Chapter 14
Mass Transfer
14119
A person is standing outdoors in windy weather. The rates of heat loss from the head by radiation,
forced convection, and evaporation are to be determined for the cases of the head being wet and dry.
Assumptions
1
The low mass flux conditions exist so that the ChiltonColburn analogy between heat and
mass transfer is applicable since the mass fraction of vapor in the air is low (about 2 percent for saturated
air at 300 K).
2
Both air and water vapor at specified conditions are ideal gases
(the error involved in this
assumption is less than 1 percent).
3
The head can be approximated as a sphere of 30 cm diameter
maintained at a uniform temperature of 30
C.
4
The surrounding surfaces are at the same temperature as
the ambient air.
Properties
The airwater vapor mixture is
assumed to be dilute, and thus we can use dry air
properties for the mixture.
The properties of air
at the free stream temperature of 25
C and 1 atm
are, from Table A15,
/s
m
10
56
.
1
s
kg/m
10
85
.
1
73
.
0
Pr
,
C
W/m
0255
.
0
2
5
5
k
Also,
s
@
.
30
5
187
10
C
kg / m s
. The
mass diffusivity of water vapor in air at the
average temperature of (25 + 30)/2 = 27.5
C =
300.5 K is, from Eq. 1415,
m²/s
10
55
.
2
atm
1
K
5
.
300
10
87
.
1
10
87
.
1
5
072
.
2
10
072
.
2
10
air

O
H
2
P
T
D
D
AB
The saturation pressure of water at 25
C is
P
[email protected] C
kPa.
3169
.
Properties of water at 30
C are
h
P
fg
v
2431
4 246
kJ / kg
and
kPa
.
(Table A9).
The gas constants of dry air and water are
R
air
= 0.287 kPa.m
3
/kg.K and
R
water
= 0.4615
kPa.m
3
/kg.K (Table A1). Also, the emissivity of the head is given to be 0.95.
Analysis
(
a
) When the head is dry, heat transfer from the head is by forced convection and radiation only.
The radiation heat transfer is
W
3
.
8
]
)
K
273
25
(
)
K
273
30
)[(
K
W/m
10
67
.
5
](
m)
3
.
0
(
)[
95
.
0
(
)
(
4
4
4
2
8
2
4
surr
4
rad
T
T
A
Q
s
s
The Reynolds number for flow over the head is
550
,
133
/s
m
10
1.56
)
m
0.3
)(
m/s
6
.
3
/
25
(
Re
2
5
D
V
Then the Nusselt number and the heat transfer coefficient become
269
10
87
.
1
10
85
.
1
73
.
0
550
,
133
06
.
0
550
,
133
4
.
0
2
Pr
Re
06
.
0
Re
4
.
0
2
Nu
4
/
1
5
5
4
.
0
3
/
2
2
/
1
4
/
1
0.4
3
/
2
2
/
1
s
C
W/m
9
.
22
(269)
m
0.3
C
W/m
0.0255
2
Nu
D
k
h
Then the rate of convection heat transfer from the head becomes
W
32.3
C
)
25
30
](
)
m
3
.
0
(
)[
C
.
W/m
9
.
22
(
)
(
2
2
conv
T
T
A
h
Q
s
s
1479
Air
25
C
1 atm
25 km/h
Head
D
=30 cm
Wet
30
C
Evaporation
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Chapter 14
Mass Transfer
Therefore,
W
40.6
3
.
8
32.3
rad
conv
dry
total,
Q
Q
Q
(
b
) When the head is wet, there is additional heat transfer mechanism by evaporation.
The Schmidt number
is
612
.
0
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '06
 Rajadas

Click to edit the document details