MECE E3311 Heat Transfer: Homework 2
Arvind Narayanaswamy, Department of Mechanical Engineering, Columbia University.
Please submit problems 1 – 3 in one document (to be corrected by Jonathan) and 4 in
another (Sybille).
Problem 1
Derive the temperature distribution for the case of uniform heat generation
in a metallic wire of radius
R
. The thermal conductivity of the material is
k
. The boundary
condition ar
r
=
R
is
T
=
T
o
. The wire is assumed to be very long in the axial direction
– you can assume the heat ﬂow only along the radial direction. What is the temperature
diﬀerence between center of the wire and
r
=
R
. Derive the results for this problem without
using any standard heat transfer text book as a reference – you will learn a lot that will be
useful for exams.
Problem 2
Example 2.8 with the following numbers: heat dissipation rate is 0.2 W, 4.0
mm OD, length is 12 mm. Air in cabinet is at 32
o
C. Natural convection is 12 Wm

2
K

1
,
and you can neglect thermal radiation for now. This is a good problem. Please do not read
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This note was uploaded on 02/23/2010 for the course MECH 3311 taught by Professor Narayanaswamy during the Spring '09 term at Columbia.
 Spring '09
 Narayanaswamy
 Heat Transfer

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