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 1.10P
To determine
Minimum thickness of Styrofoam insulation.
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2. Express the following complex numbers in rectangular form.
(a) z₁ = 2еjл/6
(b) Z2=-3e-jπ/4
(c) Z3 =
√√√3e-j³/4
(d) z4 = − j³
A prismatic beam is built into a structure. You can consider the boundary conditions at A and B to be
fixed supports. The beam was originally designed to withstand a triangular distributed load, however,
the loading condition has been revised and can be approximated by a cosine function as shown in the
figure below. You have been tasked with analysing the structure. As the beam is prismatic, you can
assume that the bending rigidity (El) is constant.
wwo cos
2L
x
A
B
Figure 3: Built in beam with a varying distributed load
In order to do this, you will:
a. Solve the reaction forces and moments at point A and B.
Hint: you may find it convenient to use the principal of superposition.
(2%)
b. Plot the shear force and bending moment diagrams and identify the maximum shear force
and bending moment.
(2%)
c. Develop an expression for the vertical deflection. Clearly state your expression in terms of x.
(1%)
Question 1: Beam Analysis
Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts
as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces
can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a
roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied
to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB
and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these
moments is PL.
Moment Release
A
B
с
°
MB = PL
Mc=
= PL
-L/2-
-L/2-
→
P
D
Figure 1: Two beam arrangement for question 1.
To analyse this structure, you will:
a) Construct the free body diagrams for the structure shown above. When constructing your
FBD's you must make section cuts at point B and C. You can represent the structure as three
separate beams. Following this, construct the…
Chapter 1 Solutions
Introduction to Heat Transfer
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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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