Water at 20°C and a flow rate of 0 .1 kg/s enters a heated, thin-walled tube with a diameter of 15 mm and length of 2 m. The wall heat flux provided by the heating elements depends on the wall temperature according to the relation q s " ( x ) = q s , o " [ 1 + α ( T s − T ref ) ] where q s " = 10 4 W / m 2 , α = 0.2 K − 1 , T r e f = 20 ° C , and T s , is the wall temperature in °C. Assume fully developed flow and thermal conditions with a convection coefficient of 3000 W / m 2 ⋅ K . (a) Beginning with a properly defined differential control volume in the tube, derive expressions for the variation of the water, T m ( x ) , and the wall, T s ( x ) ,temperatures as a function of distance from the tube inlet. (b) Using a numerical integration scheme, calculate and plot the temperature distributions, T m ( x ) and T s ( x ) on the same graph. Identify and comment on the main features of the distributions. Hint: The IHT integral function D E R ( T m , x ) can be used to perform the integration along the length of the tube. (c) Calculate the total rate of heat transfer to the water.
Water at 20°C and a flow rate of 0 .1 kg/s enters a heated, thin-walled tube with a diameter of 15 mm and length of 2 m. The wall heat flux provided by the heating elements depends on the wall temperature according to the relation q s " ( x ) = q s , o " [ 1 + α ( T s − T ref ) ] where q s " = 10 4 W / m 2 , α = 0.2 K − 1 , T r e f = 20 ° C , and T s , is the wall temperature in °C. Assume fully developed flow and thermal conditions with a convection coefficient of 3000 W / m 2 ⋅ K . (a) Beginning with a properly defined differential control volume in the tube, derive expressions for the variation of the water, T m ( x ) , and the wall, T s ( x ) ,temperatures as a function of distance from the tube inlet. (b) Using a numerical integration scheme, calculate and plot the temperature distributions, T m ( x ) and T s ( x ) on the same graph. Identify and comment on the main features of the distributions. Hint: The IHT integral function D E R ( T m , x ) can be used to perform the integration along the length of the tube. (c) Calculate the total rate of heat transfer to the water.
Solution Summary: The author explains the expressions for the variations of the water and the wall, as a function of distance from the tube inlet.
Water at 20°C and a flow rate of
0
.1 kg/s
enters a heated, thin-walled tube with a diameter of 15 mm and length of 2 m. The wall heat flux provided by the heating elements depends on the wall temperature according to the relation
q
s
"
(
x
)
=
q
s
,
o
"
[
1
+
α
(
T
s
−
T
ref
)
]
where
q
s
"
=
10
4
W
/
m
2
,
α
=
0.2
K
−
1
,
T
r
e
f
=
20
°
C
, and
T
s
, is the wall temperature in °C. Assume fully developed flow and thermal conditions with a convection coefficient of
3000
W
/
m
2
⋅
K
.
(a) Beginning with a properly defined differential control volume in the tube, derive expressions for the variation of the water,
T
m
(
x
)
, and the wall,
T
s
(
x
)
,temperatures as a function of distance from the tube inlet. (b) Using a numerical integration scheme, calculate and plot the temperature distributions,
T
m
(
x
)
and
T
s
(
x
)
on the same graph. Identify and comment on the main features of the distributions. Hint: The IHT integral function
D
E
R
(
T
m
,
x
)
can be used to perform the integration along the length of the tube. (c) Calculate the total rate of heat transfer to the water.
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Plot the displacement diagram for a cam with roller follower of diameter 10 mm. The required
motion is as follows;
1- Rising 60 mm in 135° with uniform acceleration and retardation motion.
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=
-20125
750 x2.01
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motion is as follows;
1- Rising 60 mm in 135° with uniform acceleration and retardation motion.
2- Dwell 90°
3- Falling 60 mm for 135° with Uniform acceleration-retardation motion.
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1 m
4 m
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Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning