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.
Assume multiple single degree of freedom systems with natural periods T ∈ [0.05, 2.00] seconds with in-crement of period dT = 0.05 seconds. Assume three cases of damping ratio: Case (A) ξ = 0%; Case (B)ξ = 2%; Case (C) ξ = 5%. The systems are initially at rest. Thus, the initial conditions are u(t = 0) = 0 anḋu(t = 0) = 0. The systems are subjected to the base acceleration that was provided in the ElCentro.txt file(i.e., first column). For the systems in Case (A), Case (B), and Case (C) and for each natural period computethe peak acceleration, peak velocity, and peak displacement responses to the given base excitation. Please,use the Newmark method for β = 1/4 (average acceleration) to compute the responses. Create threeplots with three lines in each plot. The first plot will have the peak accelerations in y-axis and the naturalperiod of the system in x-axis. The second plot will have the peak velocities in y-axis and the natural periodof the system in x-axis. The third plot will have…
Both portions of the rod ABC are made of an aluminum for which E = 70 GPa.
Based on the given information find:
1- deformation at A
2- stress in BC
3- Total strain
4- If v (Poisson ratio is 0.25, find the
lateral deformation of AB
Last 3 student ID+ 300 mm=L2
724
A
P=Last 2 student ID+ 300 KN
24
24
Diameter Last 2 student ID+ 15 mm
Last 3 student ID+ 500 mm=L1
724
C
B
24
Q=Last 2 student ID+ 100 KN
24
Diameter Last 2 student ID+ 40 mm
Q2Two wooden members of uniform cross section are joined by the simple scarf splice shown. Knowing that the
maximum allowable tensile stress in the glued splice is 75 psi, determine (a) the largest load P that can be safely
supported, (b) the corresponding shearing stress in the splice.
น
Last 1 student ID+5 inch=W
=9
4
L=Last 1 student ID+8 inch
=12
60°
P'
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning