoteriatios et tne intiwA
nits system ox the roux-lin-star-anaped ooplanar radiators are oaloulated
taking into aocount the mutual irradiation of all radiator elementa. the
problem is solved numerioelly uncer tne same assumptions as in the first
part. The relationships of the eimensionleas parameters are given wnich
to oaloulate all tele optimal onaraoteriatica or tne system tor any distance
between zhe adjacent radiators of' tile System. In tne third part the problem .
is discussed taking into consideration tile etteot of tne thermal reaistanoe
of the coating which may be used tor increasing the emissivity of the radia-
ting surfaoea on the tnermal radiation characteristics Of tne tour-un-
star-shaped raainters. In adoition to the above aleaumptions it was suggesteo
that trio neat rates along 'me /in in tne coating are negligiole in comparison
with the heat rates along tne tin. ins given relationsnips OI tne'dimension.0
less parameters desoribe zne erreetiveness ox trio coating zor agi'neat o011166
uuutivity or unto latter aria tne radiator parameters.
[r.
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2
I. Optimum Uontour of Heat Hejeoting Triangular Fins
witn Uutual Irraaiation between Fins and Ooolea Base Suriaues
. Let us oonsiaer tne one-aimenalonal problem of determination of Vile
Ops1MUM al).* and number ox neat rejeuting triangular tins racially arrangea
az Silo apiues ox tne polynearal prism caking into acoount. mutual irraoiatiOn
of ;nu fins ann She baa0 aurzaue (f4.1). In tne oase OI negligible base-aux-
taut) suun a problem was aisoussea Xor tat Xims ox ;no opuimum (ktei.1)
ana triangular oOnsOar (HOI.2).
We snail ?eel witn tne ;ran fins xor wniun tne Law of -menial radia-
tion sun tne equation ol tnermal usOuOuOSiOn along a fin aro srue in %nu
term Oft
-te2(x)z-A(k-x)26-
dx
67161 (x) z (x) oix
8
(a)
wnere la(x) tne neat 110W znrOu..gn Sue tin abutted With i-poeition
- 'cue fin material ;normal oonauutivity cooezXioient.
egi tne angle between tne sine laces oi a fin
q (x) ox tne resultant ractiation /rom Sno tin surzeoe element.
Bguations (1) an* (2) lean to une lollowing expreasiOn Ior tne aetut-
=nation of temperature distribution along a tin:
_ _ _ (x) 0
dare ex A
Uonsiaer Iiret tne trapeplual sans ox lengtn 6 (1018.1). In this
oase ;no DOUnnary conditions lox equation ()) may be written as
a)T. atX. 0, b) .Qat X in 4.1 (4)
CIX
(5)
Inen determining q(x) we shall assume that ;no lin shriaue raalating
element is at tn. (Antral plansann tne parameters 0/ ;no surrounaings
6our 0 1 ana 79 tia0. Tnen the expression tot q(x) will nave tne
sur
form of (Ref.))
00
(20*.z)(e0*x)s.'neecti3 (5)
= k3(x)-i if
Lia0#2)-0(e0#x)a-2(2.#2)(2,0,vccuje7*
2.71 a (ro#ye*2xsi.sititr/a)w ? 1
wnere ? is the attgle betwgwen tne oentral planes of two adjauent /ins.
In eitiaii1On (5) li(X), B JO. 31(7) Sue orient/Ate natant
xlowa per unit area and time leaving sne fin SUrtal104 470, es* et tne
prism Warsaw,. eye are ustorminett by tne follOwitig relatiOnat
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B(x)= r)*(1- 1/?.(t)
.8 r edr.(2)*(1-6)N,, #hl (a)
13,(Y) z a re v40 -6)(H,..y(Y) #H0_,,5t(y)1
where H (x). H,Sf -? oe)
kirAl X
!lows trans:mired tram the adjaoint
wniun is of interest/
14x ..s? (V), 16,s, (V) - ere
surface.
tisk and
Ry.oa (2) - are tni hest
tne prism matt:toes to tne fin
the heat flows from tile fins to ne prism
3
Tne selations determining Ha.i'in), ere evident free] aqua^
tion (5). The heat flow H (Via determrnea by the folloning expressiOnl
2 &CO, 4115? (9)
4( )i 69,- y/024e2 04- s9.vit OP.
