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-E
2.
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/BF00617408
3.
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
.10.1121/1.1908239
4.
Biot
,
M. A.
,
1962
, “
Generalized Theory of Acoustic Propagation in Porous Dissipative Media
,”
J. Acoust. Soc. Am.
,
34
(
9A
), pp.
1254
1264
.10.1121/1.1918315
5.
Biot
,
M. A.
,
1962
, “
Mechanics of Deformation and Acoustic Propagation in Porous Media
,”
J. Appl. Phys.
,
33
(
4
), pp.
1482
1498
.10.1063/1.1728759
6.
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.6836296
7.
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
.10.1190/1.1444279
8.
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:1006676801197
9.
Biot
,
M. A.
,
1956
, “
Thermoelasticity and Irreversible Thermo-Dynamics
,”
J. Appl. Phys.
,
27
(
3
), pp.
240
253
.10.1063/1.1722351
10.
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)90024-5
11.
Green
,
A. E.
, and
Lindsay
,
K. A.
,
1972
, “
Thermoelasticity
,”
J. Elast.
,
2
(
1
), pp.
1
7
.10.1007/BF00045689
12.
Chandrasekharaiah
,
D. S.
,
1986
, “
Thermoelasticity With Second Sound
,”
ASME Appl. Mech. Rev.
,
39
(
3
), pp.
355
376
.10.1115/1.3143705
13.
Green
,
A. E.
, and
Naghdi
,
P. M.
,
1993
, “
Thermoelasticity Without Energy Dissipation
,”
J. Elast.
,
31
(
3
), pp.
189
208
.10.1007/BF00044969
14.
Mc Carthy
,
M. F.
,
1972
, “
Wave Propagation in Generalised Thermoelasticity
,”
Int. J. Eng. Sci.
,
10
, pp.
593
602
.10.1016/0020-7225(72)90085-7
15.
Chadwick
,
P.
,
1979
, “
Basic Properties of Plane Harmonic Waves in a Prestressed Heat-Conducting Elastic Material
,”
J. Therm. Stresses
,
2
, pp.
193
214
.10.1080/01495737908962401
16.
Dhaliwal
,
R. S.
, and
Sherief
,
H. H.
,
1980
, “
Generalised Thermoelasicity for Anisotropic Media
,”
Quart. Appl. Math.
,
38
(
1
), pp.
1
8
.10.1090/qam/575828
17.
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)90160-6
18.
Sharma
,
M. D.
,
2006
, “
Wave Propagation in Anisotropic Generalized Thermoelastic Medium
,”
J. Therm. Stresses
,
29
, pp.
329
342
.10.1080/01495730500499100
19.
Singh
,
B.
,
2013
, “
Wave Propagation in Green-Naghdi Thermoelastic Solid With Diffusion
,”
Int. J. Thermophys.
,
34
(
3
), pp.
553
566
.10.1007/s10765-013-1444-9
20.
Sharma
,
M. D.
,
2008
, “
Wave Propagation in a Thermoelastic Saturated Porous Medium
,”
J. Earth Syst. Sci.
,
117
(
6
), pp.
951
958
.10.1007/s12040-008-0080-4
21.
Singh
,
B.
,
2011
, “
On Propagation of Plane Waves in Generalized Porothermoelasticity
,”
Bull. Seismo Soc. Am.
,
101
(
2
), pp.
756
762
.10.1785/0120100091
22.
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.i10.60
23.
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-y
24.
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
.10.1080/15397734.2019.1620529
25.
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
.10.1080/01495739.2019.1676682
26.
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/s12648-019-01593-6
27.
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/S0219876219500725
28.
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-z
29.
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
.10.1115/1.4044920
30.
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)90013-3
31.
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/BF00787910
32.
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/asy771
33.
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.2018.10.051
34.
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.99.134304
35.
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.2019.112573
36.
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
.10.1119/1.14100
37.
Swift
,
G. W.
,
1988
, “
Thermoacoustic Engines
,”
J. Acoust. Soc. Am.
,
84
(
4
), pp.
1145
1180
.10.1121/1.396617
38.
Garrett
,
S. L.
,
2004
, “
Thermoacoustic Engines and Refrigerators
,”
Am. J. Phys.
,
72
(
1
), pp.
11
17
.10.1119/1.1621034
39.
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
.10.1063/1.4868488
41.
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
.10.1190/1.1451647
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