CHE 312 (Winter 2001)
__________________
LAST NAME, FIRST
Quiz #1
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
I. A concrete wall, which has a surface area of 20 m2 and is 0.30 m thick, separates conditioned
room air from ambient air. The temperature of the inner surface of the wall is maintained at
25oK, and the thermal conductivity of the concrete is 1 W/m.oK.
1) If the outside wall temperature is – 10oC, the heat loss through the wall is
____________
2) If the heat gain through the wall is 500 W, the outside wall temperature is
____________
II. The heat flux through a wood slab 50 mm thick, whose inner and outer surface temperature
are 40 and 20oC, respectively, has been determined to be 40 W/m2.
The thermal conductivity of the wood is
____________
III. An aluminum plate 4 mm thick is mounted in a horizontal position, and its bottom surface is
well insulated. A special, thin coating is applied to the top surface such that it absorbed 90% of
any incident solar radiation, while having an emissivity of 0.20. The density  and specific heat C
of aluminum are known to be 2,700 kg/m3 and 900 J/kg.oK, respectively. Consider conditions for
which the plate is at a temperature of 25oC and its top surface is suddenly exposed to ambient air
at T = 20oC and to solar radiation that provides an incident flux of 1,000 W/m2. The convection
heat transfer coefficient between the surface and the air is h = 25 W/m2.oK. Stefan-Boltzmann
constant:  = 5.6710-8 W/m2.oK4.
1) The initial rate of change of the plate temperature is
____________
2) Neglect heat loss by radiation, the steady state temperature of the plate is
____________
3) Include heat loss by radiation, the steady state temperature of the plate is
____________
4) Neglect heat loss by radiation,
the time it takes for the plate to reach 40oC is
____________
IV. One surface of a 10-mm-thick wall of stainless steel (k = 15 W/m.oK) is maintained at 90oC
by condensing steam, while the opposite surface is exposed to an air stream for which T = 20oC
and h = 25 W/m2.oK.
Neglect radiation, the temperature of the surface adjoining the air is
V.
_______________
A. The direction of heat flow is always parallel to an isothermal surface.
B. Heat flux is a vector quantity.
a. A and B are true b. Only A is true
c. Only B is true
d. A and B are false
VI. A. The value of the thermal conductivity is independent of the coordinate direction for an
isotropic medium.
 T T  T
B. In rectangular coordinate T =
+
+
x
z
y
a. A and B are true b. Only A is true
c. Only B is true
d. A and B are false
CHE 312 (Winter 2001)
_______________________
LAST NAME, FIRST (2 pts)
Quiz #2
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
I. An aluminum plate 4 mm thick is mounted in a horizontal position, and its bottom surface is
well insulated. A special, thin coating is applied to the top surface such that it absorbed 90% of
any incident solar radiation, while having an emissivity of 0.20. The density  and specific heat C
of aluminum are known to be 2,700 kg/m3 and 900 J/kg.oK, respectively. Consider conditions for
which the plate is at a temperature of 25oC and its top surface is suddenly exposed to ambient air
at T = 20oC and to solar radiation that provides an incident flux of 1,500 W/m2. The convection
heat transfer coefficient between the surface and the air is h = 25 W/m2.oK. Stefan-Boltzmann
constant:  = 5.6710-8 W/m2.oK4.
1) The initial rate of change of the plate temperature is
____________
2) Neglect heat loss by radiation, the steady state temperature of the plate is
____________
3) Include heat loss by radiation, the steady state temperature of the plate is
____________
4) Neglect heat loss by radiation,
the time it takes for the plate to reach 40oC is
____________
II. A spherical, stainless steel canister is used to store reacting chemicals that provide for a
uniform heat flux q" = 2105 W/m2 to its inner surface. Stainless steel:  = 8055 kg/m3, Cp = 510
J/kgoK. Temperature gradient in the canister wall is negligible.
1) If the initial temperature of the wall is 500oK, the initial rate of change of the wall temperature
is
_______________
2) The steady state temperature of the wall is
_______________
For questions (3) and (4), the system is at steady state and the temperature gradient in the canister
wall is not negligible with thermal conductivity k = 60 W/moK.
