Abstract
This paper investigates the propagation of thermoelastic waves in a homogeneous, linear, and isotropic porous solid. For physical and mathematical simplicity, one-dimensional wave propagation in a porous solid rod is considered to explain the concept of heat transfer caused by motion. The solutions of governing equations show that the transfer of heat in a porous rod is not only due to the conduction but also produced by the local particle displacement phenomenon. It is observed that the time-averaged transfer of heat depends on the circular frequency, porosity, thermal conductivity, thermal relaxation, specific heat, and other material coefficients.
References
1.
Bear
,
J.
,
Sorek
,
S.
,
Ben-Dor
,
G.
, and
Mazor
,
G.
, 1992
, “
Displacement Waves in Saturated Thermoelastic Porous Media—I: Basic Equations
,” Fluid Dyn. Res.
,
9
(4
), pp. 155
–164
.10.1016/0169-5983(92)90002-E2.
Levy
,
A.
,
Sorek
,
S.
,
Ben-Dor
,
G.
, and
Bear
,
J.
, 1995
, “
Evolution of the Balance Equations in Saturated Thermoelastic Porous Media Following Abrupt Simultaneous Changes in Pressure and Temperature
,” Trans. Porous Media
,
21
(3
), pp. 241
–268
.10.1007/BF006174083.
Biot
,
M. A.
, 1956
, “
The Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid—I: Low-Frequency Range II: Higher Frequency Range
,” J. Acoust. Soc. Am.
,
28
(2
), pp. 168
–191
.10.1121/1.19082394.
Biot
,
M. A.
, 1962
, “
Generalized Theory of Acoustic Propagation in Porous Dissipative Media
,” J. Acoust. Soc. Am.
,
34
(9A
), pp. 1254
–1264
.10.1121/1.19183155.
Biot
,
M. A.
, 1962
, “
Mechanics of Deformation and Acoustic Propagation in Porous Media
,” J. Appl. Phys.
,
33
(4
), pp. 1482
–1498
.10.1063/1.17287596.
Lakes
,
R.
,
Yoon
,
H. S.
, and
Katz
,
J. L.
, 1983
, “
Slow Compressional Wave Propagation in Wet Human and Bovine Cortical Bone
,” Science
,
220
(4596
), pp. 513
–515
.10.1126/science.68362967.
Kelder
,
O.
, and
Smeulders
,
D. M. J.
, 1997
, “
Observations of the Biot Slow Wave in Water Saturated Nivelsteiner Sandstone
,” Geophysics
,
62
(6
), pp. 1794
–1796
.10.1190/1.14442798.
Gurevich
,
B.
,
Kelder
,
O.
, and
Smeulders
,
D. M. J.
, 1999
, “
Validation of the Slow Compressional Wave in Porous Media: Comparison of Experiments and Numerical Simulations
,” Trans. Porous Media
,
36
(2
), pp. 149
–160
.10.1023/A:10066768011979.
Biot
,
M. A.
, 1956
, “
Thermoelasticity and Irreversible Thermo-Dynamics
,” J. Appl. Phys.
,
27
(3
), pp. 240
–253
.10.1063/1.172235110.
Lord
,
H. W.
, and
Shulman
,
Y.
, 1967
, “
The Generalised Dynamic Theory of Thermoelasticity
,” J. Mech. Phys. Solids
,
15
(5
), pp. 299
–309
.10.1016/0022-5096(67)90024-511.
Green
,
A. E.
, and
Lindsay
,
K. A.
, 1972
, “
Thermoelasticity
,” J. Elast.
,
2
(1
), pp. 1
–7
.10.1007/BF0004568912.
Chandrasekharaiah
,
D. S.
, 1986
, “
Thermoelasticity With Second Sound
,” ASME Appl. Mech. Rev.
,
39
(3
), pp. 355
–376
.10.1115/1.314370513.
Green
,
A. E.
, and
Naghdi
,
P. M.
, 1993
, “
Thermoelasticity Without Energy Dissipation
,” J. Elast.
,
31
(3
), pp. 189
–208
.10.1007/BF0004496914.
