Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 1, Problem 1.20P
A wall has inner and outer surface temperatures of 16 and
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You are working as an engineer in a bearing systems design company. The flow of
lubricant inside a hydrodynamic bearing (p = 0.001 kg m-1 s-1) can be approximated
as a parallel, steady, two-dimensional, incompressible flow between two parallel plates.
The top plate, representing the moving part of the bearing, travels at a constant speed,
U, while the bottom plate remains stationary (Figure Q1). The plates are separated by
a distance of 2h = 1 cm and are W = 20 cm wide. Their length is L = 10 cm. By
applying the above approximations to the Navier-Stokes equations and assuming that
end effects can be neglected, the horizontal velocity profile can be shown to be
y = +h
I
2h = 1 cm
x1
y = -h
u(y)
1 dP
2μ dx
-y² + Ay + B
moving plate
stationary plate
U
2
I2
L = 10 cm
Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm,
into the page.
Question 1
You are working as an engineer in a bearing systems design company. The flow of
lubricant inside a hydrodynamic bearing (µ = 0.001 kg m¯¹ s¯¹) can be approximated
as a parallel, steady, two-dimensional, incompressible flow between two parallel plates.
The top plate, representing the moving part of the bearing, travels at a constant speed,
U, while the bottom plate remains stationary (Figure Q1). The plates are separated by
a distance of 2h = 1 cm and are W = 20 cm wide. Their length is L = 10 cm. By
applying the above approximations to the Navier-Stokes equations and assuming that
end effects can be neglected, the horizontal velocity profile can be shown to be
1 dP
u(y)
=
2μ dx
-y² + Ay + B
y= +h
Ꮖ
2h=1 cm
1
x1
y = −h
moving plate
stationary plate
2
X2
L = 10 cm
Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm,
into the page.
(a) By considering the appropriate boundary conditions, show that the constants take
the following forms:
U
U
1 dP
A =…
Question 2
You are an engineer working in the propulsion team for a supersonic civil transport
aircraft driven by a turbojet engine, where you have oversight of the design for the
engine intake and the exhaust nozzle, indicated in Figure Q2a. The turbojet engine can
operate when provided with air flow in the Mach number range, 0.60 to 0.80. You are
asked to analyse a condition where the aircraft is flying at 472 m/s at an altitude of
14,000 m. For all parts of the question, you can assume that the flow path of air through
the engine has a circular cross section.
(a)
← intake
normal
shock
472 m/s
A B
(b)
50 m/s
H
472 m/s
B
engine
altitude: 14,000 m
exhaust nozzle
E
F
exit to
atmosphere
diameter: DE = 0.30 m
E
F
diameter: DF = 0.66 m
Figure Q2: Propulsion system for a supersonic aircraft.
a) When the aircraft is at an altitude of 14,000 m, use the International Standard
Atmosphere in the Module Data Book to state the local air pressure and tempera-
ture. Thus show that the aircraft speed…
Chapter 1 Solutions
Introduction to Heat Transfer
Ch. 1 - The thermal conductivity of a sheet of rigid,...Ch. 1 - The heat flux that is applied to the left face of...Ch. 1 - A concrete wall, which has a surface area of 20m2...Ch. 1 - The concrete slab of a basement is 11 m long, 8 m...Ch. 1 - Consider Figure 1.3. The heat flux in the...Ch. 1 - Prob. 1.6PCh. 1 - The inner and outer surface temperatures of a...Ch. 1 - A thermodynamic analysis of a proposed Brayton...Ch. 1 - A glass window of width W=1m and height H=2m is 5...Ch. 1 - Prob. 1.10P
Ch. 1 - The heat flux that is applied to one face of a...Ch. 1 - Prob. 1.12PCh. 1 - Prob. 1.13PCh. 1 - Prob. 1.14PCh. 1 - The 5-mm-thick bottom of a 200-mm-diameter pan may...Ch. 1 - Prob. 1.16PCh. 1 - For a boiling process such as shown in Figure...Ch. 1 - You've experienced convection cooling if you've...Ch. 1 - Prob. 1.19PCh. 1 - A wall has inner and outer surface temperatures of...Ch. 1 - An electric resistance heater is embedded in a...Ch. 1 - Prob. 1.22PCh. 1 - A transmission case measures W=0.30m on a side and...Ch. 1 - Prob. 1.24PCh. 1 - A common procedure for measuring the velocity of...Ch. 1 - Prob. 1.26PCh. 1 - Prob. 1.27PCh. 1 - Prob. 1.28PCh. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Prob. 1.31PCh. 1 - Prob. 1.32PCh. 1 - Prob. 1.33PCh. 1 - Prob. 1.34PCh. 1 - An electrical resistor is connected to a battery,...Ch. 1 - Pressurized water pin=10bar,Tin=110C enters the...Ch. 1 - Consider the tube and inlet conditions of Problem...Ch. 1 - An internally reversible refrigerator has a...Ch. 1 - A household refrigerator operates with cold- and...Ch. 1 - Chips of width L=15mm on a side are mounted to a...Ch. 1 - Consider the transmission case of Problem 1.23,...Ch. 1 - One method for growing thin silicon sheets for...Ch. 1 - Heat is transferred by radiation and convection...Ch. 1 - Radioactive wastes are packed in a long,...Ch. 1 - An aluminum plate 4 mm thick is mounted in a...Ch. 1 - A blood warmer is to be used during the...Ch. 1 - Consider a carton of milk that is refrigerated at...Ch. 1 - The energy consumption associated with a home...Ch. 1 - Liquid oxygen, which hems a boiling point of 90 K...Ch. 1 - The emissivity of galvanized steel sheet, a common...Ch. 1 - Three electric resistance heaters of length...Ch. 1 - A hair dryer may be idealized as a circular duct...Ch. 1 - In one stage of an annealing process, 304...Ch. 1 - Convection ovens operate on the principle of...Ch. 1 - Annealing, an important step in semiconductor...Ch. 1 - In the thermal processing of semiconductor...Ch. 1 - A furnace for processing semiconductor materials...Ch. 1 - Single fuel cells such as the one of Example 1.5...Ch. 1 - Prob. 1.59PCh. 1 - Prob. 1.60PCh. 1 - Prob. 1.61PCh. 1 - A small sphere of reference-grade iron with a...Ch. 1 - A 50mm45mm20mm cell phone charger has a surface...Ch. 1 - A spherical, stainless steel (AISI 302) canister...Ch. 1 - Prob. 1.65PCh. 1 - Prob. 1.66PCh. 1 - A photovoltaic panel of dimension 2m4m is...Ch. 1 - Following the hot vacuum forming of a paper-pulp...Ch. 1 - Prob. 1.69PCh. 1 - Prob. 1.70PCh. 1 - Prob. 1.71PCh. 1 - The roof of a car in a parking lot absorbs a solar...Ch. 1 - Prob. 1.73PCh. 1 - Prob. 1.74PCh. 1 - Consider Problem 1.1. If the exposed cold surface...Ch. 1 - Prob. 1.76PCh. 1 - Prob. 1.77PCh. 1 - A thin electrical heating element provides a...Ch. 1 - Prob. 1.79PCh. 1 - Prob. 1.80PCh. 1 - Prob. 1.81PCh. 1 - The curing process of Example 1.9 involves...Ch. 1 - The diameter and surface emissivity of an...Ch. 1 - Bus bars proposed for use in a power transmission...Ch. 1 - A solar flux of 700W/m2 is incident on a...Ch. 1 - In considering the following problems involving...
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