In this research article, the combined effect of electric field and variable viscosity on the stability of dielectric nanofluid (CuO + water) within a Hele–Shaw cell is studied. The normal mode technique has been implemented for linear stability analysis and the truncated Fourier series method for nonlinear stability analysis. The effect of the Hele–Shaw number, thermorheological parameter, and alternating current electric Rayleigh number on the onset of convection and heat/mass transfer has been investigated analytically, graphically, and using tables. It is observed that the effect of the thermorheological parameter has a destabilizing effect, and the value of the parameter is always less than for this study. We also found that the Hele–Shaw number has stabilizing effect, and it is always greater or equal to for this study. The effect of alternating current electric Rayleigh number is destabilized. We observed that in the whole analysis, numerical results are better than analytical results.
WoodingRA. Instability of a viscous liquid of variable density in a vertical Hele-Shaw cell. J Fluid Mech1961; 7: 501–515.
4.
AnissSSouharMBrancherJ. Asymptotic study and weakly nonlinear analysis at the onset of Rayleigh-Benard convection in Hele-Shaw cell. Phys Fluids1995; 7: 926.
5.
YadavD. The effect of pulsating throughflow on the onset of magneto convection in a layer of nanofluid confined within a Hele-Shaw cell. J Process Mech Eng2019; 233: 1074–1085.
6.
BhadauriaBSKumarA. Throughflow and gravity modulation effect on thermal instability in a Hele-Shaw cell saturated by nanofluid. J Porous Media2021; 24: 31–51.
7.
KrishnaMVSwarnalathammaBVChamkhaAJ. Investigations of Soret, Joule and Hall effects on MHD rotating mixed convective flow past an infinite vertical porous plate. J Ocean Eng Sci2019; 4: 263–275.
8.
HaiZDaripaP. Linear instability of interfacial Hele-Shaw flows of viscoelastic fluids. J Nonnewton Fluid Mech2022; 309: 104923.
9.
ChoiS. Enhancing thermal conductivity of fluids with nanoparticles. In: Signier DA and Wang HP (eds.) Development and Applications of Non-Newtonian flows 1995; vol. 231/MD vol. 66: pp. 99–105. ASME.
10.
BuongiornoJ. Convective transport in nanofluids. J Heat Transfer2006; 128: 240–250. ASME.
11.
TzouDY. Thermal instability of nanofluids in natural convection. Int J Heat Mass Transf2008; 51: 2967–2979.
12.
KuznetsovAVNieldDA. Thermal instability in a porous medium saturated by a nanofluid: Brinkman model. Transp Porous Media2010; 81: 409–422.
13.
NieldDAKuznetsovAV. The effect of vertical through flow on thermal instability in a porous medium layer saturated by nanofluid. Transp Porous Media2011; 87: 765–775.
14.
BhadauriaBSAgarwalSKumarA. Non-linear two-dimensional convection in a nanofluid saturated porous medium. Transp Porous Media2011; 90: 605–625.
15.
BhadauriaBSSrivastavaA. Combined effect of internal heating and through-flow in a nanofluid saturated porous medium under local thermal nonequilibrium. J Porous Media2022; 25: 75–95.
16.
FaridzadehMToghraieDSNiroomandA. Analysis of laminar mixed convection in an inclined square lid-driven cavity with a nanofluid by using an artificial neural network. Heat Transf Res2014; 45: 361–390.
17.
MostafazadehAToghraieDMashayekhiR, et al. Effect of radiation on laminar natural convection of nanofluid in a vertical channel with single-and two-phase approaches. J Therm Anal Calorim2019 Oct; 138: 779–94.
18.
MashayekhiRKhodabandehEAkbariOA, et al. CFD analysis of thermal and hydrodynamic characteristics of hybrid nanofluid in a new designed sinusoidal double-layered microchannel heat sink. J Therm Anal Calorim2018 Dec; 134: 2305–15.
19.
