Heat Transfer Su Yongkang
School of Mechanical Engineering
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HEAT TRANSFER
CHAPTER 7
External flow
Heat Transfer Su Yongkang
School of Mechanical Engineering
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Looking for a job?
Heat Transfer Su Yongkang
School of Mechanical Engineering
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External Flow,Other Shapes
Topic of the Day
oven
Heat Transfer Su Yongkang
School of Mechanical Engineering
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External Flow,Other Shapes
Where we’ve been ……
Empirical correlations and analytical solutions
Where we’re going:
Applications to other shapes (cylinders and
spheres)
Brief discussion on multiple objects (tube
bundles) and jet impingement.
Internal flow next ………..
Textbook Sections § 7.4-7.8
3121x Pr Re 0,3 3 2 k xhNu xx
Heat Transfer Su Yongkang
School of Mechanical Engineering
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Historical Example
Cooling of lead shot
Molten
lead
Heat Transfer Su Yongkang
School of Mechanical Engineering
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Background – Flow Considerations
Favorable
pressure gradient
0xP
Adverse
pressure gradient
0xP
Stagnation point Separation point
Wake
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 7
Background – Flow Considerations (Cont’d)
Boundary layer transition
Momentum of fluid in a turbulent boundary
layer is greater,and thus separation occurs
further along the object.
Example
How fast must a soccer ball travel to expect a
turbulent boundary layer?
But other factors also involved (surface roughness,
wind,ball spin,etc.)
s
m
DV
D 4.14
22.0
1089.15102Re 65
Heat Transfer Su Yongkang
School of Mechanical Engineering
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Convection heat transfer for cylinder
Complicated physics makes necessary using
empirical (experimental) correlations of heat
transfer coefficient and flow conditions.
Local Nusselt number
Heat Transfer Su Yongkang
School of Mechanical Engineering
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Convection heat transfer for cylinder (Cont’d)
Generally want the overall average Nusselt
number for heat transfer with the entire object,
As with a flat plate,correlations developed from
experimental data to compute Nu as a f(Rem,Prn)
Overall Average Nusselt number
All properties are evaluated at the freestream
temperature,except Prs which is evaluated at the
surface temperature,

6
41
31
10Re1
500Pr7.0
,f o r V a l i d
Pr
Pr
Pr Re
D
s
m
DD Ck
Dh
Nu
Heat Transfer Su Yongkang
School of Mechanical Engineering
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Values for C and m
Expect accuracy within? 20% with these
correlations
The empirical correlation due to Hilpert
Values of C and m are listed in Table 7.2.
All properties are evaluated at the film
temperature.
3/1PrRe m
DD Ck
DhNu
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 11
Example,Heat Loss from Smokestack
Given,Hot gas enters a exhaust stack shown at
150o C.
Find,
– Rate of heat loss from stack
–?T of the exhaust gas
C40Ts
Tin = 150o C
V = 1 m/s
2 m
20 m
T? = 0o C
V = 5 m/s
Assume,
Ignore radiation
heat loss
Steady state
conditions
Solution Method?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 12
Example,Heat Loss from Smokestack (Cont’d)
Compute Reynolds #
From table,
Values of C and m
From Table,C= 0.076 and m=0.7
Air properties (from Tables)
Pr of freestream = 0.714 ; Prs =0.705
C40Ts
Tin = 150o C
V = 1 m/s
2 m
20 m
T? = 0o C
V = 5 m/s
Km
W
2?h
sm /103 6 4.1 25
5
5
1035.7
10364.1
25
Re

VD
D
41
31
Pr
Pr Pr Re

s
m
DD Ck
DhNu
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 13
Example,Heat Loss from Smokestack (Cont’d)
Heat loss from stack
Now for?T of stack gas at 150oC
From property table,
Mass flow of stack gas:
Temperature change of stack gas:
Kkg
kJ
m
kg
02.1c ; 8 2 3.0 p3
C
pcm
qT
)( TTDLhq s?
4
2DVm
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 14
Example,
Assume that a person can be approximated as a
cylinder of 0.3-m diameter and 1.8-m height with a
surface temperature of 24℃,Calculate the body
heat loss while this person is subjected to a 15-m/s
wind whose temperature is -5 ℃,
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School of Mechanical Engineering
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Heat Transfer Su Yongkang
School of Mechanical Engineering
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Convection heat transfer with a sphere (§ 7.5)
External flow and heat transfer relations are
similar to those around a cylinder.
Numerous correlations proposed from lab
experiments,one being,
All properties except are evaluated at,
Special case,Free falling liquid drops

