ML20010B486
| ML20010B486 | |
| Person / Time | |
|---|---|
| Site: | Browns Ferry  |
| Issue date: | 12/22/1980 |
| From: | Hunter L JOHNS HOPKINS UNIV., BALTIMORE, MD |
| To: | Feit R NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES) |
| Shared Package | |
| ML20010B468 | List: |
| References | |
| FOIA-81-204 NUDOCS 8108170065 | |
| Download: ML20010B486 (4) | |
Text
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THE JOHNS liOPKINS UNIVERSITY -
r>
APPLIED PilYSICS LABORATORY Johns HcgAms Road, t auret. Marytard 20810
' fd Telepbcce: (30119',3-7100 and 792 7800 Decenber'22, 1980 Mr..Ronaid A. Feit-U. S. Nucicar Regulatory Cotr5nission Mailstop 1130SS Washington, D.
C.' 20555
Dear Ron:
IIere is my analysis of the heat flow in the conduit planned for the Brown's Ferry replication test.
." Z = - $ff keJd
\\
teos z = o
.+
./
w a=+41 r
c
/
L l
,/
c.cnktik Q<e.
/
I..
>\\ N 4 _2-=. k -
/
j k\\cet' s'
/
A strai ht conduit of infinite length passes through a floor and is d
heightbabovethe
)
heated over a length I by a fire. The heated zone is l
floor. IIcat is conducted away from'the heated zone and then lost to the.
i-surrounding air by convection. We wish to calculate the heat flow rate
[
[
In the conduit at the floor compared to the rate at which heat enters the
- heated z'.,ne.
- 8108170065 810604-)'
I
- PDft F01 A WATKINS81-204 PDS 4
f
~
Mr.* Eonald - A.f Feit - 12/22/80 i a o pswore wt w vansitv APPLIE D PetVSICS L ABOR ATORY
- t % v..
The heat flux into the conduit from the surroundings is written H(T
-T) where H is a heat transfer coefficient, T is ~ the (unknown)
T conduit temperature, and 4
N d Z 4 b, f T
i fire-if T
2 2.
=
gas
[
T otherwise.
,,, g; j Outside the heated zone, H(I"
-T) is negative and represents a gas loss from the conduit.
In practice, H is large in the heated zone and
'cmall elsewhere.
In this calculation, however, H.
is assigned its-smaller value over its entire length, to ensure that the calculated heat
[
flow at the floor is higher than reality. As further insurance, we neglect the fact that the length of conduit in the floor is somewhat insulated.
The flow rate of heat in the conduit, in the positive z direction, is - kK(h M MI[ k,
where k is the thermal conductivity of the conduit, while a and b are the inner and outer radii. Here we drop the heat flow f rom the conduit to the 1".terior cables, making the calculated heat flow in the conduit still higher than reality.
i The heat flow rate through the floor compared to the rate at which j
heat enters the conduit is given by the ratio
//L i
r=-kv(b2hl\\
dz ub H (T,.. - T).
.. m r
CZJr= h 4 j, f
To find T, we solve the energy conservation equation yT.
2hfl (T 3 -T) = o
... (3 )
0 dz '
-k (b -o')
l subject to the boundary conditions that I
i t
l
e Mr. I'onald A. Feit 12/22/80
- -,; u
- y.. $ u..o.u r,
($PLif D f'HYSICS L ABOH A10RY s......,~.
-> l a5
-4 co,
g The last equations describe the steady sta-long time conditions.
The solution is given by
[
f(2xd) brL,2.x z <
el2,
- (+)
n e
a x
T-L
\\
_f:ccch(E' (2z/s))
<{' - 4 z < f... (5-)
-\\ l - e
(;,. g.~ lo) 2 2
-f(2z/f)
Q
.e.'.ULffx bE
' ' gg';
-t
'\\
where L 'm Il l'
.0.
..ty) h
~
2(bbOL m
The ratio, Eq. (2), may now be evaluated
- [S) f_
1.dQ
- u und)k
-,[/2 ) 5,
2 It la interesting to note that the temperature of the hot gasce does not affect this ratio.
We now apply this formula to the case of an aluminum conduit, k = 116 BTU hr~ ft~
F' The outer diameter is R b = 3}",
and ths 1
vall thickness is b - a = 7".
It is heated over a zone of length j = 4'
,k Mr. Ronald A. Felt 12/22/30 t set 4***.$ %Pw'A% LMvl pil1T 4APPtIEC PHYSICS L AttOR A10HY s.,n centered h = 6' above the floor. The value of H in the cold zone is difficult to assign with certainty but it probably exceeds 11 = 1 BTU f t~
br~
F~
With these values, we calculate 0.035 or 3}%.
(9) r =
In practice, the heat flow at the flocr will be less than Eq. (9) since the parameters were evaluated conservatively.
It is interesting to note that an additional radiation flux entering the conduit over its entire length would not affect the last result.
S in cerely, l WY L. W. l!unter I.Ull: a1 4
l
- .