Transcript Convective Heat Transfer
HEAT TRANSFER Final Review
Heat Transfer # 1 Su Yongkang School of Mechanical Engineering
Final Review Session
Heat Transfer # 2 Su Yongkang School of Mechanical Engineering
Viscous Flow
•
The Navier-Stokes Equations
Nonlinear, second order, partial differential equations.
u
t
u
u
x
v
u
y
w
u
z
p
x
g x
2
u
x
2 2
u
y
2 2
u
z
2
v
t
u
v
x
v
v
y
w
v
z
p
y
g y
2
v
x
2 2
v
y
2 2
v
z
2
w
t
u
w
x
v
w
y
w
w
z
p
z
g z
2
w
x
2 2
w
y
2 2
w
z
2
u
x
v
y
w
z
0 •
Couette Flow, Poiseuille Flow.
Heat Transfer # 3 Su Yongkang School of Mechanical Engineering
Convection
• Basic heat transfer equation
q
h A s
(
T s
T
)
h
average heat transfer coefficient • Primary issue is in getting convective heat transfer coefficient,
h h
1
A s
A s h dA s
or, for unit width :
h
1
L
L
0
h dx
•
h
relates to the conduction into the fluid at the wall
h x
-
k f
T s
T
y
y T
0 Heat Transfer # 4 Su Yongkang School of Mechanical Engineering
Convection Heat Transfer Correlations
• Key is to fully understand the type of problem and then make sure you apply the appropriate convective heat transfer coefficient correlation
External Flow
For laminar flow over flat plate
T
,
U
y
dP
0
dx
T
s
Nu x
h x k x
0.332
Re 1 2 x Pr 1 3
N u x
h x k x
0.664
Re 1 2 x Pr 1 3 For mixed laminar and turbulent flow over flat plate
h x
1
L
xc
h lam
0
dx
L xc h turb dx
Nu L
0.6
0.037
Re Pr 60 4 L 5 10 5 Re
L
Eq.
7.41
5 10 8 871 Pr 1 Re 3 x, c 5 10 5 Heat Transfer # 5 Su Yongkang School of Mechanical Engineering
External Convection Flow
For flow over cylinder
Overall Average Nusselt number Nu D
h k D
C
Re
m D
Pr 1 3 Pr Pr
s
1 4
Table 7.2 has constants C and m as f(Re)
For flow over sphere
Nu D
h k D
2 (0.4
Re 1
D
2 0.06
Re 2
D
3 ) Pr 0 .
4
s
1 4
For falling liquid drop
Nu D
2 0.6
Re 1
D
2 Pr 1 3 Heat Transfer # 6 Su Yongkang School of Mechanical Engineering
Convection with Internal Flow
• Main difference is the constrained boundary layer r o • Different entry length for laminar and turbulent flow • Compare external and internal flow: –
External flow :
Reference temperature:
T
is constant –
Internal flow :
Reference temperature:
T m
transfer is occurring!
will change if heat • •
T m
increases if heating occurs (
T s > T m
)
T m
decreases if cooling occurs (
T s < T m
) Heat Transfer # 7 Su Yongkang School of Mechanical Engineering
Internal Flow (Cont’d)
T •
For constant heat flux:
T s
(
x
)
T m
(
x
) •
T m
,
x
q
conv
c p
x
T in
,
thermal
x
x fd
For constant wall temperature
T if T s T i T
T s
if T s T i
T m T m T s
x • Sections 8.4 and 8.5 contain correlation equations for Nusselt number
q conv
A s h
T LM
Heat Transfer x # 8 Su Yongkang School of Mechanical Engineering
Free (Natural) Convection
•
Unstable, Bulk fluid motion Stable, No fluid motion
Grashof number
in natural convection is analogous to the Reynolds number in forced convection
Gr L
g
T s
2
T
L
3 Buoyancy forces Viscous forces
Gr L
Re 2
L
1
Natural convection can be neglected
Gr L
Re 2
L
1
Natural convection dominates
Heat Transfer # 9 Su Yongkang School of Mechanical Engineering
Free (Natural) Convection
Rayleigh number :
For relative magnitude of buoyancy and viscous forces
Ra x
Gr x
Pr For vertical surface, transition to turbulence at
Ra x
10 9 • Review the basic equations for different potential cases, such as vertical plates, vertical cylinders, horizontal plates (heated and cooled) • For horizontal plates, discuss the equations 9.30 9.32. (P513) • Please refer to problem 9.34.
Heat Transfer # 10 Su Yongkang School of Mechanical Engineering
T A
,
out
Heat Exchangers
T B
,
in
(shell side)
Example: Shell and Tube:
T B
,
out
•
Cross-counter Flow
Two basic methods discussed:
1. LMTD Method
T A
,
in
(tube side)
2.
q
UA
T out
ln
T in
T o T i
UA
T LMTD
-NTU Method
q
q
max
or q
:
C
min
T h
,
i
T c
,
i
NTU
UA overall
,
HX C
min
where
:
q
max
q q
max
C
min
T h
,
i
T c
,
i
f
NTU
,
C r
C r
C C
min max C r 1 Heat Transfer # 11 Su Yongkang School of Mechanical Engineering
Discussion on the U
Notice!
• Equation 11.5
Example 11.1
1
UA
1
U i A i
1
h i A i
U o R f
,
i
1
A i A o
ln(
D o
/ 2
kL D i
)
R f
,
o A o
1
h o A o
• For the unfinned, concentric, tubular heat exchangers.
• When the inner tube surface area is the reference calculating area.
1
U i
1
h i
R f
,
i
ln(
D o
/ 2
kL D i
)
A i
R f
,
o A i A o
A i h o A o
• When the inner tube surface area is the reference calculating area.
1
U o
1
h o
R f
,
o
ln(
D o
/ 2
kL D i
)
A o
R f
,
i A o A i
A o h i A i
Heat Transfer # 12 Su Yongkang School of Mechanical Engineering
Discussion on the problems
Heat Transfer # 13 Su Yongkang School of Mechanical Engineering