We immerse the bottom of a rod in ice water and record the time-dependent temperatures at positions along the length of the rod. Though the experiment is simple, a surprisingly difficult problem in heat conduction must be solved to obtain a theoretical fit to the measured data. The required equipment is very inexpensive and could be assigned as a homework exercise or a hands-on component of an online course.

1.
J.
Lienhard
and
J.
Lienhard
,
A Heat Conduction Textbook
, 2nd ed. (
Phlogiston Press
,
Cambridge, MA
,
2012
).
2.
A. E.
Biernmann
and
H. H.
Ellerbrock
, Jr.
, “
The design of fins for air-cooled engines
,” National Advisory Committee for Aeronautics (
1941
), pp.
401
424
.
3.
The Arduino Uno and the Analog Devices temperature sensor TMP36GT9Z are available at <www.digikey.com>.
4.
C. H.
Shaw
and
N.
Saunders
, “
Intermediate laboratory experiment in heat conduction
,”
Am. J. Phys.
23
,
89
90
(
1955
).
5.
H. G.
Jensen
, “
Kohlrausch heat conductivity apparatus for intermediate or advanced laboratory
,”
Am. J. Phys.
38
,
870
874
(
1970
).
6.
J. N.
Fox
and
R. H.
McMaster
, “
Measurement of the thermal properties of a metal using a relaxation method
,”
Am. J. Phys.
43
,
1083
1086
(
1975
).
7.
J. H.
Talpe
,
V. I.
Bekeris
, and
C. E.
Acha
, “
Measurement of thermal conductivity and heat capacity in an undergraduate physics laboratory
,”
Am. J. Phys.
58
,
379
381
(
1990
).
8.
J.
Brody
,
P.
Andreae
, and
C. A.
Robinson
, “
A simple optical probe of transient heat conduction
,”
Am. J. Phys.
78
,
529
531
(
2010
).
9.
M. S.
Anwar
 et al, “
Fourier analysis of thermal diffusive waves
,”
Am. J. Phys.
82
,
928
933
(
2014
).
10.
A. B.
Donaldson
and
A. R.
Shouman
, “
Unsteady-state temperature distribution in a convecting fin of constant area
,”
Appl. Sci. Res.
26
,
75
85
(
1972
).
11.
I.
Rafols
and
J.
Ortin
, “
Heat conduction in a metallic rod with Newtonian losses
,”
Am. J. Phys.
60
,
846
852
(
1992
).
12.
M. C.
Sullivan
,
B. G.
Thompson
, and
A. P.
Williamson
, “
An experiment on the dynamics of thermal diffusion
,”
Am. J. Phys.
76
,
637
642
(
2008
).
13.
Y.
Yener
and
S.
Kakac
,
Heat Conduction
, 4th ed. (
Taylor and Francis Group
,
New York
,
2008
).
14.
The reference sheet for Analog Devices temperature sensor TMP36 is available at: <http://www.analog.com/media/en/technical-documentation/data-sheets/TMP35_36_37.pdf>.
15.
See supplementary material at http://dx.doi.org/10.1119/1.4983649 for Our Arduino code.
17.
C. Y.
Ho
and
T. K.
Chu
, “
Electrical resistivity and thermal conductivity of nine selected AISI stainless steels
,” Center for Information and Numerical Data Analysis and Synthesis Report 45, Purdue University, Sept.
1977
.
18.
Selected Cryogenic Data Notebook
, edited by
J. E.
Jensen
 et al (
Brookhaven National Laboratory
,
Upton, New York
, Revised August
1980
).
19.
CRC Handbook of Chemistry and Physics
, edited by
D. R.
Lide
, 75th ed. (
CRC Press
,
Boca Raton
,
1994
).

Supplementary Material

AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.