13-102
13–116 The temperature, pressure, and composition of combustion gases flowing inside long tubes are given. The rate of heat
transfer from combustion gases to tube wall is to be determined.
atm 09.0atm) 1(09.0
2
H
===
PyP
Ow
The mean beam length for an infinite cicrcular cylinder is, from
034.0
atm 1 , =
c
and
016.0
atm 1 , =
w
0.0
6.0
06.009.0
09.0
07.0042.0028.0
=
=
+
=
+
=+=+
cw
w
wc
PP
P
LPLP
Then the effective emissivity of the combustion gases becomes
0.050.0016.01034.01
atm 1 ,atm 1 , =−+=−+=
wwccg CC
031.0
atm 1 , =
c
and
027.0
atm 1 , =
w
041.0)027.0(
K 600
K 1500
)1(
056.0)031.0(
K 600
K 1500
)1(
45.0
atm 1 ,
45.0
65.0
atm 1 ,
65.0
=
=
=
=
=
=
w
s
g
ww
c
s
g
cc
T
T
C
T
T
C
Ts = 600 K
D = 15 cm
13-103
13–117 The temperature, pressure, and composition of combustion gases flowing inside long tubes are given. The rate of heat
transfer from combustion gases to tube wall is to be determined.
atm 09.0atm) 1(09.0
2
H
===
PyP
Ow
The mean beam length for an infinite cicrcular cylinder is, from
Table 13–4,
L = 0.95(0.15 m) = 0.1425 m
Ts = 600 K
D = 15 cm
Combustion
13-104
13–118 The temperature, pressure, and composition of combustion gases flowing inside long tubes are given. The rate of heat
transfer from combustion gases to tube wall is to be determined.
atm 10.0atm) 1(10.0
2
H
===
PyP
Ow
The mean beam length for this geometry is, from Table 13–4,
L = 3.6
V
/As = 1.8D = 1.8(0.20 m) = 0.36 m
where D is the distance between the plates. Then,
atmft .1180atmm 036.0m) atm)(0.36 10.0( ==== LPLP wc
The emissivities of CO2 and H2O corresponding to these values at the gas temperature of Tg = 1200 K and 1atm are, from Fig.
13-36,
080.0
atm 1 , =
c
and
055.0
atm 1 , =
w
0025.0
5.0
10.010.0
10.0
236.0118.0118.0
=
=
+
=
+
=+=+
cw
w
wc
PP
P
LPLP
Then the effective emissivity of the combustion gases becomes
Note that the pressure correction factor is 1 for both gases since the total pressure is 1 atm. For a source temperature of Ts =
600 K, the absorptivity of the gas is again determined using the emissivity charts as follows:
atmft 0.059atmm 018.0
K 1200
K 600
m) atm)(0.36 10.0( ====
g
s
w
g
s
cT
T
LP
T
T
LP
The emissivities of CO2 and H2O corresponding to these values at a temperature of Ts = 600 K and 1atm are, from Fig. 13–36,
060.0
atm 1 , =
c
and
067.0
atm 1 , =
w
092.0)067.0(
K 600
K 1200
)1(
090.0)060.0(
K 600
K 1200
)1(
45.0
atm 1 ,
45.0
65.0
atm 1 ,
65.0
=
=
=
=
=
=
w
s
g
ww
c
s
g
cc
T
T
C
T
T
C
20 cm
Combustion
gases, 1 atm
Tg = 1200 K
13-105
Special Topic: Heat Transfer from the Human Body
13–120C Sensible heat is the energy associated with a temperature change. The sensible heat loss from a human body
13–121C Latent heat is the energy released as water vapor condenses on cold surfaces, or the energy absorbed from a warm
surface as liquid water evaporates. The latent heat loss from a human body increases as (a) the skin wettedness increases and
13–122C The insulating effect of clothing is expressed in the unit clo with 1 clo = 0.155 m2.C/W = 0.880 ft2.F.h/Btu.
13-123C Yes, roughly one-third of the metabolic heat generated by a person who is resting or doing light work is dissipated
to the environment by convection, one-third by evaporation, and the remaining one-third by radiation.
13–124C The operative temperature Toperative is the average of the mean radiant and ambient temperatures weighed by their
respective convection and radiation heat transfer coefficients, and is expressed as
surrambient
surrradambientconv
TT
ThTh
+
13-107
13-127 The average mean radiation temperature during a cold day drops to 18C. The required rise in the indoor air
temperature to maintain the same level of comfort in the same clothing is to be determined.
Assumptions 1 Air motion in the room is negligible. 2 The average clothing and exposed skin temperature remains the same.