Mc Carthy
,
M. F.
, 1972
, “
Wave Propagation in Generalised Thermoelasticity
,” Int. J. Eng. Sci.
,
10
, pp. 593
–602
.10.1016/0020-7225(72)90085-715.
Chadwick
,
P.
, 1979
, “
Basic Properties of Plane Harmonic Waves in a Prestressed Heat-Conducting Elastic Material
,” J. Therm. Stresses
,
2
, pp. 193
–214
.10.1080/0149573790896240116.
Dhaliwal
,
R. S.
, and
Sherief
,
H. H.
, 1980
, “
Generalised Thermoelasicity for Anisotropic Media
,” Quart. Appl. Math.
,
38
(1
), pp. 1
–8
.10.1090/qam/57582817.
Sharma
,
J. N.
, and
Sidhu
,
R. S.
, 1986
, “
On the Propagation of Plane Harmonic Waves in Anisotropic Generalised Thermoelasticity
,” Int. J. Eng. Sci.
,
24
(9
), pp. 1511
–1516
.10.1016/0020-7225(86)90160-618.
Sharma
,
M. D.
, 2006
, “
Wave Propagation in Anisotropic Generalized Thermoelastic Medium
,” J. Therm. Stresses
,
29
, pp. 329
–342
.10.1080/0149573050049910019.
Singh
,
B.
, 2013
, “
Wave Propagation in Green-Naghdi Thermoelastic Solid With Diffusion
,” Int. J. Thermophys.
,
34
(3
), pp. 553
–566
.10.1007/s10765-013-1444-920.
Sharma
,
M. D.
, 2008
, “
Wave Propagation in a Thermoelastic Saturated Porous Medium
,” J. Earth Syst. Sci.
,
117
(6
), pp. 951
–958
.10.1007/s12040-008-0080-421.
Singh
,
B.
, 2011
, “
On Propagation of Plane Waves in Generalized Porothermoelasticity
,” Bull. Seismo Soc. Am.
,
101
(2
), pp. 756
–762
.10.1785/012010009122.
Singh
,
B.
, 2013
, “
Reflection of Plane Waves From a Free Surface of a Porothermoelastic Solid Half-Space
,” J. Porous Media
,
16
(10
), pp. 945
–957
.10.1615/JPorMedia.v16.i10.6023.
Mondal
,
S.
, 2020
, “
Interactions of a Heat Source Moving Over a Visco-Thermoelastic Rod Kept in a Magnetic Field in the Lord-Shulman Model Under a Memory Dependent Derivative
,” Comput. Math. Model
,
31
(2
), pp. 256
–276
.10.1007/s10598-020-09490-y24.
Mondal
,
S.
, and
Kanoria
,
M.
, 2020
, “
Thermoelastic Solutions for Thermal Distributions Moving Over Thin Slim Rod Under Memory-Dependent Three-Phase Lag Magneto-Thermoelasticity
,” Mech. Based Des. Struct. Mach.
,
48
(3
), pp. 277
–298
.10.1080/15397734.2019.162052925.
Mondal
,
S.
, 2020
, “
Memory Response for Thermal Distributions Moving Over a Magneto-Thermoelastic Rod Under Eringen's Nonlocal Theory
,” J. Therm. Stresses
,
43
(1
), pp. 72
–89
.10.1080/01495739.2019.167668226.
Mondal
,
S.
,
Sur
,
A.
,
Bhattacharya
,
D.
, and
Kanoria
,
M.
, 2020
, “
Thermoelastic Interaction in a Magneto-Thermoelastic Rod With Memory-Dependent Derivative Due to the Presence of Moving Heat Source
,” Indian J. Phys.
,
94
(10
), pp. 1591
–1602
.10.1007/s12648-019-01593-627.
Mondal
,
S.
, 2020
, “
Memory Response in a Magneto-Thermoelastic Rod With Moving Heat Source Based on Eringen's Nonlocal Theory Under Dual-Phase Lag Heat Conduction
,” Int. J. Comput. Methods
,
17
(09
), p. 1950072
1.10.1142/S021987621950072528.
Mondal
,
S.
