In this article, the phenomenon of thermosolutal convection within a fluid characterized by the Brinkman–Darcy–Kelvin–Voigt (BDKV) model is delved into, while the impact of couple stresses on this process is considered. Both linear instability and nonlinear stability analyses are encompassed in our investigation. Several noteworthy observations have been made. When the fluid layer is heated from below and salt is introduced from above, it is found that the points at which stability and instability thresholds are reached coincide. This alignment is supported by the validity of the linear theory in predicting the initiation of convection under these conditions. However, the scenario changes when the layer is salted from the bottom while being heated. In this case, the stability thresholds remain constant, regardless of variations in the salt Rayleigh number. This discrepancy between the thresholds of linear instability and nonlinear stability is deemed significant. To gain a deeper understanding, numerical computations were conducted to identify and thoroughly discuss the thresholds of linear instability. These findings offer valuable insights into the behavior of the system under study. It is indicated by our results that parameters such as Brinkman, couple stresses, and Kelvin–Voigt contribute to stabilizing the system. Additionally, it was noted that the salt Rayleigh number has a stabilizing effect when the layer is salted from below, whereas it has a destabilizing effect when salt is introduced from above.
REFERENCES
1.
J. S.
Turner
, Buoyancy Effects in Fluids
(
Cambridge University Press
, 1973
).2.
J. S.
Turner
, “
Double-diffusive phenomena
,” Annu. Rev. Fluid Mech.
6
(1
), 37
–54
(1974
).3.
H. E.
Huppert
and
J.
Stewart Turner
, “
Double-diffusive convection
,” J. Fluid Mech.
106
, 299
–329
(1981
).4.
J. S.
Turner
, “
Multicomponent convection
,” Annu. Rev. Fluid Mech.
17
(1
), 11
–44
(1985
).5.
J. K.
Platten
and
J. C.
Legros
, Convection in Liquids
(
Springer Science & Business Media
, 2012
).6.
A. J.
Harfash
and
F. K.
Nashmi
, “
Triply resonant double diffusive convection in a fluid layer
,” Math. Modell. Anal.
22
(6
), 809
–826
(2017
).7.
A. A.
Hameed
and
A. J.
Harfash
, “
Unconditional nonlinear stability for double-diffusive convection in a porous medium with temperature-dependent viscosity and density
,” Heat Trans. Asian Res.
48
(7
), 2948
–2973
(2019
).8.
H. A.
Challoob
,
A. J.
Mathkhor
, and
A. J.
Harfash
, “
Slip boundary condition effect on double-diffusive convection in a porous medium: Brinkman model
,” Heat Transfer Asian Res.
49
(1
), 258
–268
(2020
).9.
A. J.
Harfash
and
A. A.
Hameed
, “
Stability of double-diffusive convection in a porous medium with temperature-dependent viscosity: Brinkman–Forchheimer model
,” Bull. Malays. Math. Sci. Soc.
44
, 1275
–1307
(2021
).10.
A. J.
Badday
and
A. J.
Harfash
, “
Chemical reaction effect on convection in bidispersive porous medium
,” Transp. Porous Med.
137
, 381
–397
(2021
).11.
A. J.
Badday
and
A. J.
Harfash
, “
Thermosolutal convection in rotating bidispersive porous media with general boundary conditions
,” Spec. Top. Rev. Porous Media
13
(6
), 29
(2022
).12.
A. J.
Badday
and
A. J.
Harfash
, “
Thermosolutal convection in a brinkman porous medium with reaction and slip boundary conditions
,” J. Porous Media
25
(1
), 15
(2022
).13.
A. J.
Badday
and
A. J.
Harfash
, “
Thermosolutal convection in a bidisperse porous medium with chemical reaction effect and relatively large macropores
,” J. Porous Media
26
(2
), 31
(2023
).14.
A. J.
Badday
and
A. J.
Harfash
, “
The effects of the soret and slip boundary conditions on thermosolutal convection with a Navier–Stokes–Voigt fluid
,” Phys. Fluids
35
(1
), 014101
(2023
).15.
K.
Roy
,
R.
Ponalagusamy
, and
P. V. S. N.
Murthy
, “
The effects of double-diffusion and viscous dissipation on the oscillatory convection in a viscoelastic fluid saturated porous layer
,” Phys. Fluids
32
(9
), 094108
(2020
).16.
K. C.
Sahu
, “
Linear instability in two-layer channel flow due to double-diffusive phenomenon
,” Phys. Fluids
32
(2
), 024102
(2020
).17.
S.
Legare
,
A.
Grace
, and
M.
Stastna
, “
Double-diffusive instability in a thin vertical channel
,” Phys. Fluids
33
(11
), 114106
(2021
).18.
B. M.
Shankar
,
J.
Kumar
, and
I. S.
Shivakumara
, “
Stability of double-diffusive natural convection in a vertical fluid layer
,” Phys. Fluids
33
(9
), 094113
(2021
).19.
D.
Yadav
,
M. K.
Awasthi
,
M.
Al-Siyabi
,
S.
Al-Nadhairi
,
A.
Al-Rahbi
,
M.
Al-Subhi
,
R.
Ragoju
, and
K.
Bhattacharyya
, “
Double diffusive convective motion in a reactive porous medium layer saturated by a non-Newtonian Kuvshiniski fluid
,” Phys. Fluids
34
(2
), 024104
(2022
).20.
D. A.
Bratsun
,
V. O.
Oschepkov
,
E. A.
Mosheva
, and
R. R.
Siraev
, “
The effect of concentration-dependent diffusion on double-diffusive instability
,” Phys. Fluids
34
(3
), 034112
(2022
).21.
A.
Jakhar
and
A.
Kumar
, “
Instability analysis of double diffusive convection under time dependent solute boundary conditions in the presence of internal heat generator
,” Phys. Fluids
35
(7
), 077101
(2023
).22.
S.
Legare
,
A.
Grace
, and
M.
Stastna
, “
Double diffusive instability with a constriction
,” Phys. Fluids
35
(2
), 024109
(2023
).23.
F.
Franchi
,
B.
Lazzari
, and
R.
Nibbi
, “
Mathematical models for the non-isothermal johnson–segalman viscoelasticity in porous media: Stability and wave propagation
,” Math. Methods Appl. Sci.
38
(17
), 4075
–4087
(2015
).24.
F.
Franchi
,
B.
Lazzari
, and
R.
Nibbi
, “
The J–S model versus a non-ideal MHD theory
,” Phys. Lett. A
379
(22–23
), 1431
–1436
(2015
).25.
S.
Gatti
,
C.
Giorgi
, and
V.
Pata
, “
Navier–Stokes limit of Jeffreys type flows
,” Physica D
203
(1–2
), 55
–79
(2005
).26.
P. M.
Jordan
and
G.
Saccomandi
, “
Compact acoustic travelling waves in a class of fluids with nonlinear material dispersion
,” Proc. R. Soc. A
468
(2147
), 3441
–3457
(2012
).27.
P. M.
Jordan
,
R. S.
Keiffer
, and
G.
Saccomandi
, “
Anomalous propagation of acoustic traveling waves in thermoviscous fluids under the Rubin–Rosenau–Gottlieb theory of dispersive media
,” Wave Motion
51
(2
), 382
–388
(2014
).28.
P. M.
Jordan
,
R. S.
Keiffer
, and
G.
Saccomandi
, “
A re-examination of weakly-nonlinear acoustic traveling waves in thermoviscous fluids under Rubin–Rosenau–Gottlieb theory
,” Wave Motion
76
, 1
–8
(2018
).29.
L. E.
Payne
and
B.
Straughan
, “
Convergence of the equations for a Maxwell fluid
,” Stud. Appl. Math.
103
(3
), 267
–278
(1999
).30.
M.
Fabrizio
,
B.
Lazzari
, and
R.
Nibbi
, “
Asymptotic stability in linear viscoelasticity with supplies
,” J. Math. Anal. Appl.
427
(2
), 629
–645
(2015
).31.
F.
Franchi
,
B.
Lazzari
, and
R.
Nibbi
, “
Uniqueness and stability results for non-linear Johnson-Segalman viscoelasticity and related models
,” Discrete Contin. Dyn. Syst., Ser. B
19
(7
), 2111
–2132
(2014
).32.
G.
Amendola
and
M.
Fabrizio
, “
Thermal convection in a simple fluid with fading memory
,” J. Math. Anal. Appl.
366
(2
), 444
–459
(2010
).33.
V.
Anand
,
J.
David
, Jr.
, and
I. C.
Christov
, “
Non-Newtonian fluid–structure interactions: Static response of a microchannel due to internal flow of a power-law fluid
,” J. Non-Newtonian Fluid Mech.
264
, 62
–72
(2019
).34.
I. C.
Christov
and
C. I.
Christov
, “
Stress retardation versus stress relaxation in linear viscoelasticity
,” Mech. Res. Commun.
72
, 59
–63
(2016
).35.
L. C.
Berselli
and
L.
Bisconti
, “
On the structural stability of the Euler–Voigt and Navier–Stokes–Voigt models
,” Nonlinear Anal.: Theory, Methods Appl.
75
(1
), 117
–130
(2012
).36.
W. J.
Layton
and
L. G.
Rebholz
, “
On relaxation times in the Navier-Stokes-Voigt model
,” Int. J. Comput. Fluid Dyn.
27
(3
), 184
–187
(2013
).37.
S.
Chiriţă
and
V.
Zampoli
, “
On the forward and backward in time problems in the Kelvin–Voigt thermoviscoelastic materials
,” Mech. Res. Commun.
68
, 25
–30
(2015
).38.
A. P.
Oskolkov
, “
Initial-boundary value problems for equations of motion of Kelvin–Voight fluids and Oldroyd fluids
,” in Trudy Matematicheskogo Instituta Imeni VA Steklova
(Russian Academy of Sciences, Steklov Mathematical Institute of Russia, 1988
), Vol.
179
, pp. 126
–164
.39.
A. P.
Oskolkov
, “
Nonlocal problems for the equations of motion of Kelvin-Voight fluids
,” J. Math. Sci.
75
, 2058
–2078
(1995
).40.
T. G.
Sukacheva
and
O. P.
Matveeva
, “
On a homogenous thermoconvection model of the non-compressible viscoelastic Kelvin-Voight fluid of the non-zero order
,” J. Samara State Tech. Univ., Ser. Phys. Math. Sci.
14
(2
), 33
–41
(2010
).41.
O. P.
Matveeva
, “
Model of thermoconvection of incompressible viscoelastic fluid of non-zero order-Computational experiment
,” Vestn. Yuzhno-Ural'skogo Univ. Ser. Mat. Model. Program.
6
(1
), 134
–138
(2013
).42.
B.
Straughan
, “
Stability for the Kelvin–Voigt variable order equations backward in time
,” Math. Methods Appl. Sci.
44
(17
), 12537
–12544
(2021
).43.
B.
Straughan
, “
Thermosolutal convection with a Navier–Stokes–Voigt fluid
,” Appl. Math. Optim.
84
(3
), 2587
–2599
(2021
).44.
B.
Straughan
, “
Continuous dependence and convergence for a Kelvin–Voigt fluid of order one
,” Ann. Univ. Ferrara.
68
(1
), 49
–61
(2022
).45.
B.
Straughan
, “
Nonlinear stability for convection with temperature dependent viscosity in a Navier–Stokes–Voigt fluid
,” Eur. Phys. J. Plus
138
(5
), 438
(2023
).46.
B.
Straughan
, “
Effect of temperature upon double diffusive instability in Navier–Stokes–Voigt models with Kazhikhov–Smagulov and Korteweg terms
,” Appl. Math. Optim.
87
(3
), 54
(2023
).47.
A. J.
Badday
and
A. J.
Harfash
, “
Thermosolutal convection in a Brinkman–Darcy–Kelvin–Voigt fluid with a bidisperse porous medium
,” Phys. Fluids
36
(1
), 014119
(2024
).48.
S.
Chandrasekhar
, Hydrodynamic and Hydromagnetic Stability
(
Courier Corporation
, 2013
).49.
V. K.
Stokes
, “
Couple stresses in fluids
,” Phys. Fluids
9
(9
), 1709
–1715
(1966
).50.
E.
Walicki
and
A.
Walicka
, “
Interia effect in the squeeze film of a couple-stress fluid in biological bearings
,” Appl. Mech. Eng.
4
(2
), 363
–373
(1999
).51.
S. N.
Gaikwad
and
S.
Kouser
, “
Double diffusive convection in a couple stress fluid saturated porous layer with internal heat source
,” Int. J. Heat Mass Transfer
78
, 1254
–1264
(2014
).52.
R.
Devi
and
A.
Mahajan
et al, “
Global stability for thermal convection in a couple-stress fluid
,” Int. Commun. Heat Mass Transfer
38
(7
), 938
–942
(2011
).53.
M. S.
Malashetty
and
B. S.
Biradar
, “
The onset of double diffusive reaction-convection in an anisotropic porous layer
,” Phys. Fluids
23
(6
), 064102
(2011
).54.
A. J.
Harfash
and
G. A.
Meften
, “
Couple stresses effect on linear instability and nonlinear stability of convection in a reacting fluid
,” Chaos, Solitons Fractals
107
, 18
–25
(2018
).55.
A. J.
Harfash
and
G. A.
Meften
, “
Couple stresses effect on instability and nonlinear stability in a double diffusive convection
,” Appl. Math. Comput.
341
, 301
–320
(2019
).56.
A. J.
Harfash
and
G. A.
Meften
, “
Poiseuille flow with couple stresses effect and no-slip boundary conditions
,” J. Appl. Comput. Mech.
