Dec 27, 2013 ... John M. Bannon. HEAT TRANSFER AND FLOW FRICTION. CHARACTERISTICS
OF PERFORATED. NICKEL PLATE-FIN TYPE HEAT ...
Calhoun: The NPS Institutional Archive DSpace Repository Reports and Technical Reports
All Technical Reports Collection
1965-06
Heat transfer and flow friction characteristics of perforated nickel plate-fin type heat transfer surfaces Bannon, John M. Monterey, California. Naval Postgraduate School http://hdl.handle.net/10945/31780 Downloaded from NPS Archive: Calhoun
John M. Bannon
•#
TA7 .U62 no. 52
-
HEAT TRANSFER AND FLOW FRICTION CHARACTERISTICS OF PERFORATED NICKEL PLATE-FIN TYPE HEAT TRANSFER SURFACES.
Library U. S. Nnval Postgraduate ScKodf
\ionterc#, California
USNPGS TR 52
UNITED STATES
NAVAL POSTGRADUATE SCHOOL
HEAT TRANSFER AND FLOW FRICTION CHARACTERISTICS OF PERFORATED NICKEL PLATE- FIN TYPE
HEAT TRANSFER SURFACES
J'.M.
BANNON //
C.H. PIERSALL.Jr.
P.F. PUCCI
30 JUNE 1965
Technical Report/Research Paper No. 52
TMA'i
\
S.
Naval Postgraduate
Monterey. California
iScoool
rary S.
Naval Postgraduate Scaou*
Monterey, California
UNITED STATES NAVAL POSTGRADUATE SCHOOL
Monterey, California
Rear Admiral E. J. O'Donnell, USN,
Dr. A.
E.
Vivell,
Academic Dean
Superintendent
ABSTRACT:
Experimental results for the convective heat transfer and flow friction characteristics of plate-fin type heat transfer surfaces are presented for eight surfaces. Six surfaces were fabricated of perforated nickel plate, one perforated nickel fins with solid nickel plate splitters and one of solid nickel plate. The heat transfer data were obtained by the transient technique and includes the effect of longitudinal conduction.
This task was supported by:
Bureau of Ships, Code 645
Prepared by:
Approved by: R.
W.
J. M.
Bannon
C.
H.
Piersall, Jr.
P.
F.
Pucci
Released by:
Bell,
C.
B.
Menneken
Chairman, Department
Dean of
of Aeronautics
Research Administration
U.
S.
Naval Postgraduate School 30 June 1965
UNCLASSIFIED ii
Technical Report No. 52
Table of Contents Page
Introduction
1
Description of Surfaces
1
Presentation of Results
3
Experimental Methods
3
Experimental Uncertainties
5
Discussion of Results
7
Conclusions
11 *
References
12
Figures 1.
Schematic of Test Apparatus
14
2.
Photograph of Test Apparatus
15
3.
Geometric and Physical Properties of Slotted Perforated Nickel (160/40 TV and 160/40 Q) "Parallel Plate" Matrices
16
4.
Geometric and Physical Properties of Round Perforated Nickel (125 M, 125 P, and 50 G) "Parallel Plate" Matrices
17
5.
Geometric and Physical Properties of Slotted Perforated Nickel Fin (160/40 TV) with Solid Splitters "Parallel Plate" Matrix
18
6.
Geometric and Physical Properties of Solid Nickel, "Parallel Plate" Matrix
19
7.
Geometric and Physical Properties of a Slotted Perforated Nickel (160/40 TV) 20° Skew Matrix
20
8.
Enlarged Photograph of the 160/40 TV Perforated Nickel Plate
21
9.
f
and
j
vs. N. 160/40 TV "Parallel Plate" Matrix
22
10.
f
and
j
vs. N_ 160/40 Q "Parallel Plate" Matrix
23
11.
f
and
j J
vs. N n 125 R
M "Parallel Plate" Matrix
24
12.
f
and
j
vs. N_ 125 P "Parallel Plate" Matrix K
25
K
iii
and
vs. N„ 50 G "Parallel Plate" Matrix R
26
13.
f
14.
f
15.
f
and
j J
vs. N„ Solid Nickel "Parallel Plate" Matrix
28
16.
f
and
j
vs. N_ 160/40 TV 20° Skew Matrix K
29
17.
Comparison of Slotted Perforated Nickel, 160/40 TV vs. Solid Stainless Steel, 20° Skew Matrices
30
18.
Comparison of Solid Nickel vs. Theoretical Solutions Parallel Plate Matrices
31
19.
Comparison of Slotted Perforated vs. Solid Nickel "Parallel Plate" Matrices
32
20.
Comparison of Round Perforated vs. Solid Nickel "Parallel Plate" Matrices
33
21.
Comparison of Slotted Perforated Fin with Solid Nickel "Parallel Plate" Matrices
34
22.
Comparison of Slotted Perforated Nickel "Parallel Plate: vs. Slotted Perforated Nickel 20° Skew Matrix
35
Flow Area Goodness Factors for the 160/40 TV Perforated Nickel and the Solid Stainless Steel 20° Skew Matrices
36
24.
