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CHEMICAL
ENGINEERING
120B
Homework 3
due
Monday,
January 31, 2010
1.
An alloy metal fin
(k
=
64 Btu/h/ft:;OF) is used on a wall with heat transfer coefficient
h
50Btu/h.ft
2
°F. The
fin has a rectangular cross section, a base 0.05 inch thick, a length of 1 inch, and a width 4 inches.
a. What is the thermal decay length>. in the fin? Is it short or long compared with the length of the fin? Based
on this, do you expect the fin efficiency to be high or low?
a. Find t he fin efficiency.
c. What is the rate of heat loss from a single fin if the wall is at 200 F and the air is at 80F?
2. Derive a differential equation for the steady temperature distribution in a circumferential fin of constant base
thickness
2b,
inner radius
RJ
and outer radius
R2
(length
L
=
R2

Rd,
sticking out of a cylinder of radius
R
1
.
Just
as in class, assume no heat transfer out the end, that convection follows Newton's law (heat transfer coefficient
It),
and conduction follows Fourier's law (thermal conductivity
k).
What are boundary conditions? Nondimensionalize
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 Fall '10
 Zasadinski

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