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MECE 4364 Heat Transfer
Prof. Dong Liu
Department of Mechanical Engineering
University of Houston
1
Lecture 21 – Oct 28, 2010
Lecture 21
Forced Convection
2
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Internal Convection: Overview
±
Laminar flow in circular tube
±
velocity boundary layer
thickens on surface of tube with increasing x
±
inviscid region of uniform velocity shrinks as boundary layer grows
±
subsequent to boundary layer merger at the centerline, the velocity profile
becomes parabolic and invariant with x
→
hydrodynamically fully developed
∂
u
x
=
0
u
x
≠
0
3
Lecture 21
Pressure Gradient and Friction Factor
±
Define the Moody (or Darcy) friction factor
±
Fanning friction factor
±
Note that
±
For fullydeveloped laminar flow in circular tube
( )
2
2
h
m
dp dx D
f
u
ρ
−
≡
4
0
22
rr
s
f
mm
du
dr
C
uu
μ
τ
ρρ
=
⎞
⎛
−
⎜⎟
⎝
⎠
≡=
4
f
f
C
=
64
Re
D
f
=
(why?)
(
)
()
2
,
2
,
o
c
c
r
A
m
co
o
urxdA
r
x
r
d
r
Ar
==
∫
∫
Lecture 21
Moody Diagram
±
Fullydeveloped turbulent flow in a
smooth
circular tube
5
( )
2
6
0.790 1n Re
1.64
3000
Re
5 10
DD
f
−
=−
≤
≤
×
1/4
4
1/5
4
0.316Re
Re
2 10
0.184Re
Re
2 10
D
D
f
f
−
−
=≤
×
=≥
×
or
Lecture 21
Pressure Drop and Pumping Power
±
The pressure drop can be determined from the friction factor f
±
For fully developed flow from the axial position x
1
to x
2
±
The
pump power
required to overcome the resistance to flow from this
pressure drop is
Δ
p
=
p
1
−
p
2
dp
p
1
p
2
∫
=
f
ρ
u
m
2
2
D
h
dx
x
1
x
2
∫
=
f
u
m
2
2
D
h
x
2
−
x
1
()
( )( ) ( )
( )
Pp
p
m
=Δ ∀=Δ
±
±
6
(apply for both laminar and turbulent flows)
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Thermal Considerations
±
Internal Flows: Thermal Effects
±
assume
laminar flow
with uniform inlet temperature T
i
±
two common boundary conditions
²
uniform heat flux
²
uniform surface temperature
±
simplest internal flow:
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This note was uploaded on 01/27/2011 for the course MECE 4364 taught by Professor Lipinglui during the Winter '10 term at University of Houston.
 Winter '10
 LipingLui

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