BazdarHToghraieDPourfattahF, et al. Numerical investigation of turbulent flow and heat transfer of nanofluid inside a wavy microchannel with different wavelengths. J Therm Anal Calorim2020 Feb; 139: 2365–80.
20.
ArastehHMashayekhiRGoodarziM, et al. Heat and fluid flow analysis of metal foam embedded in a double-layered sinusoidal heat sink under local thermal non-equilibrium condition using nanofluid. J Therm Anal Calorim2019 Oct; 138: 1461–76.
21.
ToghraieDMashayekhiRArastehH, et al. Two-phase investigation of water-Al2O3 nanofluid in a micro concentric annulus under non-uniform heat flux boundary conditions. Int J Numer Methods Heat Fluid Flow2019 Jan 25; 9: 117–133.
22.
BoroomandpourAToghraieDHashemianM. A comprehensive experimental investigation of thermal conductivity of a ternary hybrid nanofluid containing MWCNTs-titania-zinc oxide/water-ethylene glycol (80: 20) as well as binary and mono nanofluids. Synth Met2020 Oct 1; 268: 116501.
RichardsonLStraughanB. Convection with temperature dependent viscosity in a porous medium: non-linear stability and the Brinkman effect. Atti Accad Naz Lincei-Ci-Sci-Fis Mat1993; 4: 223–232.
25.
BhadauriaASrivastavaBSSiddheshwarPGHashimI. Heat transport in an anisotropic porous medium saturated with variable viscosity liquid under G-jitter and internal heating effects. Transp Porous Med2013; 99: 359–376.
26.
SrivastavaABhadauriaBSSinghA. An analytical study of heat and mass transport in Benard-Darcy convection with G-jitter and variable viscosity liquids in porous media. Spec Top Rev Porous Med: Int J2019; 10: 323–338.
27.
DassTDGunakalaSRComissiongDM. Combined effect of variable-viscosity and surface roughness on the squeeze film characteristics of infinitely wide rectangular plate with couple stress fluid, velocity-slip and ferrofluid lubricant. Mater Today: Proce2022; 56: 1717–25.
TakashimaMAldridgeKD. The stability of a horizontal layer of dielectric fluid under the simultaneous action of a vertical DC electric field and vertical temperature gradient. J Mech Appl Math1976; 29: 71–87.
SiddheshwarPGRadhakrishnaD. Linear and nonlinear electroconvection instability under AC electric field. Commun Nonlinear Sci Numer Simul2012; 17: 2883–2895.
32.
YadavDLeeJChoHH. Electrothermal instability in a porous medium layer saturated by a dielectric nanofluid. J Appl Fluid Mech2015; 9: 2123–2132.
33.
YadavD. Effect of electric field on the onset of Jeffery fluid convection in a heat-generating porous medium layer. Pramana2022; 96: 1–8.
34.
YadavDLeeJ. Onset of convection in a nanofluid layer confined within a Hele-Shaw cell. J Fluid Mech2015; 9: 519–527.
35.
KanchanaCSiddheshwarPGChoHH. Regulation of heat transfer in Rayleigh-Benard convection in Newtonian liquids and Newtonian nanoliquids using gravity, boundary temperature and rotational modulations. J Therm Anal Calorim2020; 142: 1579–1600.
36.
YadavD. The influence of pulsating throughflow on the onset of electro-thermo-convection in a horizontal porous medium saturated by a dielectric nanofluid. J Appl Fluid Mech2018; 11: 1679–1689.
37.
LandauLDLifshitzEM. Electrodynamics of continuous media. London: Pergamon Press, 1960.
38.
AgarwalSRanaPBhadauriaBS. Rayleigh-Benard convection in a nanofluid layer using a thermal non-equilibrium model. J Heat Transfer2014; 136: 122501.
39.
ChandR. Electro-thermal convection in a Brinkman porous medium saturated by nanofluid. Ain Shams Eng J2017; 8: 633–641.
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