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EML 4142 Exam 1 Structure
Time Limit: 70 minutes (The exam will be open for 85 minutes. The extra time is for students to
upload work for Problems 5 and 6).
Tentative structure and tentative point distribution:
Question 1: (5 points) multiple-choice, regarding concepts or brief calculation in Chapter 1
Question 2: (5 points) multiple-choice, regarding concepts or brief calculation in Chapter 1
Question 3: (5 points) multiple-choice, regarding concepts or brief calculation in Chapter 1
Question 4: (5 points) multiple-choice, regarding concepts or brief calculation in Chapter 1
Question 5: (40 points) problem-solving question from Chapter 2, file upload is required
Question 6: (40 points) problem-solving question from Chapter 2, file upload is required
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EML4142 Exam 1 Coverage
Modules
Lecture Slides
Sections
Homework
Assignment
1&2 (video
available)
Chapter 1
1-1, 1-2, 1-3, 1-4, 1-5,
1-6, 1-7, 1-8, 1-9
HW #1
3 (video available)
Chapter 2
1-5, 1-6, 1-7, 1-8, 1-9
HW #2
Eml4142 Heat Transfer
Module 1&2 Chapter 1
Introduction and Basic Concepts
Practice Questions
Instructor: Tian Tian
Practice Question 1
You’ve experienced convection cooling if you’ve ever extended your hand
out the window of a moving vehicle or into a flowing water stream. With
the surface of your hand at a temperature of 30 ℃, determine the
convection heat flux for (a) a vehicle speed of 35 km/h in air at -5 ℃ with a
convection coefficient of 40 W/𝑚2 ∙ 𝐾 (b) a velocity of 0.2 m/s in a water
stream at 10 ℃ with a convection coefficient of 900 W/𝑚2 ∙ 𝐾.
Practice Question 2
Why do we feel chilled in the winter but comfortable in the summer under
conditions for which the same room temperature is maintained by a heating
or cooling system?
Practice Question 3
One way of measuring the thermal conductivity of a material is to sandwich
an electric thermofoil heater between two identical rectangular samples of
the material and to heavily insulate the four outer edges, as shown in the
figure. Thermocouples attached to the inner and outer surfaces of the
samples record the temperatures. During an experiment, two 0.5-cm thick
samples 10 cm × 10 cm in size are used. When steady operation is reached,
the heater is observed to draw 25 W of electric power, and the temperature
of each sample is observed to drop from 82°C at the inner surface to 74°C at
the outer surface. Determine the thermal conductivity of the material at the
average temperature.
Practice Question 4
An 800-W iron is left on the iron board with its base exposed to the air at
20℃. The convection heat transfer coefficient between the base surface and
the surrounding air is 35 𝑊/𝑚2 ∙ 𝐾. If the base has an emissivity of 0.6 and
a surface area of 0.02 𝑚2 , determine the temperature of the base of the
iron.
Created by Dr. Tian. Do NOT post on any websites.
Eml 4142 Heat Transfer
Module 3 Chapter 2
Heat Conduction Equation
Practice Questions
Instructor: Tian Tian
Practice Question 2.1
Created by Dr. Tian. Do NOT post on any websites.
Assume steady-state, one-dimensional heat conduction through
the axisymmetric shape. Assuming constant properties and no
internal heat generation, sketch the temperature distribution?
2
Practice Question 2.2
Created by Dr. Tian. Do NOT post on any websites.
A long copper bar with width w much greater
than its thickness L,
initially in thermal equilibrium with a heat sink, then suddenly heated
by passage of an electric current
𝑒𝑔𝑒𝑛
ሶ
𝑒𝑔𝑒𝑛
ሶ
1) The differential equation?
2) The initial condition?
3) The boundary condition?
(A)
the 1st B. C. at x=0, the 1st B. C. at x=L
(B)
the 1st B. C. at x=0, the 2nd B. C. at x=L
(C)
the 1st B. C. at x=0, the 3rd B. C. at x=L
(D)
the 2nd B. C. at x=0, the 2nd B. C. at x=L
(E)
the 2nd B. C. at x=0, the 3rd B. C. at x=L
3
Practice Question 2.3
Created by Dr. Tian. Do NOT post on any websites.
(Similar to Problem 2-59 in the textbook) Consider the base plate of an 800-W
household iron with a thickness of 𝐿 = 0.6 𝑐𝑚, base area of 𝐴 = 160 𝑐𝑚2 ,
and thermal conductivity of 𝑘 = 60 𝑊/𝑚 ∙ 𝐾. The inner surface of the base
plate is subjected to uniform heat flux generated by the resistance heaters
inside. When steady operating conditions are reached, the outer surface
temperature of the plate is measured to be 112℃. Disregarding any heat loss
through the upper part of the iron, evaluate the inner surface temperature.
4
Created by Dr. Tian. Do NOT post on any websites.
5
Practice Question 2.4
Created by Dr. Tian. Do NOT post on any websites.
(Problem 2-74 in the textbook) Liquid ethanol is a flammable fluid that has
a flashpoint at 16.6 ℃. At temperatures above the flashpoint, ethanol can
release vapors that form explosive mixtures, which could ignite when
source of ignition is present. In a chemical plant, liquid ethanol is being
transported in a pipe (𝑘 = 15 𝑊/𝑚 ∙ 𝐾) with an inside diameter of 3 cm
and a wall thickness of 3 mm. The pipe passes through areas where
occasional presence of ignition source can occur, and the pipe’s outer
surface is subjected to a heat flux of 1 𝑘𝑊/𝑚2 . The ethanol flowing in the
pipe has an average temperature of 10℃ with an average convection heat
transfer coefficient of 50 𝑊/𝑚2 ∙ 𝐾. Your task as an engineer is to ensure
that the ethanol is transported safely and prevent fire hazard. Determine
the variation of temperature in the pipe wall and the temperatures of the
inner and outer surfaces of the pipe. Are both surface temperatures safely
below the flashpoint of liquid ethanol?