6
, 1069
–1083
(2020
).57.
A. J.
Harfash
, “
Three dimensional simulations for convection induced by the selective absorption of radiation for the Brinkman model
,” Meccanica
51
, 501
–515
(2016
).58.
A. J.
Badday
and
A. J.
Harfash
, “
Stability of Darcy thermosolutal convection in bidispersive porous medium with reaction
,” Asia-Pacific J. Chem. Eng.
16
(5
), e2682
(2021
).59.
H. A.
Challoob
,
A. J.
Harfash
, and
A. J.
Harfash
, “
Bidispersive thermal convection with relatively large macropores and generalized velocity and temperature boundary conditions
,” Phys. Fluids
33
, 014105
(2021
).60.
H. A.
Challoob
,
A. J.
Harfash
, and
A. J.
Harfash
, “
Bidispersive double diffusive convection with relatively large macropores and generalized boundary conditions
,” Phys. Fluids
33
(3
), 034114
(2021
).61.
A. J.
Badday
and
A. J.
Harfash
, “
Double-diffusive convection in bidispersive porous medium with chemical reaction and magnetic field effects
,” Transp. Porous Med.
139
(1
), 45
–66
(2021
).62.
Z. A.
Afluk
and
A. J.
Harfash
, “
Stability and instability of Darcy–Bénard problem in bidispersive porous medium with an exothermic boundary reaction
,” Transp. Porous Med.
150
(2
), 359
–382
(2023
).63.
M.
Singh
,
R.
Ragoju
,
G.
Shiva Kumar Reddy
, and
C.
Subramani
, “
Predicting the effect of inertia, rotation, and magnetic field on the onset of convection in a bidispersive porous medium using machine learning techniques
,” Phys. Fluids
35
(3
), 034103
(2023
).64.
F.
Capone
,
R.
De Luca
, and
G.
Massa
, “
The onset of double diffusive convection in a rotating bi-disperse porous medium
,” Eur. Phys. J. Plus
137
(9
), 1034
(2022
).65.
K.
Dev
and
O. P.
Suthar
, “
Global stability of Bénard–Marangoni convection in an anisotropic porous medium
,” Phys. Fluids
35
(10
), 104112
(2023
).66.
X.
Zheng
,
S.
Xin
,
C.
Wang
,
D. A.
Siginer
,
W.-H.
Cai
et al, “
Oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted cavity
,” Phys. Fluids
35
(2
), 023107
(2023
).67.
C.-F.
Wu
and
F.
Chen
, “
Stability transition of a solute-stratified fluid in a vertical slot imposed with a horizontal temperature gradient
,” Phys. Fluids
35
(9
), 094121
(2023
).68.
F.
Capone
,
J. A.
Gianfrani
,
G.
Massa
, and
D. A. S.
Rees
, “
A weakly nonlinear analysis of the effect of vertical throughflow on Darcy–Bénard convection
,” Phys. Fluids
35
(1
), 014107
(2023
).69.
S.
Chandrasekhar
, Hydrodynamic and Hydromaguetic Stability,(1) Over Publications
(
Dover
, 1981
).70.
S. S.
Hajool
and
A. J.
Harfash
, “
Instability of poiseuille flow in a bidisperse porous medium subject to a uniform vertical throughflow effect
,” J. Fluids Eng.
146
(5
), 051301
(2024
).71.
Z. A.
Afluk
and
A. J.
Harfash
, “
Double diffusive convection in bidispersive porous media with couple stresses effect and relatively large macropores
,” Numer. Heat Transfer, Part A
(published online).72.
K.
Al-Yasiri
,
H. A.
Challoob
,
A. J.
Harfash
, and
A. K.
Alshara
, “
Linear and nonlinear stability analyses of penetrative convection in porous media with a gravity field effect
,” Partial Differential Equations Appl. Math.
5
, 100368
(2022
).73.
A. J.
Badday
and
A. J.
Harfash
, “
Magnetohydrodynamic instability of fluid flow in a porous channel with slip boundary conditions
,” Appl. Math. Comput.
432
, 127363
(2022
).74.
A. J.
Badday
and
A. J.
Harfash
, “
Instability in Poiseuille flow in a porous medium with slip boundary conditions and uniform vertical throughflow effects
,” J. Eng. Math.
135
(1
), 6
(2022
).75.
G.
Arnone
,
J. A.
Gianfrani
, and
G.
Massa
, “
Chebyshev-τ method for certain generalized eigenvalue problems occurring in hydrodynamics: A concise survey
,” Eur. Phys. J. Plus
138
(3
), 281
(2023
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
