Heat Transfer Su Yongkang
School of Mechanical Engineering
# 1
HEAT TRANSFER
CHAPTER 8
Internal flow
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 2
Internal Flow Heat Transfer
Where we’ve been ……
Introduction to internal flow,basic concepts,
energy balance.
Where we’re going,
Developing heat transfer coefficient
relationships and correlations for internal flow
ro
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 3
Internal Flow Heat Transfer
KEY POINTS THIS LECTURE
Convection correlations
– Laminar flow
– Turbulent flow
Other topics
– Non-circular flow channels
– Concentric tube annulus
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 4
Convection correlations,laminar flow in
circular tubes
1,The fully developed region
from the energy equation,we can obtain the
exact solution,
for constant surface heat flux
for constant surface temperature
Note,the thermal conductivity k should be
evaluated at,
36.4 khDNu D Cqs
66.3 khDNu D CTs?
mT
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 5
Convection correlations,laminar flow in
circular tubes
2,The entry region
for the constant surface temperature condition
thermal entry length
3/2
PrRe
L
D
04.01
PrRe
L
D
0,0 6 6 8
3,6 6

D
D
DNu
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 6
Convection correlations,laminar flow in
circular tubes
2,The entry region(cont’d)
for the combined entry length
For values of
14.03/1
/
PrRe86.1

s
DD
DLNu?
2/)/P r / (Re 14.03/1?sD DL
All fluid properties evaluated
at the mean T 2/,,omimm TTT
CTs?
700,16Pr48.0
75.9/0044.0 s
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 7
Convection correlations,turbulent flow in
circular tubes
A lot of empirical correlations are available.
For smooth tubes,the fully developed flow
Heating,
Cooling:
For rough tubes,coefficient increases with wall
roughness,For fully developed flows
Consider the entry length
For liquid metals,see textbook p461.
4.05/4 PrRe0 2 3.0 DDNu?
3.05/4 PrRe0 2 3.0 DDNu?
)1( P r)8/(7.121
Pr)1 0 0 0) ( R e8/(
3/22/1

f
fNu D
d
fdDD NuNu,?
or
m
fdD
D
Dx
C
Nu
Nu
)/(1,
Short tubes
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 8
Internal convection heat transfer coefficient
(summary)
1,For laminar and fully developed flow (§ 8.4.1):
i,q” constant,
ii,Ts constant:
2,For laminar flow in entry region (before fully
developed flow,§ 8.4.2:
i,Ts constant,
ii,Combined entry length with full tube:
3,For turbulent and fully developed (§ 8.5)
i,Heating
ii,Cooling
3/2
PrRe
L
D
04.01
PrRe
L
D
0,0 6 6 8
3,6 6

D
D
DNu
14.03/1
/
PrRe86.1

s
DD
DLNu?
All fluid properties evaluated
at the mean T 2/,,omimm TTT
Eq,8.53
Eq,8.55
Eq,8.56
Eq,8.57
Eq,8.60
4.05/4 PrRe0 2 3.0 DDNu?
3.05/4 PrRe0 2 3.0 DDNu?
36.4?DNu
36.3?DNu
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 9
Example,Oil at 150℃ flows slowly through a long,thin-
walled pipe of 30-mm inner diameter,The pipe is suspended
in a room for which the air temperature is 20 ℃ and the
convection coefficient at the outer tube surface is 11W/m2.K,
Estimate the heat loss per unit length of tube.
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 10
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 11
Internal Flow Heat Transfer
(summary)
If constant heat flux,mean fluid temperature can be
computed directly from the pipe area and inlet
temperature
For constant wall temperature (such as if phase
change occurs on outer pipe surface),mean fluid
temperature will asymptotically approach the wall
surface temperature,Ts
Log mean temperature difference
Use appropriate correlation equations for
convection heat transfer based on flow conditions
(laminar vs,turbulent,fully developed?),
Evaluate fluid properties at mean fluid temperature
inpco n vxm Tcm
PqT x
,

hcm xPTT xTT
pims
ms
-e x p )(
,?
ln io ioLM TT TTTL M T D
L M T DAUTAUq sLMsc on v
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 12
Example,Air at 1atm and 285 K enters a 2-m long
rectangular duct with cross section 75 mm by 150 mm,The
duct is maintained at a constant surface temperature of 400 K,
and the air mass flow is 0.10 kg/s,Determine the heat transfer
rate from the duct to the air and the air outlet temperature,
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 13
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 14
Additional Topic,Noncircular Tubes
Use hydraulic diameter,Dh
For turbulent flow,reasonably good analysis
using same equations as for circular tubes.
For laminar flow,Nusselt number have been
determined for various shapes (Table 8.1)
c h a n n e l f l o w t h eofl e n g t h p e r i m e t e r t h eis P
c h a n n e l f l o w t h eof a r e a s e c t i o n a l-c r o s s t h eis
4
c
c
h
A
P
AD?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 15
Additional Topic,Concentric Tube Annulus
Heat transfer analysis for both tube surfaces
Flow in the inner tube computed using methods
already presented
Heat transfer for fluid in the tube annulus can
involve heat transfer coefficient calculation on
both inner and outer surface,Calculate using
the hydraulic diameter
Separate Nusselt # for inner and outer surface,
for example
Coefficients Nuii,etc,from Tables 8-2,8-3.
ir
orim
i Tmh
,,?
omTm,,Tho,
ioh DDD
iio iii qqNuNu 1
)(,misii TThq
)(,mosoo TThq
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 16
Additional Topic,heat transfer enhancement
Enhancement
Increase the convection coefficient
Introduce surface roughness to enhance turbulence,
Induce swirl.
Increase the convection surface area
Longitudinal fins,spiral fins or ribs.
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 17
Additional Topic,heat transfer enhancement
Helically coiled tube
Without inducing turbulence or additional heat
transfer surface area.
Secondary flow
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 18
Keep up the good work!