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Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 3, Problem 3.158P
An annular aluminum fin of rectangular profile is attached to a circular tube having an outside diameter of 25 mm and a surface temperature of
(a) What is the heat loss per tin?
(b) If 200 such fins are spaced at 5-mm increments along the tube length, what is the heat loss per meter of tube length?
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Students have asked these similar questions
1. Determine the heat flow for (i) rectangular fins and (ii) triangular fin of 20 mm length
and 3 mm base thickness. Thermal conductivity
100 W/m2K, base temperature = 120°C surrounding fluid temperature = 35°C. Determine
also the fin effectiveness.
2. A circumferential fin on a pipe of 50 mm OD is 3 mm thick and 20 mm long. Using the
property values and other parameters in 1, determine the:
= 45 W/m K. Convection coefficient h=
(i)
heat flow and effectiveness
(ii)
If the pitch is 10 mm, determine the increase in heat flow for 1 m length of pipe. Also
determine the total efficiency.
Circumferential rectangular fin
Rectangular and Triangular fins
100
100
80
80
2c
60
* 60
40
40
20
0.5
1.0
1.5
2.0
2.5
3.0
0.5
1.0
1.5
2.0
2.5
3.0
0.5
h
0.5
h
kAP
1.5
1.5
L
RAP
Le = L+
A, = t(r2 - r) A, = 2M(r2,² – r,³)
L =L+
"2, = r, + L
Rectangular fin
A, = tL,
L = L
A, = 2L, (Depth
Triangular fin
A, = L
20
Fin efficiency, %
The rate at which energy must be dissipated away from single integrated circuits (computer chips) continues to increase as transitors
continue to shrink in size and more and more computations are being completed in smaller and smaller volumes. The maximum chip
temperature, however, has not changed much over time and remains around Tc = 75 °C. To increase the rate of dissipation of thermal
energy away from a new chip, it is proposed to add a 5 x 5 array of copper pin fins to the chip. Each fin will be individually joined to the
chip surface such that there is a minimal contact resistance between the fin and the chip. The diameter of the fins is df = 1 mm and the
length is Lf = 15 mm. The chip is square, with a side length of W= 15 mm. It is so thin that it can be treated as having a single
temperature. A dielectric liquid flows over the outer surface of the chip and around the fins, with a temperature of T»,f= 20 °C and a
convection coefficient of hf = 1150 W/m²-K. The chip is joined to…
Steel pipe (outer diameter 100 mm) is covered with two layers of insulation. The inner layer, 40 mm thick, has a thermal conductivity of 0.07 W / (m K). The outer layer, 20 mm thick, has a thermal conductivity of 0.15 W / (m K). Pipes are used to deliver steam with a pressure of 800 kPa. The temperature on the outer insulation surface is 24 ° C. If the pipe is 10 m long, determine the following: (assuming that the conduction heat transfer resistance of the steel pipe and the vapor convection resistance are negligible).
a. Heat loss per hour. = AnswerkJ / hr.
b. Temperature between insulation layers. = Answer ° C.
Chapter 3 Solutions
Fundamentals of Heat and Mass Transfer
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