Tne neat now relations H (2) i a?) 3 14.01,(Y) are
at-oa 2-0,y
taind from the expressions tor ki (X)#vg ,
2-*.z "
provided that tneir variables are interonangea.Y
?
Introduce tne rol,owing dimensionless variablest
j;:. 1: ' fir -2; 7 gr ;
??ll-- I (10 )
67-v
Atter integration with H j -tn. use-131 G he seuodt boundary oOnnizion. toe ?gnat.
;ion ()) in tilese variaoles will be written as
- a'?
x ) 07x-: * 174,...6*) 0
x zia73
('f)/
.(3-1 (or 6#(?-6)/ (17)]
, fin "
De6.107,#.if#(4#x)e-e(4,01)(4#2)clue)14?
0 if p jcosdj
zy 4 (i) (.2-e# saz i)As
,
IL/(g) 86X)
x x * y tit
a
: y .1- B (O-
)
/i Y.)
" 4 [23 4?(le' aVis% -%04>t r7
i3
i4
Due to symmetr7 o? the pi:Obltimo A.C.-23W1ika?) Cif a Ita
dary condition for eguatiOn (11) will be r to oil a =0
The boun-
,
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Acoording to equation ) tne neav loss Irom tne surraces or one un
Will be written in no dimensionless varlet:lies as
(19)
Rime resultant neat flow radiated rrom tne surraue or tne oo0Lect
prism otituals? to
i(Y)r (.v)- CV- Na (9) 2o)
tits amount or tne neat in the dimensionless variables radiated from prism
surface, will be determined by tne following exoressiOn:
eciTi
' z;ygici)-}7,..1,(4-7)-fist,s,(mds:
(21)
Let us find tne emission coefficient of the system, whiOli is tne
ratio or tne neat .( tin + pr) n radiated by tne system to the neat
3idear wrildb wo uld be radiated by this system if tne fin material oondueti-.
vity were infinitely nign and ? were one ( Rc . ).
Tne expression for ?usa tne torsi
vanowc
Le0;;Ra (bi# a,) 7;
and the emission coefficient is determineo by
I
affzes 6i)C4f#A2;s (9)6i'q
0
from wnion it is seen tnt tnis ooerxicient is a function of
(22)
(2)
tne parameters
/vIae,'eo and 6 . TnNS, tne neat radiated by idle system equals to
9r Leoli izellooe-067:4siarA
(24)
Tne solution or tne set of equations (11) Inrou.gn (1e) and (23) Sor the
triangular fins was derived numerically as an asymptotioal one at X, -4e 1,0
and ti ---?? 0
me relationanips between tne emission oderXi oient ,and tne dimen-
sionless tnermal oonountion parameterNare given in figures 2,3,4 and 5 tors
various values of the parameters r, and 6 .
By using tne relationsnips or rugures 2 througn 5 and naving a number
of fins and6 seleoted, the optimum geometry of triangular fins can be easy
determined provided *mat tne temperature re , tne prism sip goarca Mt,
amount or tne radiatea heat are known. Really, using ttie relation-snips
tt(V)tor seleotee 11,4 cra,d eovaluee, one can determine 04 from
expressions (12) aixl (24) Xor a number of .4d values and, tnus, evaluate tne
minimum area. of a fin. This calculation results are represented in figures
,zat
0?7 and wnere P and c?ar? the dimensionless variables, related with
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pnysioal magnetudes oy the following expressions:
where
1'r
I.
F' is the total oroes-tseotion
gular fins, Rcpt. 'Ae.elir.)
mum tin of minimum weight (Ref.4)?
In figure 9 the relationsnips between 144
them togepner with tne figures b,(,8 tne optimum
mined immediately.
Vie relations F2FOZ)at Lf2 0 , represented in
correspond to the ease of the negligible prism size.
joAt- 9r
20
n.
(2j)
area of the system of the optimum trianeu
is the oross-eoution area of the op ;i
and 0a re given. Using
fin geometry oan'be Oster.
figures b,7
and
8,
In a000rdanoe el th' ettatiOn (24), at_ t'042 an J7.4, 4.4? a oemp lets
aegeneration of fins odours (in tnis ease Ir 0 and 4,1t oci).
I; is evident that equally witn inoreasidg the optimum tin number
vinen tile emissivity aiminidnes the optimum fin number inoreases with the
inorease ox the parameter
The dotted ourve for tne system of the optimum fine e4ually spaoed
arounn a base prism is given in figure b (Ref.1). It is seen that at
V2 0 Linn e: : 4o tne onange ot the optimum time by tne triangu-
lar tins results in the increase of tne zin oross-seecion oy about o per
oent.
? 2. The0 re Viva 1 Investleation of Tnermal Raaiation
Unaradteriatioe of infinite parallel star-6 _aped
Radiator System
U?nSider tne problem of naloulation of the tnermal radiation onarao-
teristice Of the infinite raoial ooplanar radiator system having Ulu neat
rejeoting triangular fins (Fig.10).
rue mattematioal moael ox vne radiator system section is :mown in
figure 10a with the main geometrioal parameters.
The governing "%tuition for the problem solution are tne energy
conservation egnationa tor tne arbitrary elemeuts G(Vi rof vne
transversal and longitudinal radiator tins (fig.10b)
where
Xaoes
write
aer (.z) -
arx a ? 6.`k
getes (4) 0
.A. ? ?44
(2b)
(21)
qt.ze.pc) 8 9eut (4) are the resulting raalation flows from tne sioe
GeS0 of vuo elements ci V;
First, consider the trapezoidal fins (ii8.10b). In Ude oase One can
the following boundary obnditions tor ovations (208 (20s
5
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73=7; at ixx0 (2d)
061.
C6C
ro at 2
air oi)
?g o ezi
Cd2
souoroing to the method of tne resulting radiatiOn, =precisions describing
toe flows Of the resulting radiat4on 912ets(x) gesei(2) nave the following
fermi
Izas (.r): (.x)- ,14..a(x)-(x) -4..2(.432 )
(33)
latas (2): Ree(1)--iet....,162)- Hy?-?264)- 4,2(1)- (A)
(29)
(30)
Wiler0
46,(x): 6 6 7; 461e) +0- Ny.,x (x)#,4' (x)
(4)
# (.r)* iti-ox (r) 7.-1-/i-?x 641
is the flow of the effective radiation from the side face dSior the ele-
ment
4(2)? d 7;4(2) #0- glix-.2(2) #,4y.....2(2)0. (35) ?
is the fiow of the efieotive radiation from the side race Cam Or toe ele-
ment C1Via (rig.10b),
1/.2..?.306x); AY...W.10; Ne-?z(a); Hd..x(x)1 Hoe..x621)
are the total neat flows radiated from the surfaces denoted by the first
letter of the index to the surtaoo Cat, Hx...i(2);Ny-4-aCAL?hii...20);
are the total heat flows radiated from tne surfaoes hti ; oje
to the elemental surface eiSe
Similarly, toe now of resulting radiation leaving tne 0080 surface
equals to
Peej (Y) r 133(Rx4/Y)-1/2-..y(Y)- (Y) ('D)
wnere?-//? (Y) (-9) ? ? ?
-.?if ? 1
43.0.26147;.#(/-0/71.*.y(9)416..y0)14/1..e
0
G'
472
47.6
-ea
Q6
Q4
ta-11
Q2
4q4