See Video "EML4142 Module 3 Chapter 2 Practice Question 2.4" for
detailed explanation
https://www.youtube.com/watch?v=8XcpiA5z7fw&feature=youtu.be
6
Created by Dr. Tian. Do NOT post on any websites.
7
Extra Practice Question 1
KNOWN: Length, diameter, surface temperature and emissivity of steam line. Temperature
and convection coefficient associated with ambient air. Efficiency and fuel cost for gas fired
furnace.
FIND: (a) Rate of heat loss, (b) Annual cost of heat loss.
SCHEMATIC:
= 0.8
ASSUMPTIONS: (1) Steam line operates continuously throughout year, (2) Net radiation
transfer is between small surface (steam line) and large enclosure (plant walls).
ANALYSIS: (a) From Eqs. (1.3a) and (1.7), the heat loss is
(
)
4 ⎤
q = q conv + q rad = A ⎡ h ( Ts − T∞ ) + εσ Ts4 − Tsur
⎣
⎦
where A = π DL = π ( 0.1m × 25m ) = 7.85m 2 .
Hence,
(
)
q = 7.85m 2 ⎡10 W/m 2 ⋅ K (150 − 25 ) K + 0.8 × 5.67 × 10−8 W/m 2 ⋅ K 4 4234 − 2984 K 4 ⎤
⎣
⎦
q = 7.85m 2 (1, 250 + 1,095 ) W/m 2 = ( 9813 + 8592 ) W = 18, 405 W
<
(b) The annual energy loss is
E = qt = 18, 405 W × 3600 s/h × 24h/d × 365 d/y = 5.80 × 1011 J
With a furnace energy consumption of E f = E/ηf = 6.45 × 1011 J, the annual cost of the loss is
C = Cg Ef = 0.02 $/MJ × 6.45 × 105 MJ = $12,900
<
COMMENTS: The heat loss and related costs are unacceptable and should be reduced by
insulating the steam line.
Extra Practice Question 2
KNOWN: Steady-state, one-dimensional heat conduction through an axisymmetric
shape. FIND: Sketch temperature distribution and explain shape of curve.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state, one-dimensional conduction, (2) Constant properties, (3) No
internal heat generation.
& in − E& out = 0, it
ANALYSIS: Performing an energy balance on the object according to Eq. 1.12c, E
follows that
E& in − E& out = q x
bg
and that q x ≠ q x x . That is, the heat rate within the object is everywhere constant. From Fourier’s
law,
q x = − kA x
dT
,
dx
and since qx and k are both constants, it follows that
Ax
dT
= Constant.
dx
That is, the product of the cross-sectional area normal to the heat rate and temperature gradient
remains a constant and independent of distance x. It follows that since Ax increases with x, then
dT/dx must decrease with increasing x. Hence, the temperature distribution appears as shown above.
COMMENTS: (1) Be sure to recognize that dT/dx is the slope of the temperature distribution. (2)
What would the distribution be when T2 > T1? (3) How does the heat flux, q ′′x , vary with distance?
Extra Practice Question 3
2-24
2-61
An engine housing (plane wall) is subjected to a uniform heat flux on the inner surface, while the outer surface is
subjected to convection heat transfer. The variation of temperature in the engine housing and the temperatures of the inner and
outer surfaces are to be determined for steady one-dimensional heat transfer.
Assumptions 1 Heat conduction is steady and one-dimensional. 2 Thermal conductivity is constant. 3 There is no heat
generation in the engine housing (plane wall). 4 The inner surface at x = 0 is subjected to uniform heat flux while the outer
surface at x = L is subjected to convection.
Properties Thermal conductivity is given to be k = 13.5 W/m∙K.
Analysis Taking the direction normal to the surface of the wall to be the x direction with x = 0 at the inner surface, the
mathematical formulation can be expressed as
d 2T
0
dx 2
Integrating the differential equation twice with respect to x yields
dT
C1
dx
T ( x) C1 x C2
where C1 and C2 are arbitrary constants. Applying the boundary
conditions give
q0
k
x 0:
k
dT (0)
q 0 kC1
dx
x L:
k
dT ( L)
h[T ( L) T ] h(C1 L C 2 T )
dx
C1
kC1 h(C1 L C2 T )
Solving for C2 gives
q k
k
C2 C1 L T 0 L T
h
k
h
Substituting C1 and C2 into the general solution, the variation of temperature is determined to be
k
T ( x) C1 x C1 L T
h
T ( x)
q 0 k
L x T
k h
The temperature at x = 0 (the inner surface) is
T (0)
q 0 k
6000 W/m2 13.5 W/m K
0.010 m 35C 339C
L T
2
k h
13.5 W/m K 20 W/m K
The temperature at x = L = 0.01 m (the outer surface) is
T ( L)
q 0
6000 W/m2
T
35C 335C
h
20 W/m2 K
Discussion The outer surface temperature of the engine is 135°C higher than the safe temperature of 200°C. The outer surface
of the engine should be covered with protective insulation to prevent fire hazard in the event of oil leakage.
PROPRIETARY MATERIAL. © 2015 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course
preparation. If you are a student using this Manual, you are using it without permission.
Extra Practice Question 4
...