Onset of Thermal Convection in a Rotating Nanofluid Layer Saturating a Darcy-Brinkman Porous Medium: A More Realistic Model

Rana, G. C.; Chand, Ramesh

doi:10.1615/jpormedia.v18.i6.60

Cited by 23 publications

(9 citation statements)

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“…In the limit of small Peclet numbers, expression (43) coincides with the result first obtained by Kopp and Yanovsky [41] when there is no rotation (Ta = 0) and internal heat source (R = 0) i . When there are no microorganisms present ( 0 = 0 n ), the critical Rayleigh number is the same as the results for the Darcy-Brinkman model of a rotating porous medium (without nanoparticles) that was derived by Chand and Rana [43]- [44]. However, if there is no heating or rotation within the system, ordinary bioconvection is observed, which is caused by the motion of microorganisms.…”

Section: Weak Nonlinear Analysissupporting

confidence: 75%

Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source

Kopp,

Yanovsky

2024

East Eur. J. Phys.

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In this paper, the influence of gravitational modulation on weakly nonlinear biothermal convection in a porous rotating layer is investigated. We consider a layer of porous medium saturated with Newtonian fluid, containing gyrotactic microorganisms, and subject to gravitational modulation, rotation, and internal heating. To analyze linear stability, it is sufficient to represent disturbances in the form of normal modes, while nonlinear analysis includes a truncated Fourier series containing a harmonic of the nonlinear interaction. A six-dimensional nonlinear Lorentz-type model is constructed, exhibiting both reflection symmetry and dissipation. We determined heat and mass transfer using a weakly nonlinear theory based on the representation of a truncated Fourier series. Additionally, the behavior of nonstationary Nusselt and Sherwood numbers was investigated by numerically solving finite amplitude equations. Applying the expansion of regular perturbations in a small parameter to a six-dimensional model of Lorentz equations with periodic coefficients, we obtained the Ginzburg-Landau (GL) equation. This equation describes the evolution of the finite amplitude of the onset of convection. The amplitude of convection in the unmodulated case is determined analytically and serves as a standard for comparison. The study examines the effect of various parameters on the system, including the Vadasz number, modified Rayleigh-Darcy number, Taylor number, cell eccentricity, and modulation parameters such as amplitude and frequency. By varying these parameters, in different cases, we analyzed heat and mass transfer, quantitatively expressed by the Nusselt and Sherwood numbers. It has been established that the modulation amplitude has a significant effect on the enhancement of heat and mass transfer, while the modulation frequency has a decreasing effect.

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Section: Weak Nonlinear Analysissupporting

confidence: 75%

Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source

Kopp,

Yanovsky

2024

East Eur. J. Phys.

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“…Kuznetsov (2014a, 2014b) suggested the more realistic flow on the boundaries. After that many research articles (Rana and Chand, 2015;Saini and Sharma 2017, 2018a studied the onset of convection using the revised boundary conditions and found that revised boundary conditions(zero flux) have more destabilizing effect as compared to previous boundary conditions (constant nanoparticle fraction). Very recently, Yadav and Wang (2018) examined the convective heat transport in a non-Newtonian nanofluid.…”

Section: Introductionmentioning

confidence: 99%

Double-Diffusive Bioconvection in a Suspension of Gyrotactic Microorganisms Saturated by Nanofluid

Saini

Sharma

2019

JAFM

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This paper focuses on analytical and numerical investigation of double-diffusive bioconvection in a porous media saturated by nanofluid using the modified mass flux condition. Normal mode technique is employed to solve the governing equations of the Brinkman-Darcy model. The Galerkin weighted residual method (singleterm and six-term) is used to obtain numerical solution of the mathematical model. It is found that due to the presence of gyrotactic microorganisms, Rayleigh number is decreased substantially which shows that convection sets in earlier as compared to nanofluid without microorganisms and this destabilizing effect is more predominant for faster swimming microorganisms. modified Darcy number number, Soret parameter, and porosity postpone the onset of the bioconvection, whereas nanoparticle Rayleigh number, bioconvection Rayleigh number, nanoparticle Lewis number, Dufour parameter, Péclet number, and Lewis number pre-pone the onset of bioconvection under certain conditions.

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“…The stabilizing impact of rotation parameter was established in their work. Agarwal [76], Rana and Chand [77] and Yadav et al [78] re-explored the problem of convective motions in a nanofluid layer subjected to rotation with new boundary conditions (nanoparticle flux is zero across the boundaries) for porous and nonporous medium. Yadav et al [78] solved the eigenvalue problem numerically using 6-term Galerkin method for water based nanofluid with alumina and copper nanoparticles.…”

Section: Effect Of Rotationmentioning

confidence: 99%

Rayleigh–Bénard instability in nanofluids: a comprehensive review

Ahuja¹,

Sharma

2020

Micro and Nano Syst Lett

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The extraordinary enhancement in heat transfer efficiency of nanofluids at extremely low volume fractions has attracted a lot of attention in identifying the governing mechanisms. The nanoscale effects, Brownian motion (random motion of particles inside the base fluid) and thermophoresis (diffusion of particles due to temperature gradient) are found to be important slip mechanisms in nanofluids. Based on these findings, a set of partial differential equations for conservation laws for nanofluids was formed. Since then, a large number of mathematical studies on convective heat transfer in nanofluids became feasible. The present paper summarizes the studies pertaining to instability of a horizontal nanofluid layer under the impact of various parameters such as rotation, magnetic field, Hall currents and LTNE effects in both porous and non-porous medium. Initially, investigations were made using the model considering fixed initial and boundary conditions on the layer, gradually the model was revised in the light of more practical boundary conditions and recently it has been modified to get new and more interesting results. The exhaustive analysis of instability problems is presented in the paper and prospects for future research are also identified.

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Onset of Thermal Convection in a Rotating Nanofluid Layer Saturating a Darcy-Brinkman Porous Medium: A More Realistic Model

Cited by 23 publications

References 0 publications

Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source

Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source

Double-Diffusive Bioconvection in a Suspension of Gyrotactic Microorganisms Saturated by Nanofluid

Rayleigh–Bénard instability in nanofluids: a comprehensive review

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