Flow Area Goodness Factors for the Slotted Perforated Nickel and the Solid Nickel Parallel Plate Matrices
37
25.
Flow Area Goodness Factors for the Round Perforated Nickel and the Solid Nickel Parallel Plate Matrices
38
26.
Heat Transfer Power vs. Flow Friction Power Per Unit Area for the Slotted Perforated Nickel and Solid Nickel "Parallel Plate" Matrices
39
27.
Heat Transfer Power vs. Flow Friction Power per Unit Area for the Round Perforated Nickel and Solid Nickel and Solid Nickel "Parallel Plate" Matrices
40
28.
Heat Transfer Power vs. Flow Friction Power per Unit Area for the 160/40 TV Perforated Nickel and the Solid Stainless Steel 20° Skew Matrices
41
29.
Enlarged Photograph of the 20° Skew Matrix, 160/40 TV Perforated Nickel
42
30
Enlarged Photograph of the Modified Parallel Plate Matrix, 160/40 TV Perforated Nickel
42
.23.
J1
and j vs. N 160/40 TV Fin with Solid Nickel Splitters "Parallel Plate" Matrix
R
iv
27
31.
Matrix Holder (Upstream View)
43
32.
Matrix Test Section Disassembled (Downstream View)
44
33.
Velocity Profile and Temperature Distribution Measurement Device
45
34.
Nichrome Wire Heater (Upstream View)
46
35.
Close-up of Apparatus Test and Heater Sections
47
36.
Recorder Trace of Actual Cooling Curve for 160/40 Q Perforated Nickel, "Parallel Plate" Matrix
48
Summary of Heat Transfer and Friction Results 160/40 TV Perforated Nickel, "Parallel Plate" Matrix
49
Summary of Heat Transfer and Friction Results 160/40 Q Perforated Nickel, "Parallel Plate" Matrix
50
III
Summary of Heat Transfer and Friction Results 125 M Perforated Nickel, "Parallel Plate" Matrix
51
IV
Summary of Heat Transfer and Friction Results 125 P Perforated Nickel, "Parallel Plate" Matrix
52
Summary of Heat Transfer and Friction Results 50 G Perforated Nickel, "Parallel Plate" Matrix
53
Summary of Heat Transfer and Friction Results 160/40 TV Perforated Nickel Fins with Solid Nickel Splitters, "Parallel Plate" Matrix
54
VII
Summary of Heat Transfer and Friction Results Solid Nickel, "Parallel Plate" Matrix
55
VIII
Summary of Heat Transfer and Friction Results 160/40 TV Perforated Nickel, 20° Skew Matrix
56
Tables I
II
V
VI
C-l
Table of Geometric Properties of Perforated Nickel as Specified by the Manufacturer
NOMENCLATURE English Letter Symbols
Matrix total heat transfer area, ft 2
A A
c
Matrix minimum free flow area,* ft
2
2
A_
Matrix total frontal area,' ft
A
Solid matrix cross sectional area available for thermal o conduction, ft z
fr
s
A,
Conduction area corrected for effect of perforations, ft
A*
Plane surface area, ft
a
Plate thickness, ft
a
Short side of a rectangular flow passage, ft
b
Plate spacing, ft or in.
b
Long side of a rectangular flow passage, ft
C
Flow stream capacity rate, (mc ), Btu/fhr °F)
C s
Matrix capacity, W
c s
2
2
Btu/°F
,
s
Specific heat at constant pressure, Btu/(lbm°F)
c c 5
Matrix material specific heat, Btu/(lbm°F)
D„ n
Hydraulic diameter,
d
Inside pipe diameter, in.
E
Flow friction power per unit area, HP/ft
f
Mean friction factor, dimensionless. This is the "small" or "Fanning" friction factor. (Ratio of wall shear stress to the fluid dynamic head.)
4r,
n
2
»\
Exchanger flow stream mass velocity, (m/A ), lbm/(hr ft
Proportionality factor in Newton's Second Law, g - 32.2 C (lbm ft)/(lbf sec 2 ) Unit conductance for thermal convection heat transfer, Btu/(hr ft z F) , or heat transfer power per unit area per degree temperature difference, Btu/(hr ft 2 °F)
vi
)
English Letter Symbols (continued)
Colburn factor = Ng T dimensionless
j
j'
Colburn
j
2/3 fl
pR
,
heat transfer characteristic,
factor based on plane surface area, A*, dimension-
less
K
,
K
Contraction loss coefficient for flow at heat exchanger entrance or exit respectively, dimensionless
k
Unit thermal conductivity, Btu/(hr ft 2 °F/ft)
k
s
Matrix thermal conductivity, Btu/(hr ft
2
°F/ft)
L
Total matrix flow length, ft
m
Mass flow rate, lbm/hr
P
Pressure, lbf/ft
p
Porosity for matrix surfaces, dimensionless
q
Heat transfer rate, Btu/hr
R
Gas constant, (ft lbf)/(lbm °R)
,
r.
