14–81
14–82
Mass Convection
14-118C The region of the fluid near the surface in which concentration gradients exist is called the concentration
99.0
,
,=
−
−
sA
AsA
14-119C The dimensionless Schmidt number is defined as the ratio of momentum diffusivity to mass diffusivity
AB
D/Sc
=
, and it represents the relative magnitudes of momentum and mass diffusion at molecular level in the velocity
and concentration boundary layers, respectively. The Schmidt number corresponds to the Prandtl number in heat transfer. A
AB
14-122C Mass convection is expressed on a mass basis in an analogous manner to heat transfer as
)( ,,massconv
−= AsAs
Ahm
where hmass is the average mass transfer coefficient in m/s, As is the surface area in m2, and
,, and AsA
are the densities of
14-124C Yes, the Grasshof number evaluated using density difference instead of temperature difference can also be used in
14-125C The relation f Re / 2= Nu = Sh is known as the Reynolds analogy. It is valid under the conditions that the Prandtl,
AB
14–83
14-126C The relation f / 2 = St Pr2/3 = StmassSc2/3 is known as the Chilton-Colburn analogy. Here St is the Stanton number,
Pr is the Prandtl number, Stmass is the Stanton number in mass transfer, and Sc is the Schmidt number. The relation is valid
for 0.6 < Pr < 60 and 0.6 < Sc < 3000. Its importance in engineering is that Chilton-Colburn analogy enables us to determine
the seemingly unrelated friction, heat transfer, and mass transfer coefficients when only one of them is known or measured.
14-127C Using the analogy between heat and mass transfer, the mass transfer coefficient can be determined from the
relations for heat transfer coefficient using the Chilton-Colburn Analogy expressed as
3/2
3/2
3/2
heat Le
Sc
h
14-128C The relation hheat =
cp hmass is the result of the Lewis number Le = 1, and is known as the Lewis relation. It is
valid for air-water vapor mixtures in the temperature range encountered in heating and air-conditioning applications. The
14-129C A convection mass transfer is referred to as the low mass flux when the flow rate of species undergoing mass flow
14-130 Carbon dioxide and air are separated by a flat rubber plate. The mass concentration gradient of carbon dioxide at the
DAB = 1.6 × 10−5 m2/s (Table 14-2).
Analysis With the CO2 diffuses through the rubber plate being convected by air on the other side, we can write the mass
transfer at the air-side plate surface as
sAAA jjj ,conv,diff, ==
A
d
14–84
14-131 A film of water on a concrete is undergoing mass convection to air. The mass fraction gradient of water at the surface
is to be determined.
14–85
14-132 The average Reynolds number, Schmidt number, Sherwood number, and friction coefficient for (a) an evaporation
process and (b) a sublimation process are to be determined.
14–86
14–87
14–88
14-135 Ethyl alcohol is spread over a flat table where dry air is blowing over it. The average mass transfer coefficient is to be
determined.
Assumptions 1 The low mass flux model and thus the analogy between heat and mass transfer is applicable. 2 The critical
Reynolds number for flow over a flat plate is 500,000.
44.183)3017.1()020,64(664.0ScRe664.0Sh 3/15.01/35.0 ===
m/s 0.00220=
==
−
m 1
/s)m 102.1)(44.183(
Sh 25
mass L
D
hAB
14–89
14-136 A wet flat plate is dried by blowing air over it. The mass transfer coefficient is to be determined.
Assumptions 1 The low mass flux model and thus the 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 The critical Reynolds number for flow over a
flat plate is 500,000.
s/m 1078.2
atm 839.0
)K 288(
1087.1
25
072.2
10
−
−
=
=
The Reynolds number of the flow is
m) m/s)(2 3(
VL
14–90
14–91
14-138 Wet steel plates are to be dried by blowing air parallel to their surfaces. The rate of evaporation from both sides of a
plate is to be determined.
Assumptions 1 The low mass flux model and thus the 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 The critical Reynolds number for flow over a
Pr = 0.7309
25C
6 m/s
14–92
14-139E Air is blown over a square pan filled with water. The rate of evaporation of water and the rate of heat transfer to the
pan to maintain the water temperature constant are to be determined.
Assumptions 1 The low mass flux model and thus the analogy between heat and mass transfer is applicable since the mass
( )
/sft102.734=/sm1054.2
atm1
K300
1087.11087.1 2425
072.2
10
072.2
10
air–OH2
−−−− ==== P
T
DDAB
the entire surface. The Schmidt number in this case is
/sft10697.1
24
−
1 atm
10 ft/s
30% RH
air
14–93
14-140E Air is blown over a square pan filled with water. The rate of evaporation of water and the rate of heat transfer to the
pan to maintain the water temperature constant are to be determined.
Assumptions 1 The low mass flux model and thus the analogy between heat and mass transfer is applicable since the mass
( )
/sft102.53=/sm1035.2
atm1
K9.288
1087.11087.1 2425
072.2
10
072.2
10
air–OH2
−−−− ==== P
T
DDAB
ft/s 0.0323
ft 15/12
/s)ft10 53.2)(5.159(
Sh 24
mass =
==
−
L
D
hAB
00325.0
lbmollbm/29
lbmollbm/18
psia14.7
psia) 2563.0)(3.0(
,, =
===
air
A
sat
A
sAsA M
M
P
P
M
M
yw
01082.0
lbmollbm/29
lbmollbm/18
psia14.7
psia) 2563.0)(0.1(
,, =
===
air
A
sat
air
A
AA M
M
P
P
M
M
yw
Then the rate of mass transfer to the air becomes
3
14–94
14–95
14–96
14-143 A wet flat plate is dried by blowing air over it. The mass transfer coefficient is to be determined.
Assumptions 1 The low mass flux model and thus the analogy between heat and mass transfer is applicable since the mass
s/m 101.702= 25−
Analysis The mass diffusivity of water vapor in air
s/m 1077.2
atm 1
)K 313(
1087.1
1087.1
25
072.2
10
072.2
10
air–OH2
−
−
−
=
=
=
=
P
T
DDAB
1517)614.0)(871100,175,1037.0(871)ScRe037.0(Sh 3/18.01/38.0 =−=−=
m/s 0.00525=
==
−
m 8
/s)m 1077.2)(1517(
Sh 25
L
D
hAB
mass
Dry air
40C
1 atm
2.5 m/s
Wet
14–97
14–98
14-145 A raindrop is falling freely in atmospheric air. The terminal velocity of the raindrop at which the drag force equals the
weight of the drop and the average mass transfer coefficient are to be determined.
Assumptions 1 The low mass flux model and thus the analogy between heat and mass transfer is applicable since the mass
14–99
14-146E The liquid layer on the inner surface of a circular pipe is dried by blowing air through it. The mass transfer
coefficient is to be determined.
s/ft 1073.2
s/m 1054.2
1
)8.1/540(
1087.1
1087.1
24
25
072.2
10
072.2
10
air–OH2
−
−−
−
=
==
== P
T
DDAB
Wet pipe
Air, 540 R
1 atm, 6 ft/s
14-100
14-147 The liquid layer on the inner surface of a circular pipe is dried by blowing air through it. The mass transfer coefficient
is to be determined.
Assumptions 1 The low mass flux model and thus the 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 The flow is fully developed.
ℎmass = Sh𝐷𝐴𝐵
(3.66)(2.54 ×10−5 m2
s)