Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
18-43
18-58 Tomatoes are placed into cold water to cool them. The heat transfer coefficient and the amount of heat transfer are to
be determined.
Assumptions 1 The tomatoes are spherical in shape. 2 Heat conduction in the tomatoes is one-dimensional because of
symmetry about the midpoint. 3 The thermal properties of the tomatoes are constant. 4 The heat transfer coefficient is
18-44
18-59 An egg is dropped into boiling water. The cooking time of the egg is to be determined.
Assumptions 1 The egg is spherical in shape with a radius of r0 = 2.75 cm. 2 Heat conduction in the egg is one-dimensional
because of symmetry about the midpoint. 3 The thermal properties of the egg are constant. 4 The heat transfer coefficient is
constant and uniform over the entire surface. 5 The Fourier number is > 0.2 so that the one-term approximate solutions (or
9925.1 and 0533.3 11 A
Then the Fourier number and the time period become
1633.0)9925.1(
1008
10060 2
2
1)0533.3(
1
0
,0
eeA
TT
TT
i
sph
15.0
435.0
1008
10060
0276.0
2.36
1
Bi
1
2
0
o
i
r
t
TT
TT
Then,
m) 0275.0)(15.0(
2
2
o
r
18-47
0.63
)(
1
16.1
1
TT
TrT
r
r
rh
k
Bi
o
o
o
(Fig. 18-15b)
C6.1)]15(3.11[63.0)15()(63.0 0 TTTTsurface
18-48
18-62 Prob. 18-61 is reconsidered. The effect of the initial temperature of the apples on the final center and surface
temperatures and the amount of heat transfer is to be investigated.
Analysis The problem is solved using EES, and the solution is given below.
k=0.418 [W/m-C]
rho=840 [kg/m^3]
c_p=3.81 [kJ/kg-C]
alpha=1.3E-7 [m^2/s]
18-49
0 5 10 15 20 25 30
-8
-4
0
4
8
12
16
20
Ti [C]
T [C]
T0
Tr
0 5 10 15 20 25 30
8
10
12
14
16
18
20
22
Ti [C]
Q [kJ]
18-51
18-64 A rib is roasted in an oven. The heat transfer coefficient at the surface of the rib, the temperature of the outer surface of
the rib and the amount of heat transfer when it is rare done are to be determined. The time it will take to roast this rib to
medium level is also to be determined.
18-52
Discussion The temperature of the outer parts of the rib is greater than that of the inner parts of the rib after it is taken out of
the oven. Therefore, there will be a heat transfer from outer parts of the rib to the inner parts as a result of this temperature
difference. The recommendation is logical.
18-54
Alternative solution: This problem can also be solved using transient temperature and heat transfer charts as follows:
2.0
Bi
1
543.0
1635.4
16377
1881.0
m) 08603.0(
60)s15+3600/s)(4m 1091.0(
0
2
27
2
TT
TT
r
t
i
o
(Fig. 18-15a)
C. W/m2.26
)m 08603.0(
)2.0/1)(C W/m.45.0( 2
o
o
r
kBi
h
k
hr
Bi
18-56
18-67E The center temperature of oranges is to be lowered to 40F during cooling. The cooling time and if any part of the
oranges will freeze during this cooling process are to be determined.
Assumptions 1 The oranges are spherical in shape with a radius of ro =1.25 in = 0.1042 ft. 2 Heat conduction in the orange is
843.1
FBtu/h.ft. 0.26
)ft 12/25.1(F).Btu/h.ft 6.4(
Bi
2
k
hro
From Table 18-2 we read, for a sphere, 1 = 1.9569 and A1 = 1.447. Substituting
426.0= 447.1
2578
2540
2
2
1)9569.1(
1
0
0
eeA
TT
TT
i
which is greater than 0.2 and thus the one-term solution is applicable. Then the cooling
oo
i
oo
i
o
irr
TT
rr
TT
rr
TT
/
/
/
1
1
1
Substituting,
F32.1=)(
1.9569
rad) 9569.1sin(
2578
2540
2578
25)(
o
orT
rT
which is above the freezing temperature of 31F for oranges. Therefore, no part of the oranges will freeze during this cooling
34.0
283.0
2578
2540
543.0
ft) F)(1.25/12.ºBtu/h.ft (4.6
FBtu/h.ft.º0.26
1
2
0
2
o
i
o
r
t
TT
TT
rh
k
Bi
Fig. (18-19a)
5/12ft)(0.43)(1.2
2
2
o
r
Orange
D = 2.5 in
85% water
Ti = 78F
Air
25F
1 ft/s
18-57
Transient Heat Conduction in Semi-Infinite Solids
18-68C A thick plane wall can be treated as a semi-infinite medium if all we are interested in is the variation of temperature
18-70C The total amount of heat transfer from a semi-infinite solid up to a specified time t0 can be determined by integration
from
t
18-58
4–72 A curing kiln is heated by injecting steam into it and raising its inner surface temperature to a specified value. It is to be
determined whether the temperature at the outer surfaces of the kiln changes during the curing period.
Assumptions 1 The temperature in the wall is affected by the thermal conditions at inner surfaces only and the convection
heat transfer coefficient inside is very large. Therefore, the wall can be considered to be a semi-infinite medium with a
18-73 The water pipes are buried in the ground to prevent freezing. The minimum burial depth at a particular location is to be
determined.
Assumptions 1 The temperature in the soil is affected by the thermal conditions at one surface only, and thus the soil can be
considered to be a semi-infinite medium with a specified surface temperature. 2 The thermal properties of the soil are
constant.
18-59
18-74 With the highway surface temperature maintained at 25°C, the temperature at the depth of 3 cm from surface and the
heat flux transferred after 60 minutes are to be determined.
Assumptions 1 The highway is treated as semi-infinite solid. 2 Thermal properties are constant. 3 Heat transfer by radiation
is negligible.
40.1
)s 6060)(/sm 10186.3(2
m 03.0
228
αt
x
C 53.6 C 55)04772.0)(C 55C 25(erfc(1.40))()s 3600 m, 03.0( iis TTTT
The heat flux transferred from the highway after 60 minutes is
TTk
)(
2
K )2555)(K W/m062.0(
18-75 An aluminum block is subjected to heat flux. The surface temperature of the block is to be determined.
Assumptions 1 All heat flux is absorbed by the block. 2 Heat loss from the block is disregarded (and thus the result obtained
is the maximum temperature). 3 The block is sufficiently thick to be treated as a semi-infinite solid, and the properties of the
18-60
4–76 A thick refractory brick wall is subjected to uniform heat flux. The temperature at the depth of 10 cm from the wall
surface after an hour is to be determined.
Assumptions 1 The wall is thick and can be treated as a semi-infinite medium with a specified surface heat flux. 2 The
thermal properties of the wall are constant.
169.1
)s 3600)(/sm 1008.5(2
m 1.0
227
t
x
C15
)s 3600)(/sm 1008.5(2
m 1.0
erfc)m 1.0(
)s 3600)(/sm 1008.5(4
)m 1.0(
exp
)s 3600)(/sm 1008.54(
K W/m0.1
W/m000,20
),(
27
27
227
2
txT
C64.5),( txT
where x = 0.1 m and t = 3600 s
Discussion At the wall surface after one hour, the temperature is 980°C
)s 3600)(/sm 1008.54(
K W/m0.1
W/m000,20
27
2
