The transient heat transfer process is studied in rarefied gas confined between two stationary concentric cylinders. The inner cylinder (filament) is subjected to a periodically heating-cooling cycle. The energy transfer is modeled with a continuous model based on Navier-Stokes-Fourier (NSF) equations of motion and energy transfer and with a statistical Direct Simulation Monte Carlo Method (DSMC). Numerical results for the temperature, thermodynamic pressure and pressure difference between thermodynamic pressure and radial stress tensor component are obtained for different circular frequencies of heating cooling cycle of filament and for different filament radii. The pressure variation at the end of any local heating stage of heating-cooling cycle is close to the value of equilibrium thermodynamic pressure. The results are applicable in designing the pulsed Pirani gauges.

1.
S.
Chapman
and
T.
Cowling
,
The Mathematical Theory of Non-Uniform Gases
(
Cambridge University Press
,
Cambridge
,
1952
).
2.
S.
Albertoni
,
C.
Cercignani
, and
L.
Gotusso
(
1963
)
Numerical evaluation of the slip coefficient
,
Phys. Fluids
6
,
993
996
.
3.
C.
Cercignani
and
F.
Sernagiotto
(
1967
)
Cylindrical Couette flow of a rarefied gas
,
Physics of Fluids
10
,
1200
1204
.
4.
M.
Cole
(
1988
)
New thermal pulse vacuum gauge
,
Vacuum
38
(
8-10
),
897
899
.
5.
G. A.
Bird
,
Molecular Gas Dynamics and the Direct Simulation of Gas Flows
(
Oxford University Press
,
Oxford
,
1994
).
6.
C.
Cercignani
,
Rarefied Gas Dynamics, From Basic Concepts to Actual Calculations
(
Cambridge University Press
,
Cambridge
,
2000
).
7.
R.
Bird
,
W.
Stewart
, and
E.
Lightfoot
,
Transport Phenomena
, 2nd edn (
John Wiley
,
New York
,
2002
).
8.
W.
Jitschin
und
S.
Ludwig
(
2004
)
Pulsed hot filament vacuum gauge with Pirani sensor
,
Vakuum in Forschung und Praxis
16
,
23
29
.
9.
J.
Park
,
P.
Bahukudumbi
, and
A.
Beskok
(
2004
)
Rarefaction effects on shear driven oscillatory gas flows: A DSMC study in the entire Knudsen regime
,
Phys. Fluids
16
,
317
.
10.
H.
Ploechinger
and
F.
Salzberger
,
Pulsed Pirani vacuum gauge
(
2005
)
Vakuum in Forschung und Praxis
, author profiles for this publication at: http://www.researchgate.net/publication/260123890.
11.
F
Sharipov
and
G
Bertoldo
, “Numerical modelling of Pirani sensor”, in
XVIII IMEKO World Congress, Metrology for a Sustainable Development, Rio de Janeiro
,
Brazil
, September, 17-22,
2006
.
12.
D.
Emerson
,
Gu
Xiao-Jun
,
S.
Stefanov
,
S.
Yuhong
, and
W.
Barber
(
2007
)
Nonplanar oscillatory shear flow: From the continuum to the free-molecular regime
,
Phys. Fluids
19
,
107105
.
13.
P.
Tzeng
,
W.
Chou
,
C.
Liu
, and
W.
Li
(
2011
)
Improvement of the gas-surface collision rule for adiabatic walls in DSMC modeling of rarefied gas convection in a micro enclosure
,
Journal of Aeronautics, Astronautics and Aviation, Series A
43
(
3
),
147
158
.
14.
F.
Sharipov
(
2011
)
Data on the velocity slip and temperature jump on a gas-solid interface
,
J. Phys. Chem. Ref. Data
40
,
023101
.
15.
P.
Gospodinov
,
V.
Roussinov
, and
S.
Stefanov
(
2012
)
Nonisothermal oscillatory cylindrical Couette gas, flow in the slip regime: A computational study
,
European Journal of Mechanics B/Fluids
33
,
68
77
.
16.
D.
Kalempa
and
F.
Sharipov
(
2014
)
Numerical modeling of thermoacoustic waves in a rarefied gas confined between coaxial cylinders
,
Vacuum
109
,
326
332
.
17.
P.
Gospodinov
,
V.
Rousinov
, and
M.
Mironova
, “
Cylindrical nonisothermal oscillatory Couette gas flow in the slip regime: Wall shear stress and energy transfer, numerical investigation
”,
IntellectualArchive.com online publications, Intellectual Archive Bulletin
, Feb. 19,
2014
, pp.
2
19
.
18.
A.
Mohammadzadeh
,
A.
Rana
, and
H.
Struchtrup
(
2016
)
DSMC and R13 modeling of the adiabatic surface
,
International Journal of Thermal Sciences
101
,
9
23
.
19.
P.
Gospodinov
,
D.
Dankov
, and
V.
Roussinov
, “
Thermo acoustic waves in rarefied gas between two coaxial cylinders at a sudden change of the temperature of the outer cylinder
,” in
AMiTaNS’16
,
AIP Conference Proceedings
1773
, edited by
M.D.
Todorov
(
American Institute of Physics
,
Melville, NY
,
2016
), paper
080001
, 7p.
20.
P.
Gospodinov
,
D.
Dankov
,
V.
Roussinov
, and
S.
Stefanov
, “
Stationary cylindrical Couette flow at different temperature of cylinders: the local Knudsen number effect
,” in
AMiTaNS’11
,
AIP Conference Proceedings
1404
, edited by
M.D.
Todorov
and
C.I.
Christov
(
American Institute of Physics
,
Melville, NY
,
2011
), pp.
451
456
.
This content is only available via PDF.
You do not currently have access to this content.