, 2020
, “
Interactions Due to a Moving Heat Source in a Thin Slim Rod Under Memory-Dependent Dual-Phase Lag Magneto-Thermo-Visco-Elasticity
,” Mech. Time-Dependent Mater.
,
24
(2
), pp. 233
–252
.10.1007/s11043-019-09418-z29.
Sarkar
,
N.
, and
Mondal
,
S.
, 2019
, “
Thermoelastic Interactions in a Slim Strip Due to a Moving Heat Source Under Dual-Phase-Lag Heat Transfer
,” ASME J. Heat Transfer
,
141
, p. 124501
.10.1115/1.404492030.
Chadwick
,
P.
, 1962
, “
On the Propagation of Thermal Disturbances in Thin Plates and Rod
,” J. Mech. Phys. Solids
,
10
(2
), pp. 99
–109
.10.1016/0022-5096(62)90013-331.
Boer
,
R.
,
Ehlers
,
W.
, and
Liu
,
Z.
, 1993
, “
One-Dimensional Transient Wave Propagation in Fluid-Saturated Incompressible Porous Media
,” Arch. Appl. Mech.
,
63
(1
), pp. 59
–72
.10.1007/BF0078791032.
Magana
,
A.
, and
Quintanilla
,
R.
, 2006
, “
On the Exponential Decay of Solutions in One-Dimensional Generalized Porous-Thermo-Elasticity
,” Asymptotic Anal.
,
49
, pp. 173
–187
.https://content.iospress.com/articles/asymptotic-analysis/asy77133.
Hollkamp
,
J. P.
,
Sen
,
M.
, and
Semperlotti
,
F.
, 2019
, “
Analysis of Dispersion and Propagation Properties in Aperiodic Rod Using a Space-Fractional Wave Equation
,” J. Sound Vib.
,
441
, pp. 204
–220
.10.1016/j.jsv.2018.10.05134.
Wang
,
Y.-F.
,
Liang
,
J.-W.
,
Chen
,
A.-L.
,
Wang
,
Y.-S.
, and
Laude
,
V.
, 2019
, “
Wave Propagation in One-Dimensional Fluid-Saturated Porous Metamaterials
,” Phys. Rev.
,
B99
, p. 134304
.10.1103/PhysRevB.99.13430435.
Miranville
,
A.
, and
Quintanilla
,
R.
, 2020
, “
Exponential Decay in One-Dimensional Type-II Thermoviscoelasticity With Voids
,” J. Comput. Appl. Math.
,
368
, p. 112573
.10.1016/j.cam.2019.11257336.
Wheatley
,
J.
,
Hofler
,
T.
,
Swift
,
G. W.
, and
Migliori
,
A.
, 1985
, “
A Thermoacoustic Oscillator Powered by Vaporized Water and Ethanol
,” Am. J. Phys.
,
53
(2
), pp. 147
–162
.10.1119/1.1410037.
Swift
,
G. W.
, 1988
, “
Thermoacoustic Engines
,” J. Acoust. Soc. Am.
,
84
(4
), pp. 1145
–1180
.10.1121/1.39661738.
Garrett
,
S. L.
, 2004
, “
Thermoacoustic Engines and Refrigerators
,” Am. J. Phys.
,
72
(1
), pp. 11
–17
.10.1119/1.162103439.
Swift
,
G. W.
, 2007
, Springer Handbook of Acoustics
,
T. D.
Rossing
, ed.,
Springer
,
New York
, pp. 239
–255
.40.
Semperlotti
,
F.
, and
Sen
,
M.
, 2014
, “
On the Existence of Motion-Induced Heat-Flux Due to Thermoelastic Waves in a One-Dimensional Solid Rod
,” Appl. Phys. Lett.
,
104
(10
), p. 104103
.10.1063/1.486848841.
Rasolofosaon
,
P. N. J.
, and
Zinszner
,
B. E.
, 2002
, “
Comparison Between Permeability Anisotropic and Elasticity Anisotropy of Reservoir Rocks
,” Geophysics
,
67
(1
), pp. 230
–240
.10.1190/1.1451647Copyright © 2021 by ASME
You do not currently have access to this content.