Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Textbook Question
Chapter 3, Problem 3.66P
In Example 3.6. an expression was derived for the critical insulation radius of an insulated, cylindrical tube. Derive the expression that would be appropriate for an insulated sphere.
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Scenario
A pipe made from martensitic steel, with inner and outer diameters of 56 mm and 60 mm,
respectively, has been fixed perpendicularly to a wall, and the pipe lies along the X-axis, as
presented in Fig. 1a. Two steel arms of the same length have been welded perpendicularly
(along the Y-axis) to the pipe, on the same X-Y plane (Fig. 1b, view along the X-axis), and the
arms are parallel to the wall (Fig. 1c, view along the Z-axis). The two arms are subjected to
external vertical loading (along the Z-axis) in opposite directions with equal magnitude (Fig.
1a). The arms are made of the same material as the pipe, and they can be assumed to be
rigid (no deflection within the arms). Please note the lengths and diameters of the
pipe/arms in the figure are not to scale.
(a)
L3
‒‒‒‒‒‒‒‒‒‒‒‒ţ
L1 = 64(in cm)
L2 = 48 (in cm)
L3 = 83(in cm)
F = 63(in N)
L1
L1
L2
F
B
(b)
Figure 1: A steel pipe with two horizontal arms.
(c)
A2)
Calculate the von Mises equivalent stress at position C for your…
Scenario
A pipe made from martensitic steel, with inner and outer diameters of 56 mm and 60 mm,
respectively, has been fixed perpendicularly to a wall, and the pipe lies along the X-axis, as
presented in Fig. 1a. Two steel arms of the same length have been welded perpendicularly
(along the Y-axis) to the pipe, on the same X-Y plane (Fig. 1b, view along the X-axis), and the
arms are parallel to the wall (Fig. 1c, view along the Z-axis). The two arms are subjected to
external vertical loading (along the Z-axis) in opposite directions with equal magnitude (Fig.
1a). The arms are made of the same material as the pipe, and they can be assumed to be
rigid (no deflection within the arms). Please note the lengths and diameters of the
pipe/arms in the figure are not to scale.
(a)
L3
‒‒‒‒‒‒‒‒‒‒‒‒ţ
L1 = 64(in cm)
L2 = 48 (in cm)
L3 = 83 (in cm)
F = 63(in N)
L1
L1
L2
F
B
(b)
Figure 1: A steel pipe with two horizontal arms.
(c)
A2)
Providing the applied load F is no longer derived from your student…
Scenario
A pipe made from martensitic steel, with inner and outer diameters of 56 mm and 60 mm,
respectively, has been fixed perpendicularly to a wall, and the pipe lies along the X-axis, as
presented in Fig. 1a. Two steel arms of the same length have been welded perpendicularly
(along the Y-axis) to the pipe, on the same X-Y plane (Fig. 1b, view along the X-axis), and the
arms are parallel to the wall (Fig. 1c, view along the Z-axis). The two arms are subjected to
external vertical loading (along the Z-axis) in opposite directions with equal magnitude (Fig.
1a). The arms are made of the same material as the pipe, and they can be assumed to be
rigid (no deflection within the arms). Please note the lengths and diameters of the
pipe/arms in the figure are not to scale.
(a)
L3
‒‒‒‒‒‒‒‒‒‒‒‒ţ
L1 = 64(in cm)
L2 = 48 (in cm)
L3 = 83 (in cm)
F = 63(in N)
L1
L1
L2
F
B
(b)
Figure 1: A steel pipe with two horizontal arms.
(c)
A1)
Produce a Mohr's circle for the stress state of a 2D plane stress…
Chapter 3 Solutions
Fundamentals of Heat and Mass Transfer
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