2.30.1
106.7Re5.3
380Pr71.0
,f o r V al i d
Pr)Re 0,0 6 Re ( 0,4 2
4
41
4.03221
s
D
s
DDD
k
Dh
Nu
3121 Pr Re 0,6 2 DDNu
sT
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 17
Back to cooling of lead shot example
How would you go about analyzing the cooling
of molten lead drops in this case?
Issues
Free-fall velocity,
terminal velocity
Transient conduction
in drop
Phase change energy
transfer
Radiation heat
transfer significant?
Convection heat
transfer coefficient
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 18
Convection heat transfer with banks of tubes
Typically,one fluid moves over the tubes,while a
second fluid at a different temperature passes
through the tubes,(cross flow)
The tube rows of a bank are staggered or aligned,
The configuration is characterized by the tube
diameter D,the transverse pitch and
longitudinal pitch,T
S
LS
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 19
Convection heat transfer with banks of tubes
(cont’d)
For tube bundles composed of 10 or more rows
3/1
1 PrRe13.1 m a x,
mD
DCNu?

10
0,7r
104Re2 0 0 0
,f o r v a l i d
4
m a x,
L
D
N
P
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 20
Convection heat transfer with banks of tubes
(cont’d)
All properties are evaluated at the film temperature.
Values for C and m,
For Reynolds number
DV
D m a xm a x,Re?
VDS SV
T
T
m a x VDS
SV
D
T
)(2m a x
If staggered and 2 DSS T
D
or
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for
large
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 21
Convection heat transfer with banks of tubes
(cont’d)
If a correction factor may be applied
And values for are from table
10?LN
)10(2)10(
LL N
DND NuCNu
2C
Heat Transfer Su Yongkang
School of Mechanical Engineering
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Convection heat transfer with banks of tubes
(cont’d)
More recent results have been obtained by
Zhukauskas.
All properties except are evaluated at the
arithmetic mean of the fluid inlet and outlet
temperatures.
Values for C and m.
If,a correction factor my be applied
4/1
36.0
Pr
PrPrRe
m a x,

s
mD
DCNu?

20
500r7.0
102Re1 0 0 0
,f o r v a l i d
6
m a x,
L
D
N
P
sPr
20?LN
)20(2)20( LL NDND NuCNu
Values for C2
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for
large
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 23
Convection heat transfer with banks of tubes
(cont’d)
For aligned tubes,typically the convection
coefficient of a row increases with increasing
row number until the fifth row.
For small values of,upstream rows
shield downstream rows form much of the flow,
and heat transfer is adversely affected,
is undesirable.
For the staggered array,
heat transfer enhanced is
favored by the more
Tortuous flow,
LT SS /
7.0/?LT SS
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 24
Convection heat transfer with banks of tubes
(cont’d)
For large change in temperature,the temperature
difference in Newton’s law of cooling should be the
log mean temperature difference.
Where and are temperature of the fluid as it
enters and leaves the bank.
Where N is the total number of tubes in the bank and
is the number of tubes in the transverse plane,
The heat transfer rate per unit length of the tubes is
)]/()l n [ (
)()(
osis
osis
lm TTTT
TTTTT

iT oT
TTi

pTTis
os
cSVN
hDN
TT
TT
e x p
TN
)( lmTDhNq
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 25
Convection heat transfer with banks of tubes
(cont’d)
The power required to move the fluid across the
bank is directly proportional to the p?
fVNp L

2
2
m a x
Correction factor
Friction factor
Aligned tubes
staggered tubes
Heat Transfer Su Yongkang
School of Mechanical Engineering
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Example,A preheater involves the use of condensing
steam at 100℃ on the inside of a bank of tubes to heat air
that enters at 1 atm and 25 ℃,The air moves at 5 m/s in
cross flow over the tubes,Each tube is 1 m long and has
an outside diameter of 10 mm,The bank consists of 196
tubes in a square,aligned array for which
mm,What is the total rate of heat transfer to the air?
What is the pressure drop associated with the airflow?
15 LT SS
Heat Transfer Su Yongkang
School of Mechanical Engineering
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Heat Transfer Su Yongkang
School of Mechanical Engineering
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External Flow,Summary and Review
KEY POINTS
External flow:
Boundary layer develops freely,without
constraints
Turbulent convective heat transfer generally
higher than laminar due to mixing effect within
boundary layer
Analytical solutions possible for simple cases
(laminar flow over flat plate)
3121x Pr Re 0,6 6 4 k xhuN xx
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 29
External Flow,Summary (Cont’d)
Difference in boundary layer growth for high
and low Pr number fluids
- impact on rate of heat transfer?
More complicated shapes like cylinders,spheres,
etc,solved using experimental correlations of
heat transfer coefficient,geometry and flow
conditions
y
x
th?
For large Pr (oils):
Pr > 1000
y
x
th?
For small Pr (liquid metals):
Pr < 0.1
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 30
Large photos for this lecture
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School of Mechanical Engineering
# 31
Large photos for this lecture
Heat Transfer Su Yongkang
School of Mechanical Engineering
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Have a good time!