3) The outside surface temperature (at ro) of the wall is
_______________
4) The inside surface temperature (at ri) of the wall is
_______________
III. Liquid oxygen, which has a boiling point of 90oK and a latent heat of vaporization of 214
kJ/kg, is stored in a spherical container whose outer surface is of 0.50 m diameter and at a
temperature of 263oK. The container is house in a laboratory whose walls are at 298oK. The
surface emissivity is 0.4 and the heat transfer coefficient associated with free convection at the
outer surface of the container is 10 W/m2oK. If 0.002 kg/s of oxygen must be vented from the
system, the air temperature in the laboratory is
CHE 312 (Winter 2001)
___________
_______________________
LAST NAME, FIRST (2 pts)
Quiz #3
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
I. A spherical, stainless steel canister is used to store reacting chemicals that provide for a
uniform heat flux q" = 3105 W/m2 to its inner surface. Stainless steel:  = 8055 kg/m3, Cp = 510
J/kgoK. Temperature gradient in the canister wall is negligible.
1) If the initial temperature of the wall is 500oK, the initial rate of change of the wall temperature
is
_______________
2) The steady state temperature of the wall is
_______________
For questions (3) and (4), the system is at steady state and the temperature gradient in the canister
wall is not negligible with thermal conductivity k = 60 W/moK.
3) The outside surface temperature (at ro) of the wall is
_______________
4) The inside surface temperature (at ri) of the wall is
_______________
II. The temperature distribution for a long fin with uniform cross section is
 = bexp(-mx) where  = T - T
(1)
A long copper rod of diameter D = 1 cm and thermal conductivity 380 W/moK is in air at 25oC
with a convection coefficient of 20 W/ m2oK. The temperature at the base is 100oC
1) For this rod, m from eq. (1) is
__________
2) If m = 5.0 m-1, the temperature at x = 10 cm is
__________
3) If m = 5.0 m-1, the heat transfer rate from the rod to the air is
__________
4) If the temperatures from a fixed distance x1 from the base are 75oC for the copper rod and
60oC for another long rod with different material, the thermal conductivity of this material is
25oC
Note: Both rods are in air at
with a convection coefficient of 20 W/
base temperature of 100oC and the same diameter.
___________
with the same
m2oK
III. A long cylindrical rod of diameter 200 mm with thermal conductivity of 1.0 W/moK
experiences uniform volumetric heat generation of 24,000 W/m3. The rod is encapsulated by a
circular sleeve having an outer diameter of 400 mm and a thermal conductivity of 4.0 W/moK.
The outer surface of the sleeve is exposed to air at 25oC with a convection coefficient of 20 W/
m2oK.
The temperature on the outer surface of the sleeve is
____________
CHE 312 (Winter 2001)
_______________________
LAST NAME, FIRST (2 pts)
Quiz #4
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
I. The temperature distribution for a long fin with uniform cross section is
 = bexp(-mx) where  = T - T
(1)
A long copper rod of diameter D = 0.5 cm and thermal conductivity 380 W/moK is in air at 25oC
with a convection coefficient of 25 W/ m2oK. The temperature at the base is 150oC
1) For this rod, m from eq. (1) is
__________
2) If m = 5.0 m-1, the temperature at x = 8 cm is
__________
3) If m = 5.0 m-1, the heat transfer rate from the rod to the air is
__________
4) If the temperatures from a fixed distance x1 from the base are 75oC for the copper rod and
60oC for another long rod with different material, the thermal conductivity of this material is
___________
Note: Both rods are in air at 25oC with a convection coefficient of 25 W/ m2oK with the same
base temperature of 150oC and the same diameter.
II. The steady-state temperature (oC) associated with selected nodal
points of a two-dimensional system having a thermal conductivity
of 2.0 W/moK are shown on the right. The isothermal surface is at
180oC.
1) The temperature at node 1 is
____________
2) The temperature at node 2 is
____________
3)
The
temperature
____________
at
node
3
is
4) Calculate the heat transfer rate per unit thickness normal to the page from the bottom half of
the right surface to the fluid.
______________
III. The outer surface of a hollow sphere of radius r2 is subjected to a uniform heat flux q 2" . The
inner surface at r1 is held at a constant temperature Ts,1. If the inner and outer sphere radii are r1 =
50 mm and r2 = 100 mm, what heat flux q 2" is required to maintain the outer surface at Ts,2 =
60oC, while maintain the inner surface is at Ts,1= 20oC? The thermal conductivity of the wall
material is k = 40 W/moK.
____________
CHE 312 (Winter 2001)
_______________________
LAST NAME, FIRST (2 pts)
Quiz #5
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
1
2
3
T2 = 444.32, T4 = 377.53, T6 = 419.36,
Thermal conductivity of the rod is 10 W/moK, x = y = .005 m
4
5
6 I. Steady state temperatures (oK) at three nodal point (2), (4), and (6)
of a long rectangular rod are as shown. The rod experiences a uniform
volumetric generation rate of 4107 W/m3. Two of its sides (left and
bottom) are maintained at a constant temperature of 300oK, while
others are insulated.
