Feasibility of using elastic deformation to predict heat transfer rates across joined smooth-metal surfaces under high vacuum conditions and light load

Mckinzie, D. J., Jr.

English

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N A S A  T E C H N I C A L  
M E M O R A N D U M  
EFFECT OF PLASTIC SET 
ON THERMAL CONDUCTANCE 
AT LIGHT LOADING 
Lewis Research C e ~ t e r  
Clmeldnd, Obis 44135 
MATIOMAL AERONAUTICS AND SPACE ADYINISTIATIOI  WASHIWGTOI,  D. €.:'. SEPTEMBER 1971 
https://ntrs.nasa.gov/search.jsp?R=19710026885 2020-03-23T16:06:17+00:00Z
4. Title and Subt~tle 
EFFECT OF PLASTIC SET ON THERMAL CONDUCTANCE AT 1 
LIGHT LOADING de  
1 Report No. I 1 2 Government Access~on No. NASA TM X-2385 
1 7. Author(s) 1 8. Performing Organization Pr-por? No 
3. Rec~p~ent's Catalog Nc 
I 
Daniel J. McKinzie, Jr. E-6402 
-- 
10. Work Unit No 
9. Performing Organization Name and Address 124-09 
Lewis Research Center 
National Aeronautics and Space Administration 
National Aeronautics and Space Administration 
Washington, D. C. 20546 
16. Abstract 
Smooth metal surfaces joined together (e. g., by rivets, bolts, etc. ) a r e  commonly e n e ~ ~ i n t e r e d  
in spacecraft. To predict the heat-transfer ra tes  for  high-vacuum conditions across  such sur -  
faces, the theories of A. M. Clausing and B. T. Chao and B. B. Mikic and W. Psi. Rohsenow 
a r e  often used. Experimental data presented in this report indicate that the assumption elf 
elastic deformation made in these theories i s  inadequate for accurate prediction of heat .t:-ans- 
fe r  with light loads. 
17. Key Words (Suggested by Author(s)) 18. Distribution Statement 
H&t transfer Unclassified - unlimited 
Thermodynamics 
"or sale by the National Technical  Information Service, Springfield, Virginla 22151 
EFFECT OF PLASTIC SET ON THERMAL CONDUCTANCE AT  LIGHT LOADING 
by Dan ie l  J. McK inz i e ,  Jr. 
Lewis  Research C e n t e r  
SUMMARY 
Smooth meta l  surfaces joined together (e. g. , by rivets,  bolts, etc. ) a r e  com~.,monl~ 
encountered in spacecraft. To predict the heat-transfer r a t e s  fo r  high-vacuum e ~ n d i -  
tions ac ros s  such surfaces,  theories such a s  those of A. M. Clausing and 13, T. Chao 
and B. B. Mikic and W. M. Rohsenow a r e  often used. These theories assume that 
macroscopic elastic deformation occurs  during the formation of such joints with an as- 
sociated effect on the heat-transfer rates.  Experimental data presented in this  report 
indicate that this assumption i s  inadequate for  accurate prediction of heat transfer wi th  
light loads. 
INTRODUCTION 
The prediction of heat-transfer r a t e s  ac ros s  smooth metal  surfaces joined together 
by fasteners  i s  required fo r  spacecraft  thermal  design. The theories of ref erenltees 
1 and 2 a r e  frequently used to predict the thermal  balance a c r o s s  such surfaces under 
high-vacuum conditions and light loads. These theories  assume that macroseopir elas- 
t ic deformation occurs  during the formation of such joints with an  associated effect on 
the heat-transfer rates .  Experimental data obtained from two Armco iron cylindrical 
specimens a r e  presented in this report  which provide new physical insight into the 
thermal  contact conductance phenomenon at vacuum conditions of 1 .2x10 -~  t o r r  and  
6 6 
contact p re s su re s  which range from O.45X10 to 3.44X10 newtons per  square meter,  
EXPERIMENTAL PROCEDURE 
The contact surfaces of the two specimens investigated had arithmetic average 
roughness heights ranging from 0. d l  to 0. 1 micrometer .  Both were 2. 54-centimeter- 
diameter Armco iron cylinders, the ends of which were placed in contact. '"i$he 
sontact~ng surfaces were analyzed with a stylus type of surface analyzer before the tes t s  
were conducted and were found to approximate convex spherical segments .  The tes t s  
-vere conlduesed in the facility described in reference 3. 
After the outgassed surfaces of a specimen were placed in contact a t  a loading p r e s -  
5 
slare 31 4. 48x40 newtons per  square meter ,  the interface temperature was raised to 
aj:prc.x?mately 367 K. The contact p re s su re  was then varied through two monotonically 
In;.reasing tken decreasing loading cycles while a constant interface temperature was 
i-aainta17ed. At each test  point, a minimum of 50 hours of data were taken to a s s u r e  
t ~ a t  steady-state conditions were achieved. Both specimens were instrumented as de- 
scribed in reference 3. 
RESULTS A N D  DISCUSSION 
Figure I shows the cyclic thermal  contact conductance as a function of apparent 
zonlazt p ressure  for  specimen 1. The specimen was loaded through two cycles. The 
mean *ni;erface temperature of the specimen was kept a t  369 K with one exception noted 
2 
ai' the  end of the f i r s t  loading, where it was raised a t  constant p re s su re  (350 N/m ) to 
4'77 K. It remained a t  this  temperature for  50 hours. While s t i l l  a t  this pressure ,  the 
interface temperature was then lowered to 369 K and the p re s su re  cycling was continued. 
The dala obtained fo r  the f i r s t  loading followed the generally recognized trend exhibited 
when m,~croseopic elastic deformation of contacting surfaces takes place. However, a 
comparlssn with the theoretical predictions from references 1 and 2 has  shown the data 
cbtana~ed here to be low by several  factors.  All data following the f i r s t  loading fell re- 
productbly very nearly on a curve having a s lope of approximately 1, which is charac- 
t e r ~ s t i c  f o r  2 specimen a s  moderate loading pressures  a r e  reached (ref.  4) .  F o r  the 
xrnallesr. apparent contact pressures  these thermal conductance coefficients were  con- 
sistent!] lower  than those obrained initially. Therefore,  i t  may be surmised that the 
specimen took a permanent s e t  after the initial loading. 
The' resu i t s  from the second specimen, under almost identical experimental condi- 
t loi~s,  3re shown in figure 2. This specimen, however, was not exposed to a tempera- 
. t~rre xcurston. In this case,  a l l  the data appear to follow the accepted trend for  e las-  
1.1: deforrnatlon. However, c loser  examination of the data obtained a t  the lowest loading 
pressures shows a consistent and reproducible decrease  in the conductance, perhaps 
indicaci~g an increasing permanent set. 
Ti-e contacting surfaces were reexamined with a surface analyzer af ter  each tes t  
v - 1 ~  completed. Table I presents  the surface half-wave height d of each specimen ob- 
tained cefore and after the tests.  The half-wave height of the top of specimen I in- 
(I e a s w  by 3. 35 micrometers  and that of the bottom by 2. 10 micrometers .  The top of 
specimen 2 increased by 1.49 micrometers  and that of the bottom by 1.22 mlccsmeters.  
Thus, both specimens deformed plastically with the attendant changes in the eoefracient 
of thermal  contact conductance noted in the experimental data. The interface temper- 
a ture  excursion apparently caused specimen 1 to deform more  than did specimen :!* 
Changes in  the half-wave surface heights of specimens during t e s t s  may explain 
why the experimental data of references 1 and 5, to mention two, were not i n  good 
aier-  agreement with such macrostructural  elastic deformation theories a s  those af rUA 
ences 1 and 2. If macrostructural  plastic deformation occurs  during a test ,  a bazic as- 
sumption of these theories  i s  violated, and disagreement between experiment and theory 
is to b e  expected. 
Lewis Research Center,  
National Aeronautics and Space Administration, 
Cleveland, Ohio, July 8, 1971, 
624-09. 
REFERENCES 
I. Clausing, A. M. ; and Chao, B. T. : Thermal  Contact Resistance in a Vacuum En-  
vironment. Rep. ME - TN 242-1, Univ. 111. Eng. Experiment Station, 1963.. 
2. Mikic, B. B. ; and Rohsenow, W. M. : Thermal  Contact Resistance. Rep. 74542-4- 1
Sept. 1966, Massachusetts Inst. Tech. (NASA CR-78319), Sept. 1966. 
3. McKinzie, Daniel J . ,  Jr. : Experimental Confirmation of Cyclic Thermal  J o i ~  C m -  
ductance. Paper  70-853, AIAA, June 1970. 
4. Yovanovich, M. Michael: Thermal  Contact Conductance of Nominally Flat, Roxgh 
Surfaces in a Vacuum Environment. Thermophysics and Temperature C c~n~r;! of 
Spacecraft and Entry Vehicles. Vol. 18 of P r o g r e s s  in Astronautics and Aeronau- 
t ics.  6. B. Heller, ed. ;  Academic P r e s s ,  1966, pp. 773-794. 
5. Fletcher,  L. S. ; and Gyorog, D. A. : Prediction of Thermal  Contact Conduetaace 
Between Similar Metal Surfaces. Paper  70-852, AIAA, June 1970. 
TABLE I .  - HALF-WAVE SURFACE HEIGHT 
FOR ARMCO IRON SPECIMENS 
J p/ 'Reference curve,  
d slope = 1 
ln ter face 
6 K 
o First  loading 369 
o First  loading 477 
First  unloading 
o Second loading 1 369 
a Second unloading 
Apparent contact pressure, P,  ~ l m '  
F l g ~ i r e  1. Tl iermal  contact conductance as func t ion  of 
;~ressure for A rmco i r o n  specimen 1. Ar i thmet i c  
average roughness height  of surface; top, 0.02 m i -  
crometer; bottom, 0.014 micrometer .  
F i rst  loadiny 
Fi rst  unloading 
C‘ 6 3 Second loading , 
4 6 8 lo6 2 4 6 
Apparent contact pressure, P, Nlm 2 
Figure 2. - Thermal  contact conductance as 
func t ion  of pressure for  A rmco i r o n  speci- 
men 2. Inter face temperature, 367 K; 
a r i thmet i c  average roughness height  of 
surface; top, 0.038 micrometer; bottom, 
0.102 micrometer .  
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Effect of plastic set on thermal conductance at light loading

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