3 The latent heat loss from the body remains constant. 4 Heat transfer through the lungs remain constant.
Properties The emissivity of the person is 0.95 (from Appendix tables). The convection heat transfer coefficient from the
13-109
13-129 Chilled air is to cool a room by removing the heat generated in a large insulated classroom by lights and students.
The required flow rate of air that needs to be supplied to the room is to be determined.
Assumptions 1 The moisture produced by the bodies leave the room as vapor without any condensing, and thus the classroom
has no latent heat load. 2 Heat gain through the walls and the roof is negligible.
Properties The specific heat of air at room temperature is 1.00 kJ/kgC (Table A-15). The average rate of metabolic heat
kg/s 0.725=
−
=
=
C15)C)(25kJ/kg (1.0
kJ/s 25.7
sensible total,
air Tc
Q
m
p
75 Students
13-110
13–130 A car mechanic is working in a shop heated by radiant heaters in winter. The lowest ambient temperature the worker
can work in comfortably is to be determined.
Assumptions 1 The air motion in the room is negligible, and the mechanic is standing. 2 The average clothing and exposed
skin temperature of the mechanic is 33C.
Properties The emissivity and absorptivity of the person is given to be 0.95. The convection heat transfer coefficient from a
W175 W)350(5.05.0
W200=kW 2.0kW) 4(05.005.0
totalgen,sensible gen,
totalrad,incident rad,
===
===
QQ
QQ
Under steady conditions, and energy balance on the body can be
0 W175)K) 306)[(K W/m10)(5.67m 8.1(95.0
)306)(m K)(1.8 W/m0.4( W)200(95.0
0)()(
4
surr
4428–2
surr
22
sensible gen,
4
surr
4
surrconvincident rad,
=+−−
−−
=+−−−−
T
T
QTTATTAhQ ssss
C11.8= =K 284.8
surr
T
13-131E An average person produces 0.50 lbm of moisture while taking a shower. The contribution of showers of a family of
four to the latent heat load of the air-conditioner per day is to be determined.
Properties The latent heat of vaporization of water is given to be 1050 Btu/lbm.
13-112
Review Problems
13–133 Two diffuse surfaces A1 and A2 placed at an specified orientation, (a) the expression for the view factor F12 in terms
of A2 and L, and (b) the value of the view factor F12 when A2 = 0.02 m2 and L = 1 m are to be determined.
Assumptions 1 The surfaces A1 and A2 are diffuse. 2 Both A1 and A2 can be approximated as differential surfaces since both
are very small compared to the square of the distance between them.
Analysis (a) The view factor for surfaces A1 and A2 can be determined using the integral
2
2
21
21
2
21
1
21
2
21
1
21
2
21
1
12
coscos
coscos
1
coscos
1
coscos
1
2
2 1
A
r
AA
r
A
dAA
r
A
dAdA
r
A
F
A
A A
=
=
=
=
 
21
21 coscos
and
1
cos2
Lr =
(2)
Substituting Eqs. (1) and (2) into the expression for F12, we get
2
2
2
2
1
2
1
12 4)cos2(
)(cos
L
A
A
L
F==
2
2
4L
Discussion The view factor F21 can simply be determined with the reciprocity relation as
2
1
12
2
1
21 4L
A
F
A
A
F==
13–134 An enclosure consisting of eight surfaces is considered. The number of view factors this geometry involves and the
number of these view factors that can be determined by the application of the reciprocity and summation rules are to be
determined.
4
3
1
6
5
2
13-114
13–136 Two parallel black disks are positioned coaxially, where the lower disk is heated electrically. The temperature of the
upper disk is to be determined.
4.0
25.0
2/2.0
2/
1
1=== L
D
R
and
8.0
25.0
2/4.0
2/
2
2=== L
D
R
)8.0(1
1
2
2
2=
+
+
R
13-115
13-137 A simple solar collector is built by placing a clear plastic tube around a garden hose. The rate of heat loss from the
water in the hose by natural convection and radiation is to be determined.
Assumptions 1 Steady operating conditions exist 2 The surfaces are opaque, diffuse, and gray. 3 Air is an ideal gas with
constant specific heats.
1–
25
K 003273.0
K )2735.32(
1
7275.0Pr
/sm 10632.1
C W/m.02607.0
=
+
=
=
=
=
−
k
D2 =6 cm
Plastic cover,
2 = 0.9, T2 =40C
Water
T = 25C
Tsky = 15C
13-119
13-141 Radiation heat transfer occurs between two parallel coaxial disks. The view factors and the rate of radiation heat
transfer for the existing and modified cases are to be determined.
13-120
13-142 Radiation heat transfer occurs between two square parallel plates. The view factors, the rate of radiation heat transfer
and the temperature of a third plate to be inserted are to be determined.