1) The temperature at node 1 is
________
2) The temperature at node 3 is
________
3) The temperature at node 5 is
________
4) The heat transfer rate per unit length (W/m) from the rod is
________
5) The heat transfer rate per unit length from the left-bottom quarter of the rod is _______
II. A slab with a thickness of 0.050 m is at an initial temperature of 25oC. The slab is heated by
passing a hot gas over its surfaces, with the gas temperature and the convection coefficient
assumed to have constant values of T = 600oC and h = 100 W/m2oK. Slab is made from a
materials with k = 0.50 W/moK and  = 3.510-7 m2/s.
1) The time required to achieve 75% of the maximum possible energy transfer is __________
2) After 30 minutes, the highest temperature in the slab is
__________
3) After 30 minutes, the lowest temperature in the slab is
__________
III. Asphalt pavement may achieve temperatures as high as 50oC on a hot summer day. Assume
that such a temperature exists throughout the pavement, when suddenly a rainstorm reduces the
surface temperature to 20oC. The total amount of energy (J/m2) that will be transferred from the
asphalt over a 30-min period in which the surface is maintained at 20oC can be determined from
the following formula
A)
k (Ts  Ti )
t
B)
k (Ts  Ti )t 1 / 2

C)
2k (Ts  Ti )t 1 / 2

D) None of the above
CHE 312 (Winter 2001)
______________________
LAST NAME, FIRST (8 pts)
Final Exam
(Note: Your numerical answers must be correct to 3 significant figures. There are 25 questions with 4
points each, however you can only obtain a maximum of 100 points. That means you can miss 2 questions
and still get 100% score.)
This test is given under the Honor System and by signing here ______________________
you have agreed that the work submitted is your work alone and that you neither sought
nor received help from others.
1
2
3
T2 = 408.24, T4 = 358.15, T6 = 389.52,
Thermal conductivity of the rod is 20 W/moK, x = y = .005 m
4
5
6 I. Steady state temperatures (oK) at three nodal point (2), (4), and (6)
of a long rectangular rod are as shown. The rod experiences a uniform
volumetric generation rate of 6107 W/m3. Two of its sides (left and
bottom) are maintained at a constant temperature of 300oK, while
others are insulated.
1) The temperature at node 1 is
________
2) The temperature at node 3 is
________
3) The temperature at node 5 is
________
4) The heat transfer rate per unit length (W/m) from the rod is
________
5) The heat transfer rate per unit length from the left-bottom quarter of the rod is _______
II. A sphere with a diameter of 0.050 m is at an initial temperature of 25oC. The sphere is heated
by passing a hot gas over its surface, with the gas temperature and the convection coefficient
assumed to have constant values of T = 600oC and h = 100 W/m2oK. Sphere is made from a
materials with k = 0.50 W/moK and  = 3.510-7 m2/s.
1) The time required to achieve 85% of the maximum possible energy transfer is __________
2) After 10 minutes, the highest temperature in the sphere is
__________
3) After 10 minutes, the lowest temperature in the sphere is
__________
III. Asphalt pavement may achieve temperatures as high as 50oC on a hot summer day. Assume
that such a temperature exists throughout the pavement, when suddenly a rainstorm reduces the
surface temperature to 25oC. Calculate the total amount of energy (J/m2) that will be transferred
from the asphalt over a 20-min period in which the surface is maintained at 25oC. Asphalt: k =
0.062 W/moK,  = 3.210-8 m2/s.
IV. Two large blocks of copper and concrete have been sitting in a room (23oC) for a very long
time. If a heat loss of 5 W occurs when your hand (37oC) touches the concrete block, estimate the
heat loss when you hand touches the copper block. Concrete: k = 1.4 W/moK,  = 6.910-7 m2/s.
Copper: k = 401 W/moK,  = 1.210-4 m2/s.
___________
V. An aluminum plate 4 mm thick is mounted in a horizontal position, and its bottom surface is
well insulated. A special, thin coating is applied to the top surface such that it absorbed 90% of
any incident solar radiation, while having an emissivity of 0.20. The density  and specific heat C
of aluminum are known to be 2,700 kg/m3 and 900 J/kg.oK, respectively. Consider conditions for
which the plate is at a temperature of 25oC and its top surface is suddenly exposed to ambient air
at T = 20oC and to solar radiation that provides an incident flux of 1,200 W/m2. The convection
heat transfer coefficient between the surface and the air is h = 25 W/m2.oK. Stefan-Boltzmann
constant:  = 5.6710-8 W/m2.oK4. The surrounding temperature is assumed to be 0oK.