Hydraulic radius, (A L/A)
(4r,
s
Solidity of a perforated material, 1-u, dimensionless
T
Absolute temperature, degrees Rankine, °R
t
Temperature, degrees Fahrenheit, °F
2
,
ft,
(53.35 for air) = hydraulic diameter)
3
V
Matrix volume, ft
V
Material volume corrected for effects of perforations
m
W s
x
Mass of matrix,* lbm
Distance along the flow passage in direction of flow, ft
Greek Letter Symbols a
Aspect ratio of a rectangular flow passage, b/a, dimensionless
6
Comp actness; ratio of total heat transfer area to the volume between een the plates, ft /ft
A
Denotes difference
6
Fin thickness, ft
vii
Greek Letter Symbols (continued) C
Conduction area reduction ratio due to perforations in perforated material; cross sectional area of perforations/ cross sectional area, dimensionless Time
A
k A s s Longitudinal conduction parameter, tj
— C
,
dimensionless
P t
Time parameter
y
Fluid viscosity coefficient, lbm/hr ft
u
Area reduction ratio due to perforations in perforated material, dimensionless
p
Density, lbm/ft
3
Ratio of freeflow area to frontal area, A /A, c
8
,
Summation
Local atmosphere
f
Fluid
i
Initial, individual
k
Equivalent
m
Mean or matrix, as appropriate At orifice
s
STD
dimensionless
Compactness for perforated material including the effect of area reduction, A*s/V dimensionless
Subscripts
atm
,
Denotes "function of"
m
1
fr
(Matrix material) solid
Standard temperature and pressure
1
Upstream
2
Downstream
viii
Dimensionless Groupings N N
Reynolds number,
K
,
v
(4r,
n
G/u)
Stanton number, (h/Gc
N
Nusselt number, (h4r, /k)
N
Prandtl number, (uc /k) lu
j
f
a flow modulus
Reynolds number for pipe, (dG/u)
N„ bt
N_
,
)
a heat transfer
,
modulus
p
,
a heat
,
transfer modulus
a fluid properties modulus
Number of heat transfer units, (hA/mc
)
p
Generalized zed heat transfer grouping - Colburn "j" factor, 2 (Ng Np z/J This factor versus N R defines heat transfer ). t r characteristics of the surface. I
Mean friction factor. This is the "small" or "Fanning" friction factor (Ratio of wall shear stress to the fluid dynamic head) This factor versus N^ defines the friction characteristics of the surface. .
X
Conduction parameter, k g A s /mLc for solid material; kgAfc/mLcp for perforated material
A,
Equivalent conduction parameter (corrected for equivalent length in perforated material) Xtk hA Time parameter, rj ,
t
w c s
s
ix
INTRODUCTION
The present investigation is an outgrowth of the continuing program at Stanford University [8]
for the evaluation of heat transfer surfaces.
The experimental work reported by Howard [4] was performed at the U. S.
Naval Postgraduate School, Monterey, and a continuation of that work is
presented herein.
DESCRIPTION OF SURFACES The eight compact heat exchanger surfaces tested were: 1.
Skewed passage a.
2.
20° total skew angle;
160/40 TV perforated nickel
Modified parallel plate a.
160/40 TV perforated nickel
b.
160/40 Q perforated nickel
c.
125 M perforated nickel
d.
125 P perforated nickel
e.
50 G perforated nickel
f.
160/40 TV perforated nickel fins with solid nickel splitters
g.
solid nickel
The skewed passage surface employs corrugated sheets of 160/40 TV per-
forated nickel, stacked alternately with the lines of corrugations 10* from the flow direction, thereby forming a total angle of 20* between
Numbers in brackets refer to numbered items listed in References.
adjacent stacked plates.
Howard [4].
It is the same geometry as one employed by
The modified parallel plate surfaces were made by alternately
stacking a formed plate and a plane splitter plate to prevent nesting, as
shown in the sketch below and in the enlarged photograph of Figure 30.
T~
—^ vA v V^ -r V^—V^— 7^—
—v^—
a.
The flow channels formed by this geometry may be compared to rectangular
channels with an aspect ratio, a = b/a, of about
7.
The perforated nickel plate employed is an electro-deposited metallic sheet of integral structure manufactured by Perforated Products, Incorporated. This material is described in detail in Appendix C.
The geometrical and
physical properties of the surfaces are given in Figures
3
through
7
.
All matrices formed had a frontal cross section of approximately 3.2 inches square and a length of 2.0 inches in the flow direction.
matrices had flow passages with a hydraulic diameter of approximately .002 feet, thus the L/D
ratio in all cases was of the order of 83. rl
All
PRESENTATION OF RESULTS Heat transfer and flow friction data for each matrix investigated are given in both tabular and graphical form, TABLES I through VIII and
Figures
9
through 16, using the Colburn
and Reynolds number.
j
modulus, Fanning friction factor,
In evaluating the Reynolds number, the hydraulic
diameter, which is defined as four times the hydraulic radius, was used.
The effects of entrance, exit, and flow acceleration have been considered in the evaluation of
f.
(See Appendix A).
Figures 17 through 22 show heat transfer and friction comparisons
between various matrices investigated.
Also plotted in Figure 18 for
comparison purposes are the theoretical laminar flow solutions for parallel plates and rectangular passages [6, 8, 11].
