This paper develops the dynamics and thermodynamics of Stirling engines that run with temperature differences below 100 °C. The working gas pressure is analytically expressed using an alternative thermodynamic cycle. The shaft dynamics is studied using its rotational equation of motion. It is found that the initial volumes of the cold and hot working gas play a non-negligible role in the functioning of the engine.

1.
D.
García Menéndez
, “
Desarrollo de motores de Stirling para aplicaciones solares,” Ph.D. thesis
(
Universidad de Oviedo
,
2013
).
2.
C. C.
Lloyd
, “
A low temperature differential Stirling engine for power generation,” Master of Engineering thesis
(
University of Canterbury
,
2009
).
3.
J. S.
Reid
, “
Stirling stuff
,” e-print arXiv:1604.02362.
4.
R.
Sier
,
Hot Air Caloric and Stirling Engines: A History
(
L. A. Mair
,
Chelmsford, UK
,
1999
), Vol.
1
.
5.
G.
Walker
and
J. R.
Senft
,
Free Piston Stirling Engines
(
Springer-Verlag
,
Berlin
,
1980
).
6.
R.
Darlington
and
K.
Strong
,
Stirling and Hot Air Engines
(
The Crowood Press
,
Marlborough
,
2005
).
7.
J. R.
Senft
, “
Optimum Stirling engines geometry
,”
Int. J. Energy Res.
26
,
1087
1101
(
2002
).
8.
K.
Ivo
,
Stirling Motor—History, Theory, Practice
(
Zagreb University Publications
,
Dubrovnik
,
1991
).
9.
I.
Kolin
,
S.
Koscak-Kolin
, and
M.
Golub
, “
Geothermal Electricity Production by Means of the Low Temperature Difference Stirling Engine
,” in
Proceedings World Geothermal Congress
, Kyushu, Japan,
2000
, pp.
3199
3203
.
10.
J. R.
Senft
,
An Introduction to Low Temperature Differential Stirling Engines
(
Moriya Press
,
1996
).
11.
J. R.
Senft
, “
Theoretical limits on the performance of Stirling engines
,”
Int. J. Energy Res.
22
,
991
1000
(
1998
).
12.
B.
Kongtragool
and
S.
Wongwises
, “
Thermodynamic analysis of a Stirling engine including dead volumes of hot space, cold space and regenerator
,”
Renewable Energy
31
,
345
359
(
2006
).
13.
G.
Barreto
and
P.
Canhoto
, “
Modelling of a Stirling engine with parabolic dish for thermal to electric conversion of solar energy
,”
Energy Convers. Manage.
132
,
119
135
(
2017
).
14.
H.
Jokar
and
A. R.
Tavakolpour-Salej
, “
A novel solar-powered active low temperature differential Stirling pump
,”
Renewable Energy
81
,
319
337
(
2015
).
15.
L. G.
Thieme
,
S.
Qiu
, and
M. A.
White
, “
Technology development for a Stirling radioisotope power system
,”
Report No. NASA TM-2000-209791
(
2000
).
16.
R. G.
Lange
and
W. P.
Carroll
, “
Review of recent advances of radioisotope power systems
,”
Energy Convers. Manage.
49
,
393
401
(
2008
).
17.
I. M.
Santos Ráez
, “
Estudio de un motor Stirling con absorbedor interno alimentado con energía solar,” Ph.D. thesis
(
Universidad de Málaga
,
2015
).
18.
M. W.
Zemansky
and
R. H.
Dittman
,
Heat and Thermodynamics
(
McGraw-Hill
,
London
,
1997
).
19.
A.
Romanelli
, “
Alternative thermodynamic cycle for the Stirling machine
,”
Am. J. Phys.
85
,
926
931
(
2017
).
20.
A.
Romanelli
, “
The Fluidyne engine
,”
Am. J. Phys.
87
,
33
37
(
2019
).
21.
A.
Romanelli
,
I.
Bove
, and
F.
González
, “
Air expansion in a water rocket
,”
Am. J. Phys.
81
,
762
766
(
2013
).
22.
G.
Schmidt
, “
Theorie der Lehmann'schen kalorischen Maschine
,”
Z. Ver. Dtsch. Ing.
15
,
1
12
(
1871
).
23.
I.
Urieli
and
D.
Berchowitz
,
Stirling Cycle Engine Analysis
(
Adam Hilger
,
Bristol
,
1983
).
24.
F.
Formosa
and
G.
Despesse
, “
Analytical model for Stirling cycle machine design
,”
Energy Convers. Manage.
51
,
1855
1863
(
2010
).
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.