Quiz+3A
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University of Texas, Arlington *
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Course
3314
Subject
Aerospace Engineering
Date
Jan 9, 2024
Type
Pages
2
Uploaded by DrDovePerson615
Hyejin Moon (Hyejin.moon@uta.edu)
MAE 3314: Heat Transfer
TYPE A
Quiz #3 (10/9/2023) 15 min
Bonus Point 20
Name: ________________________
1.
Select
all
true statement(s) about Biot number (Bi). [5 pts]
(a) Dimensionless time
(b) Dimensionless thermal conductivity
(c)
!"#$%"&’ #)$%*&’ %$+,+#&"-$
$.#$%"&’ #)$%*&’ %$+,+#&"-$
(d) Bi decreases as the characteristic length of the conducting medium increases.
(e) Bi decreases as the thermal conductivity of the conducting medium increases.
2.
Figure below shows a plane wall being cooled by the cold fluid following over its surfaces.
(2-1)
Which case does have the largest Bi? [5 pts]
(2-2)
Which case will you apply the lumped capacitance method? [5 pts]
3.
Consider heat transfer between two identical hot solid bodies and their environments.
•
Case A
: The solid is dropped in a large container filled with water vigorously stirred by an agitator.
•
Case B
: The solid is allowed to cool naturally in the calm air.
For which case is the lumped capacitance analysis more likely to be applicable?
[5pts]
4.
Consider transient conduction in two metal spheres. Sphere A has a diameter 1000 times larger than that
of Sphere B. Which sphere is more likely good to go with a lumped method solution?
[5 pts]
5.
Consider a baked turkey out of the oven just now. It takes 1 minute for the turkey to drop its temperature
by 1
o
C. How long would it take to drop another 1
o
C of this turkey? [5 pts]
(a) 1 min
(b) less than 1 min
(c) longer than 1 min
6.
[T/F questions] For the
lumped capacitance method
solution; [5 pts each]
•
______ Spatial variation of temperature within conducting body is
considerably large
.
•
______ The temperature of a body approaches the ambient temperature
T
∞
linearly w.r.t time
.
•
______ The temperature of the body changes rapidly in the beginning, but rather slowly later on.
•
______ A larger thermal time constant (
τ
t
=
ρVc
p
/
h
A
s
) indicates that the body approaches the
environment temperature within a shorter time.
(a)
(b)
(c)
Hyejin Moon (Hyejin.moon@uta.edu)
7.
Consider an infinite cylinder under the transient conduction. If Bi >> 1, the
temperature solution with spatial effect is given as:
/(
%
,#)
3
/
!
/
"
3
/
!
= ࠵?
4
exp
(
−
࠵?
4
5
࠵?࠵?)
࠵?
6
(
࠵?
4
࠵?
∗
)
(7-1)
If you are finding the temperature of the surface of the cylinder, what
is the dimensionless position? [5 pts]
(a) 0
(b) 1
(c) r
0
(d) r
0
/2
(e) r
0
/3
(f) r
(7-2)
If you are finding the temperature of the centerline of the cylinder, what is the dimensionless
position? [5 pts]
(a) 0
(b) 1
(c) r
0
(d) r
0
/2
(e) r
0
/3
(f) r
(7-3)
If the dimensionless temperature at the center (
r
= 0) at
t
=
t
1
is
1.0
, what is the dimensionless
temperature at the surface of the cylinder (
r = r
0
) at
t = t
1
? [5 pts]
(a) C
1
(b) C
1
exp(-ζ
1
2*
Fo)
(c) J
0
(ζ
1
)
(e) ζ
1
(f) 0
(g) 1
(h)
r/r
0
8.
The ground soil was initially at a uniform temperature of -8
o
C. At t=0, suddenly, the ground surface is
exposed to the hot wind with the temperature of 40
o
C and the convection heat transfer coefficient of 50
W/m
2
-K for 10 hours. To determine the soil temperature at distance 20 cm from the earth’s surface at
the end of 10-h period, which equation would you use? [5 pts]
(a)
(b)
(c)
(d)
9.
Which
boundary
and/or
initial
condition(s) will be used to solve the differential equation in Problem 8?
Choose all. [5 pts]
(a)
(b)
(c)
(d)
(e)
10.
Which plot is the temperature profile of Problem 8? [5 pts]
(a)
(b)
(c)
d
2
T
dx
2
+
d
2
T
dy
2
=
0
d
2
T
dx
2
+
d
2
T
dy
2
=
1
α
∂
T
∂
t
1
x
∂
∂
x
(
x
∂
T
∂
x
)
=
ρ
c
p
k
∂
T
∂
t
∂
2
T
∂
x
2
=
1
α
∂
T
∂
t
@
x
=
0,
∂
T
∂
x
x
=
0
=
0
@
x
→ ∞
,
T
(
x
,
t
)
=
T
i
@
x
→ ∞
,
T
(
x
,
t
)
=
T
∞
@
x
=
0,
−
k
∂
T
∂
x
x
=
0
=
h
[
T
−
T
∞
]
@
t
=
0,
T
=
T
i
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