Both solutions are
for an infinite length to hydraulic diameter ratio, and the heat transfer
solutions are for constant wall temperature.
In Figures 23 through 25,
"figure of merit" type curves are presented.
The j/f versus Reynolds
number thus plotted gives an indication of the required matrix flow frontal area for a given pressure drop.
Lastly, in Figures 26 through 28, heat transfer power versus flow
friction power curves on a unit area basis, evaluated for fluid properties at standard conditions of dry air at 500°F and one atmosphere, are
presented (See Appendix A).
EXPERIMENTAL METHODS To obtain the heat transfer data, a transient technique was employed.
Briefly, this method consists of heating the test matrix by heated air to a uniform temperature (approximately 20°F above ambient in these tests)
and then subjecting the matrix to a step change in the air flow tempera-
ture to ambient temperature
.
The air temperature ddwnstream of the
matrix is monitored and recorded versus time. of constructing such a test rig [4, 10, 12],
There are several ways
The one used in these tests
is shown in Figure 1, and described in detail in
Appendix
B,
A series of fine nichrome wire heaters were installed upstream of the matrix to heat the air.
Turning off the heaters provides the step
change in temperature of the air without disturbing the flow.
By
referencing the thermocouples downstream of the matrix to the thermocouples upstream of the heaters, the initial temperature difference can be very closely controlled.
This temperature difference is continuously
recorded by a strip chart recorder when a run is made.
This recorded
trace has the distinct advantage in that there is no transposition of
data required which would produce increased uncertainties.
Reduction of
the data follows the method of Locke [10] and Howard [5], whereby the N
of the surface can be evaluated by determining the maximum slope of
the fluid temperature difference versus time curve during the cooling
transient.
Pressure drop data for evaluating the friction factor were obtained from static pressure taps located in the test section immediately upstream and downstream of the matrix.
The static pressure immediately upstream
of the matrix was also recorded.
Velocity profiles were taken just
upstream of the matrix to assure that uniform flow conditions were being
maintained by the screen pack straightener and by the wire heaters.
The
flow was measured by an A.S.M.E. standard D and D/2 orifice meter with
:
changeable orifice plates [14], and was located downstream of the test section.
Various manometers were used consistent with the pressure
range encountered.
All pressure drop data for evaluating the friction
factor were taken under ambient air conditions (i.e., isothermal flow). The data reduction relationships are given in detail in Appendix A.
EXPERIMENTAL UNCERTAINTIES The experimental uncertainties can be considered to be in two catagories.
First, in the manner in which the experimental gear attempts to
meet the idealizations of the experimental method.
These are discussed
in detail by Howard in [A] and [5]. By insuring uniform flow to the matrix, minimizing the temperature
change to minimize fluid property changes, and in the careful design of the fluid heater, these idealizations are met.
The second catagory
can be grouped in three areas (1) uncertainty of physical constants,
(2)
inaccuracy in the geometric measurements , and
(3)
instrumentation inaccuracies.
For the determination of the uncertainties reported, the method of Kline
and McClintock [9] was used. (1)
[1],
Values for the physical constants required were obtained from
[2], and [3].
The uncertainties in these values, as best as can be
determined, are listed below: ±
0.5%
±
0.5%
N„ Pr
±
2.0%
k
*
o.5%
±
1.0%
c s
c
P
s
u
It is noteworthy that the accuracy for the value of c
the metal used.
depends upon
Where pure metals are used the accuracy quoted is
feasible; however, this is not the case with alloys.
Thus the tolerance
can be a major cause for inaccuracy [10].
of c
Due to inconsistencies in construction of the matrices, errors
(2)
in lineal dimensions are considered to be
±
0,5%.
Inasmuch as the
weight of the matrix can be determined as accurately as desired, the error in W
is considered negligible.
Based on this, the uncertainties
in geometric measurements are considered to be as follows:
A' A
fr'
VVV
'°*
*
l
L
±
0o5%
W
» 33
c o O,
s 5
o
o, ^^^^ {>>
-p •H CO
o ^ O cu
Ph
•H S3
•3
160/40 TV Fins Solid Nickel Splitters
Matrix Material Specific Heat (c g ) Btu/lb
0.1065
°F
Thermal Conductivity (k s ) Btu/ hr ft
°F
38.7
Fin Thickness, inches
0.0022
Splitter Thickness, inches
0.0020
Total Heat Transfer Area (A)
Frontal Area (A f
Total Conduction Area (A k ) Free Flow Area (A c )
Matrix Density
(
Porosity (p)
Figure 5.
0.00689 0.05883
ft3
0.011588 lb/ft 3
Hydraulic Diameter (D^)
Compactness (§)
ft
Tt*
^ m)
19.3084 0.06953
ft
)
Matrix Volume (Vm )
ft
ft 2/ft^
ft
69.1
0.00194 1666.2 O.846
Geometric and Physical Properties of Slotted Perforated Nickel Fin (160/40 TV) with Solid Splitters, "Parallel Plate" Matrix
Matrix Material
Solid Nickel
Specific Heat (c s ) Btu/lb °F
0.1065
Thermal Conductivity (kg ) Btu/ hr ft °F
38.7
Material Thickness, inches
0.0020 ft 2
Total Heat Transfer Area (A) Frontal Area (A fr )
ft
2
0.06953
Total Conduction Area (A g ) Free Flow Area (A c )
Matrix Volume (Vm ) Matrix Density
(
.-.....'.
'
0.01014 0.05939
0.011588 lb/ft 3
Hydraulic Diameter (D^)
Compactness
ft
3
m)
20.1875
2 3 ft /ft
ft
77.7
0.001961 1742.1
0.854
Geometric and Physical Properties of a Solid Nickel "Parallel Plate" Matrix
6
7
8
9
Q
THEL.S.STARRETTCO.
20 Degree Skew 160/40 TV Perf .Nickel
Matrix Material Specific Heat (c ) Btu/lb s
F
0.1065
Thermal Conductivity (k ) Btu/ hr ft s
Material Thickness, inches Total Heat Transfer Area (a)
Frontal Area (A ) fr
Matrix Density (^ ) m
ft 2
Porosity (p)
Figure 7.
ft 2 /ft 3
15.U
ft 2
0.00349 0.06412
0.01211
lb/ft 3
Hydraulic Diameter (D ) H
Compactness ($)
ft 2
0.0734
ft 3
Matrix Volume (V ) m
38o7
0.0022
ft 2
Total Conduction Area (A ) k Free Flow Area (A ) c
F
ft
50.1
0.00252 1272.8 0.873
Geometric and Physical Properties of a Slotted Perforated Nickel (I6O/4O TV) 20° Skew Matrix
-5
X3 0)
a.
> o
s -p
o j=
a
aj Sh
O -P a,
•a
v
hi-
ll a)
W CO
f-i
'
l
!
ms^
1.0 I
!.;:uii;uii:ritauiiuiiiiiiiiiite#E^
Modified Parallel Plate Perforated Nickel, 160/40 TV
.6
•4
f
•
.2
.1
K3 .06 S«*
.04
.02
.01
NsiW*
.006
/:;: ;j '''
.,:•'
;
'
f
*v!'
-'.-*
.004
;
j*g .#
.002
.001
Figure 9.
Surface Heat Transfer and Friction Data "Parallel Plate", 160/40 TV Perforated Nickel
'.
:
.
Figure 10.
Surface Heat Transfer and Friction Data "Parallel Plate", 160/40 Q Perforated Nickel
1.0
.6
.4 i
.2
.1
==
.06
.04
J
.02
.01
.006
.004
.002
.001
Figure 11.
Surface Heat Transfer and Friction Data "Parallel Plate", 125 M Perforated Nickel
Figure 12.
Surface Heat Transfer and Friction Data "Parallel Plate", 125 P Perforated Nickel
t
Modified Parallel Plate Perforated Nickel, 50 G -
Porosity, p = 0.883 Compactness,
@
=
966.8 f 2 /f\?
Hydr. Diana., D H = 0.002028 ft.
'«,.-
-
•':;
-
-.
:
40
'
60
NR
Figure 13.
Surface Heat Transfer and Friction Data "Parallel Plate", 50 G Perforated Nickel
\
\
.001
10
20
40
100
60
200
500
NR
Figure 14«
Surface Heat Transfer and Friction Data "Parallel Plate", 160/40 TV Fins with Solid Nickel Splitter Plates
1000
rmmiW
•'immimm i
#p
.006 ""
-
.004
Figure 15.
Surface Heat Transfer and Friction Data "Parallel Plate", 0.002" Solid Nickel
40
Figure 16.
60
100
Surface Heat Transfer and Friction Data 20* Skew, 160/40 TV Perforated Nickel
1.0
i Is
M
Figure 17.
Comparison of Slotted Perforated Nickel, 160/40 TV vs. Solid Stainless Steel, 20° Skew Matrices
.004
.002
(T)
Theoretical Solution, Infinite Parallel Plates
(2)
Theoretical Solution, Rectangular Passage b/a= 7.
(3)
Solid Nickel, Modified Parallel Plate Matrix:
,001
10
20
40
100
60
200
500
1000
II-
R
Figure 18.
Comparison of Solid Nickel vs. Theoretical Solutions Parallel Plat© Matrices
a?
-
.-.
*
*
3f
.
'*
'"-
;
r
- -t»'
U>
Figure 19.
60
100
Comparison of Slotted Perforated vs. Solid Nickel "Parallel Plate" Matrices
«s
.003.
10
20
Figure 20,
40
60
100
200
500
Comparison of Round Perforated vs. Solid Nickel "Parallel Plate" Matrices
1000
flW
;1
.1 "
'
.06 ;
.04 -
i
" -
.01 '
3
.006
-
.004
Wk --'
.002
.001
10
20
40
60
100 N
'*
Figure 21. :
200
500
1000
R
Comparison of Slotted Perforated Fin with Solid Nickel Splitters vs. Solid Nickel "Parallel Plate" Matrices
40
Figure 22.
60
100
Comparison of Slotted Perforated Nickel "Parallel Plate" vs. Slotted Perforated Nickel 20° Skew •
Matrix:
X! •p TJ
S
H
i
a>
^5
O
•H S3 •d -..
a>
•p ctf
h
o
«H St
o
(U
> 6H e I
O -* o © NO o H •HU
"V^
CO
Q)
-P
U
JS p a
^ o
1= 0)
i0) c>
p CO 01 05 «J u u o ID tH 1 fc O
cu cu
!ni3
x> Q O •
w O CO
© C «H 3 CO O +3 c rt a
«H
fci
S3 f-i
CO
t-i
J3
oiS
S-t
a s
^S OH cd
0)
as
O•
ON ON
to
H•
3 o l-J
• to
vo
-
|
s Ottf
.
O !>
M &3 a to
NO 9i -4
to
S3 a
&«
CO
vO £
.
;
is O
o o rH H o O CM -4-
**}
r-\
8
O
8
o H, un O O
t» to
UN
ON t> CM
O O
-4 CM ^ -4 O O UN O O nO H
ON UN ON
O O
o
8
UN
UN
c»-
CV
O
H UN to
8
P-.
r-i
su
»
CM
co
(U ss -P co
e->
E-»
s§
•o
s
co
w CG
c-
8
O O
r-\
ON ON nO
H O
C
ON CM
O
NO ON
O
*
UN C*-
nO
O
> #~ o CM HI
.
a
«
NO O o £o to
CO
U ON ON • -4
C»-
•
•
•
UN
NO CM
UN
Q -4
H• to o ON
C*N
-4-
UN
< £
pie Jp N g
to
u\ UN NO
E-i "S.
Ko B CG S
•-«
CM
Oi
CM
H ON
to
ON C-
O CM
H £
to
NO
C»
ON
CM
nO
•
•
-4
CM CM
On
•
ON
•
1
a O
r-i
CO
cc
g
t^-
O NO a o
i
O m o
to
s u
Y
B H O £
vO to
'H
oS
3
vO
O
CO
q -4
m O O
i-l
UN
-4
en ON -4
CO
un.
o
r>-
u\ •
nO ON
CM
CO
r-i
•
•
•
en
vO
ON
-4 UN c-
o ON o o
o un 3 O
H ON 3 o
un.
UN r• -4
ON
CM
-* CO H NO 3 cO u\ o -4-
H
cm
3 O
nO CO
en u\
•
•
•
vO
-4 en
Q -S
•
CM
rH
UN.
r-i
r-i
•
un o -4
C*-
•
H
O
o
-4 un
4 cm
ON n0
UN.
CA
8 CM
r-i
csO ON -*
c-~
o
t> nO
r-i
O•
O
•
CO
CO
r-i
-4 UN
* -4 *NO J
n to
X
CO
It
O
3
•
-4
3
£•
O
UN.
en nO
-a ON
O
o o o £U
CO
UN UN cvO
vO r-i r-i
O O
-4 Oun
•
UN.
CM
-4
H O
H O
CO
ON
O
UN.
m ON
•
•
•
-4
NO
o-
un.
un.
un
UN
vO C— nO C-
3 en
CO CO
vtn
o o
r-i
CO
UN.
cm
O -4 o
o NO O
UN. £>• •
•ON
o
O O
o
4
en
o o
8 o
8 o
en U"\ ON
O
r-i
r— -4
CO
en
UN.
r-i
«H
CM
i-l
.
r-i
CM CM
vO
*H un.
#
•
•
un -4
H ON
3 C-
NO vO
r-i
en ON
U\
o cm
r-i
en
cv
CO
-4
-
o o
II
•
ft
o o
•
•
p-4
o CV
t>
•
•
•
en
en
-4
^ -4-
t-j
xJ
si
cv o
a, o ^
u\
CM to
en
O
sO
to
o
-*
-4
CV
to
Q -4
•
•
•
•
-4
vO
to
cv
CV
O
IT\
-4 v0
SO
ITS
to to
o
to
ITS
H O-
o-
to
t> -4
ON
* ir\
en
en
cv
rH
o en
•
•
H vO ^ -4 NO s to o o O o
c^-
c>-
-ct-
r-i
o o -d-
o
•
f"9
to CV
*
en en
r-l
•
.
^H •
to
in
>
a to oto
o OS
»
M Eh O tD Q o O
CO
rH
C>-
ir\
en
O O
o O o O cv en O en o cv o o H o o $ o
o rH
«r\
P-,
u o > «H
O
CO
M M
o J*>
cv co Eh t-q
C3 CO
1
rH »
h
aa. -p CO a
T9
& $ O o o rH o•
o
•
H NO
-J-
vO
>o ON
to
cv
-4"
vO
rH
rH
So rH
•
•
•
•
O
O
o
CV
O
cv
cv
en t-
^ O•
O o •
ir\
*
rH
ON
o•
t>
* ir\
o-
H
•
to
-
CO
3p5 o a
o. cS
g|© 2 W
o sf
ir\
CV
cv
•
•
• lf\
E^
Cd ^5
o
Pr -* o-
Eh
s ^! O © oi a
H
cv
-rr;
-H-
rH
ITN
-J;
en
cv cv
en
-4"
>j\
vO
Q -*
c^•
cn
to
vO
u Cto
o to
•
•
en -4
to rH
to
•ON
O r-i
o #
CO
CO 25
o M
o
OS M Eh O O M
E-i C_>
Cn r
-H
O o cm o
to
u-\
cn UN
O-
8
O -4 O
en
O u\ -4 o
NO cv
cn u\
O
CM o
*0 vO t>
o
rH
vO c-
H c-
H
m m cn
cv
vO o-
to rH
cn
en -4 vO
cn
to
cm
CO
nO So
O CO
CM rH CM
M
in
to
•
to
• _4"
CM
C>-
o en
to
o
•
•
O Q -4 rH
w r
o O en
n
•r?
3
EH
ir\
in CO to
U\
o
CS)
rH CM fH
O
O
8
vO
o
O O
O o
c*-4" •
CM
to
»n
-4
rH
O-
CM
CM
CM
cn
-4
• ir\
•
o o
•
m
•
in
*
cn
to
o
#
to
IN•
t>•
o•
rH rH
to rH
cn
vO UN -4 ON
o OCM O ON
O o U\ en O o
to
o
O
o•
O
CM O CM O
to
vO
*
o -4 •
CM to
co
u> O rH o 3 H un.
CD
en
•5e'-
to
to
r>-
en o-
o
*
o
rH
3
NO
CM
o CM
CM rH
en
en
3
UN.
NO
to
ON
O
-4 rH
d CM
o O
•
en
to
•
nO en ON -4
rH
*~ o o O o ON UN o o
CM
rH
& £>
en
-4
cv
*
o o CM CM
en en
O rH
.
CO
CO
o BO
r-i
!-;
£5 o H OO M O E ff!
E-i
E-i
.
-
r-»
to
CM
O
CM
f-S
r-i
CM
-4 UN
NO
UN
*
•
un
CO
-4 NO
rf
On
o
r-l
On
o o
NO ON
ON
to
CM
ON NO
•
• e»-
o
(Al
fee
W £H n •
O
sO
H en
*n t> P-
o CO
so C-
CO
irv
o c-
P-
o
CO
8
8
-dtj-
lf\
r>-
o o
,
o o
uv
•
3 o-
O
-tf
in
m -*
H rH O
to
rH
a en
OrH
O
-J
a
nO
p-
-tf
8 en
CO
o o
o
cv o cv
o
CV •
ir\
o
to
to m 3 cnO cn o rH o cv
o
rH rH
in
o
.
CO
jen
cv
w y PQ
co
«s;
B-i
NO
••
00
-P CO
""3
—
o cn
rH
rH
cv
o
o
«nO
in
H o
cv
O
cv
3 cn
*
o O
3
o
*
cn
in in
cv o o
O
*
o
ON
a
co
UN.
NO r>-
o 5s cr;
to
O
o
O cv
i
Sn
to
t>-
nO
ON
•
•
tr\
»
•
•
cv
ITN
ON
r-i
to
On
ON
vO
-J"
cn
CV
rH
cv
en
in
NO
•
to rH rH
• t>-
nO
to
-
en o» vO en
o rHo
CO
I CO
o en
25
O H O OH
o H
to cm
o
o
to
en en
vO o o o H vO o CM en rvO ro c- to
O
3 o
LTN
ITS
-±
o
to
ir\
3 CV o en
H CV
cv
o
O
rH to CV
H
S3
E-
•
ms
n
etJ
co 03
oen
CN CV J>-
o cv o o
*
vO
-4"
to •
i/\ ir\ •
*-a
to
C-
vO en
o
vO
u-\ -d-
•
•
cv
-*
to cv
to iH
u>
vO
=»
-d-
t>-
O•
*
cn
d
.
i-* •
-* vO
r-i
CV -
lf\
cn
3
C\2
cn
oz
/
to
I
•
o
g u
00 Eh
i 3 o M EH o o Eh O a «S Cn
2
m o CO O ON rH 3 H en O -4 en
erf
o H Eh O H
irv
*H
-4-
LT\
O
O
o
o
vO
o s>
O o
rH
O o o & -4 c— O 8 O 2> to -4 cv c^ vO sO NO cv o -4 o H CM o H
vO cv
irv
o co
if\
c«-
.
fc«
as
CO
o a
£f
SM Crf
CM erf
• IT\
&
S3
0}
•
•
CM
-4 to
o to
C^
rH
o O
en
O
u>
•
•
•vO -4 c-
o
ON en
CV
o o
3
H •
ir\
en vO
o o •
en vO -4
On vO
-4
-^f
nO
•-4
IT\
•
'
o
• ir\
CN-
-4
en
CM
in
ir\
O
NO
.
in
C-
•
•
to
-4
-4
to
C*r
H
•
-
-4
-4
CM
r-i
to
ir\
nO
8
O o
o e— o o
en
2 m O rH
ir\
o
r-J
NO
r-» •
o nO rH o
O O r-i
*
ON -4
*
O o
NO
en
ITV
o
o H
*
in
*. -4
NO
•
•
5
en
CM
O CM
en
to
2T>
r-i
>"'
O
rH
CM
£>
II
C-
3
rH
9w
nO nO -5 en u\
3S E§
fe
cv
o ON
NO en
•
•
•
•
en
H*
l/\
NO
CM m
O CM
en
-4
-i
-co
C^
o
m vOo Om vO
-4 vO
lf\
-4
CM
rH
en
ON -4
nO r—
r-i
O O
rH
r-i
rH
nO
o o
8
o o
H.
