Heat Transfer Su Yongkang
School of Mechanical Engineering
# 1
HEAT TRANSFER
CHAPTER 9
Free Convection
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 2
Natural Convection
Where we’ve been ……
Up to now,have considered basic concepts of
natural convection,the governing equations
and laminar free convection on vertical surface.
Where we’re going:
Consider empirical correlations for natural
convection.
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 3
Empirical Correlations
Typical correlations for heat transfer coefficient
developed from experimental data are expressed as:
Vertical Plate
For an plate at
constant Ts

3 Pr LTTg GrRa s
LL?

LRaLog 10
LNuLog 10
n
LL C R ak
LhNu
Rayleigh number

3/1
4/1
n
n
For T
For L
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 4
Empirical Correlations (Cont’d)
Vertical Plate (Cont’d)
Alternative applicable to entire Rayleigh
number range (for constant Ts)
Vertical Cylinders
Use same correlations for vertical flat plate
if:
Inclined Plate

2
27/816/9
6/1
P r )/492.0(1
387.0825.0

LL RaNu
4/1
35 ~
LGrL
D?
Eq
9.26
See Figure 9.7
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 5
Empirical Correlations (Cont’d)
Horizontal Plate
Cold Plate
(Ts < T?)
Hot Plate
(Ts > T?)
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 6
Empirical Correlations (Cont’d)
Horizontal Plate (Cont’d)
Define the characteristic length,L as
Upper surface of heated plate,or
Lower surface of cooled plate,
Lower surface of heated plate,or
Upper surface of cooled plate,

1173/1
744/1
1010 15.0
1010 54.0

LLL
LLL
RaRaNu
RaRaNu
1054/1 1010 27.0 LLL RaRaNu
Note,Use fluid properties at the
film temperature 2 TTT sf
P
AL s?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 7
Empirical Correlations (Cont’d)
Long Horizontal Cylinder
Very common geometry (pipes,wires)
For isothermal cylinder
surface,use general
form equation for
computing Nusselt #
Constants for general
Nusselt number equation
RaD C n
0,3 3 3 0,1 2 5 10 - 10
0,2 5 0 0,4 8 0 10 - 10
0,1 8 8 0,8 5 0 10 - 10
0,1 4 8 1,0 2 10 - 10
0,0 5 8 0,6 7 5 10 - 10
127
74
42
22
210

Table 9.1
Eq
9.33 n
DD C R ak
DhNu
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 8
Example,Heated Wire
Given:
Coil of wire in an electrical resistance baseboard
heater
Assume that the wire can be treated as a
horizontal cylinder
Wire is 1 mm in diameter
Find:
Heat loss to room per unit length of wire
Using air properties at a film temperature of
oC
C120sT
C20T
702TTT sf
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 9
Example,Heated Wire
At a Rayleigh # of,C =,n=
Compute Nusselt # and convection coefficient
Rate of heat transfer to air is:
l en g t h of W / m)T-D ( Th sq

3 DTTg Ra s
D

n
DD C R ak
DhNu
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 10
Example,Determine the average convection heat
transfer coefficient for the 2.5-m high vertical walls of
a home having respective interior air and wall surface
temperature of (a) 20 and 10 oC and (b) 27 and 37 oC,
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 11
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 12
Example,An electrical heater in the form of a horizontal
disk of 400-mm diameter is used to heat the bottom of a
tank filled with engine oil at a temperature of 5 oC,
Calculate the power required to maintain the heater
surface at 70 oC,
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 13
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 14
Natural (Free) Convection
KEY POINTS OF FREE CONVECTION
Natural or free convection is common
phenomena,but generally has lower heat
transfer rates than in forced convection for
similar temperature differences
Grashof number for free convection is similar
to Reynolds number in forced convection
Rayleigh number is used to account for relative
impact of buoyancy and viscous forces acting as
same time
Most problems solved using equations derived
from empirical data of the form:
Evaluate fluid properties at the film temperature

f o r c e s V i s c o u s
f o r c e sB u o y a n c y
2
3
LTTgGr s
L

P r Pr 3
2
3 LTTgLTTg GrRa ss
LL

nDD RaCk DhNu