1) The initial rate of change of the plate temperature is
____________
2) Neglect heat loss by radiation, the steady state temperature of the plate is
____________
3) Include heat loss by radiation, the steady state temperature of the plate is
____________
4) Neglect heat loss by radiation,
the time it takes for the plate to reach 40oC is
____________
VI. A spherical, stainless steel canister is used
to store reacting chemicals that provide for a
uniform heat flux q" = 3105 W/m2 to its inner
surface. Stainless steel:  = 8055 kg/m3, Cp =
510 J/kgoK. The system is at steady state and
the thermal conductivity k of the wall is 50
W/moK.
1) The outside surface temperature (at ro) of the wall is
_______________
2) The inside surface temperature (at ri) of the wall is
_______________
VII. Consider steady-state conditions for one-dimensional
conduction in a plane wall having a thermal conductivity k
= 60 W/moK and a thickness L = 0.50 m, with no internal
heat generation.
Determine the unknown quantity for each case.
CASE
T1(oC)
T2(oC)
dT/dx (K/m)
1
50
-10
_________
2
70
________
160
3
________
40
-80
T1
T2
x
L
VIII. A spherical object, 0.10 m in diameter, is suspended in still air. The temperature of the
object is uniform and radiation exchange with its surroundings is negligible. The ambient air
temperature is 25oC and the object has a mass of 2.0 kg and a specific heat of 2700 J/kgoK.
1. The area (m2) for heat transfer between the object and the ambient air is
___________
2. At the instant of time when the object temperature is 100oC and the change in the object
temperature with time is 0.03 K/s,
the rate of change of energy storage in the object is
____________
IX. Liquid oxygen, which has a boiling point of 90oK and a latent heat of vaporization of 214
kJ/kg, is stored in a spherical container whose outer surface is of 0.50 m diameter and at a
temperature of 263oK. The container is house in a laboratory whose walls are at 298oK. The
surface emissivity is 0.4 and the heat transfer coefficient associated with free convection at the
outer surface of the container is 10 W/m2oK. If the air temperature is 298oK, the rate in kg/s, at
which oxygen must be vented from the system is
____________
X. A long cylindrical rod of diameter 200 mm with thermal conductivity of 1.0 W/moK
experiences uniform volumetric heat generation of 30,000 W/m3. The rod is encapsulated by a
circular sleeve having an outer diameter of 400 mm and a thermal conductivity of 4.0 W/moK.
The outer surface of the sleeve is exposed to air at 25oC with a convection coefficient of 10 W/
m2oK.
The temperature on the outer surface of the sleeve is
____________
XI. In an orbiting space station, an electronic package is housed in a compartment having a
surface area As = 1 m2 which is exposed to space. The surface emissivity is 1.0. Under normal
operating conditions, the electronics dissipate 500 W, all of which must be transferred from the
exposed surface to space.
1) If the surface is not exposed to the sun, what is it steady-state temperature? _____________
2) If the surface is exposed to a solar flux of 750 W/m2 and its absorptivity to solar radiation is
0.25, what is it steady-state temperature?
_____________
CHE 312 (Winter 2001)
Answers to Quiz #1
I.
III.
IV.
VI.
1) 2,333 W, 2) 32.5oC
II. 0.1 W/moK
1) 0.0705 oK/s, 2) 329oK, 3) 324oK, 4) 257.2 s
88.85oC
V. c
b
Answers to Quiz #2
I.
1) 0.1168 oK/s, 2) 347oK, 3) 340o9K, 4) 142.1 s
III. 1) 0.1124 oK/s, 2) 577.8K, 3) 577.8K, 4) 855.6oK
IV. 310.5oK
Answers to Quiz #3
I.
1) 0.313 oK/s, 2) 716.7oK, 3) 716.7oK, 4) 1133oK
II. 1) 4.588m-1, 2) 70.5oC, 3) 11.2 W, 4) 107.5 W/moK
III. 55oC
Answers to Quiz #4
I.
1)
2)
3) 4.67 W, 4) 197 W/moK
o
II. 1) T1 = 155.7 C, T2 = 95.6oC, T3 = 52.2oC, b) 560 W/m
III. -16,000 W/m2
7.25m-1,
108.8oC,
Answers to Quiz #5
I.
1) 399.84oK, 2) 456.84oK, 3) 410.3 oK, 4) 6000 W/m, 5) 2163 W/m
II. 1) 1340 s, 2) 568.2oC, 3) ) 474.8oC
III. C