«
.
•
o
C^>
^4
ir\
ITv
nO
O
o o
o o 3 CM en
en V/N. -4
ON NO en c-
to
O O
O co
en
rH
en .
o in o o r>-
o o
8
i
*
CM
»rs
CM CM
to CM
2
en r-i
to CM
o ON
en
en
l/N.
r-i
o
CM
* * O O o o in
-4
o
o
r-4
••
JU
en NO
eo
a.
ITN
53 -P CO
8
o o
o Of
NO nO
•
•
CM (-• r-H
5 co B i
.0188
L.
k i
The solid cross sectional area for heat conduction, the path length.
The area, A^
A,
Ki
varies along
selected was the cross sectional area
,
between the slots normal to the flow direction, i.e., = (0.0095) (0.0022) - 0.0000209 in.
A.
K
2
i
Just as L = EL is the flow length
and m _
is
A,
EA^
where L is the total matrix flow length and L
between two successive perforations; so does
In evaluating A^
.
r employed and is defined as
therefore, i.e.
.
,
A,
,
.
,
„
,
c
,
=
L,
= ZL,
a conduction area reduction ratio
—
cross sectional area of: perforations c cross sectional area
is the solid cross sectional area multiplied by 1 - £
,
71
;
\
= A (l-C) s
- 1.6058
6102 in
- 0oG0424 £
160/400,
.00(0}"
A
=
ch
A
(»
0063 )( 02 5) - =0001575 in. =
- (.0019) (.0161) - .00003059 in=
SX
C
\
v = .1942
- A 8
(l-0 =
002887
ft.
- .8058
s
7— L
- .655
=0.3351, same
as
160/40TV
k
125M «
T .O07fsir\60
A
^
ch
A,
.
nole
(°
00684) (.0079) - .00005404 in,
- y(. 00366) 4
2
,00001052 in
c
v = s
no le
A
ch
- .8053
e
.00001052 00005404
H
0.19466
—
,007?"
T JLj, •
The equivalent conduction length, L^
,
s .00?$ sin 6o° =. 0QG84-
is computed in the case of
i
round perforations assuming the path to be as shown above, i.e.,
where
r,
Thus
.liX 1 22291.
-00827
k
3
l
.00684 = .82709 .00827
2
..
and
1^.
is determined as C
2Trr
—r
k
is the radial distance equal to one-half the center to center
distance.
A,
M
=
in the case of the slotted perforations.
diam. of hole x plate thickness center to center distance x plate thickness
_ (.00366)(.Q016) _
(,0079)(.0016)
Therefore,
A^ - A
^ DJ:>
(l-O - 1.1679
in.
2
(1-.4633)
2 - .6268 in. 2 = .00435 ft.
73
125P
d-JOQZ?!
A
=
.
en
(
Anole
o
-
.
00684)
f4
(o
0079) =
(,00291)
2
«
.
.
00005404
"
in'
A^ = A (1-;) = ,00640
00000665
ft'
v = 0,12307 i
= 0,8769
s
J
J
00827"
ki
= .82709
ki C
= 0,3684
50G
Jm.OtJt*
-
L^
A
=
(°
ch
A
01706 XoQ197) s ,00033608 in
=7(,0138)
.
nole
4
2
= ,00014957 in.
c
2
= .82697 J
v s
Lk
.0\97 sin 60°
k.
l
.44504
= ,55496
C
- .02063"
= .7005
A^ - A (l-O = .00243 ft
74
l
CO 0) 1-1
-(
cu
CO c
O^ i-l
o 4-»
cu
cu
C
4-1
ccj
C 4)
m CN o o
X
X
en sO
en so
o
•
e
CU 4-1
cd
•
u o
U
m CN o o
4->
CO
o o o
o o o
o CN O o
e
CT>
cy.
r*
r^
•
•
o o o
o o o
i-l
o
U O n cu
(u
o CO CU 1-1
4J >-i
to CO cu
c9 cu
i
H Ay a CU I-l
o Pd
00
(3 f-4
sw
o o
X
X
00
o o o o
o
O
T-4
1-4
CO
CO
o
>
CU
fX
£
J
•
{3
a.
w
I-l
o o
i-l
cu
o
CO
r»~ i-i
C o o sO
H O sr o SO
*»»»
*»«»
i—
i-l
m o o
«cr f-4
o> en
CO
e
•
o
o
o o o
T3
•o
•a
e 3 o M
O o m
O O
a 3 O
(3
M
3 O M
S3 m CM
Pm CM
i-i
i-i
75
-
=T=S£
-