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 1.25P
A common procedure for measuring the velocity of an airstream involves the insertion of an electrically heated wire (called a hot-wire anemometer ) into the airflow, with the axis of the wire oriented perpendicular to the flow direction. The electrical energy dissipated in the wire is assumed to be transferred to the air by forced convection. Hence, for a prescribed electrical power, the temperature of the wire depends on the convection coefficient, which, in turn, depends on the velocity of the air. Consider a wire of length
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2. In a particular section of a fluid system, a 30% ethylene glycol mixture is flowing through a 6-
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1. Steam leaves the boiler of a power plant at 5 MPa, 500°C as shown in the following figure. As
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a heat loss through the pipe's insulation. The pressure drop in the pipe connecting the boiler to
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P = 5 MPa
T₁ = 500°C
Boiler
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Τ =496°C
7 = 85%
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P=1 atm
To=25°C
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An aluminum rod of length L
=
1m has mass density p = 2700 kg and
Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact
natural eigenfrequencies of the rod are wexact
E
=
√
ρ
for n=1,2,3,. . . .
1. What is the minimum number of linear elements necessary to
determine the fundamental frequency w₁ of the system? Discretize
the rod in that many elements of equal length, assemble the global
system of equations KU = w² MU, and find the fundamental
frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact
Sketch the fundamental mode of vibration.
2. Use COMSOL to solve the same problem. Show the steps necessary
to find the fundamental frequency and mode of the rod. What is the
relative error using linear elements and a normal mesh?
Chapter 1 Solutions
Introduction to Heat Transfer
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