Couple stresses effect on linear instability and nonlinear stability of convection in a reacting fluid

Harfash, Akil J.; Meften, Ghazi Abed

doi:10.1016/j.chaos.2017.12.013

Cited by 20 publications

(9 citation statements)

References 30 publications

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“…The values of

R_{c}

were taken between

0

and

20

when the layer is salted below and between

0

and

6

for salted above layer. The eigenvalue systems of linear instability and nonlinear stability theories have been solved using the Chebyshev collocation method, for more details see Harfash et al…”

Section: Stability Analysis Resultsmentioning

confidence: 99%

“…The values of R c were taken between 0 and 20 when the layer is salted below and between 0 and 6 for salted above layer. The eigenvalue systems of linear instability and nonlinear stability theories have been solved using the Chebyshev collocation method, for more details see Harfash et al [28][29][30][31][32][33][34][35] The linear instability and nonlinear stability thresholds are presented in Figure 1A,B when the layer is salted below H = 1 and above H = −1, respectively. The critical Rayleigh number is plotted against R c for a a = 0.1, = 0.1, Γ = 0.1, Γ = 0.1 .…”

Section: Nonlinear Stability Analysismentioning

confidence: 99%

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Unconditional nonlinear stability for double‐diffusive convection in a porous medium with temperature‐dependent viscosity and density

Hameed

Harfash

2019

Heat Trans. Asian Res.

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In this study, fluid flow in a porous medium is analyzed using a Forchheimer model. The problem of double‐diffusive convection is addressed in such a porous medium. We utilize a higher‐order approximation for viscosity‐temperature and density‐temperature, such that the perturbation equations contain more nonlinear terms. For unconditional stability, nonlinear stability has been achieved for all initial data by utilizing the L3 or L4 norms. It also shows that the theory of L2 is not sufficient for such unconditional stability. Both linear instability and nonlinear energy stability thresholds are tested using three‐dimensional (3D) simlations. If the layer is salted above and salted below then stationary convection is dominant. Thus the critical value of the linear instability thresholds occurs at a real eigenvalue σ, and our results show that the linear theory produces the actual threshold. Moreover, it is known that with the increase of the salt Rayleigh number, Rc, the onset of convection is more likely to be via oscillatory convection as opposed to steady convection. The 3D simulation results show that as the value of Rc increases, the actual threshold moves towards the nonlinear stability threshold, and the behavior of the perturbation of the solutions becomes more oscillatory.

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“…The values of

R_{c}

were taken between

0

and

20

when the layer is salted below and between

0

and

6

for salted above layer. The eigenvalue systems of linear instability and nonlinear stability theories have been solved using the Chebyshev collocation method, for more details see Harfash et al…”

Section: Stability Analysis Resultsmentioning

confidence: 99%

Section: Nonlinear Stability Analysismentioning

confidence: 99%

Unconditional nonlinear stability for double‐diffusive convection in a porous medium with temperature‐dependent viscosity and density

Hameed

Harfash

2019

Heat Trans. Asian Res.

Self Cite

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“…conditions, or just neglected from the practical point of view of the problem. The Navier-Stokes equation may contain couple stresses discussed in [19,20] or the case of a transverse seepage is analyzed in [21]. The heat conduction equation also may contain sources or sinks, however a natural source term is the viscous heating [22,23,25].…”

Section: Introductionmentioning

confidence: 99%

Self-similar analysis of a viscous heated Oberbeck–Boussinesq flow system

Barna¹,

Mátyás²,

Pocsai³

2020

Fluid Dyn. Res.

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The simplest model to couple the heat conduction and Navier-Stokes equations together is the Oberbeck-Boussinesq(OB) system which were investigated by E.N. Lorenz and opened the paradigm of chaos. In our former studies -Chaos Solitons and Fractals 78, 249 (2015), ibid, 103, 336 (2017) -we derived analytic solutions for the velocity, pressure and temperature fields. Additionally, we gave a possible explanation of the Rayleigh-Bènard convection cells with the help of the self-similar Ansatz. Now we generalize the OB hydrodynamical system, including a viscous source term in the heat conduction equation. Our results may attract the interest of various fields like micro or nanofluidics or climate studies.

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“…Recent related literature where the linear and the nonlinear Boussinesq approximation are explored can be found in Ref . In these works, they established that the nonlinear approximation is of great application in climate change and weather forecast.…”

Section: Introductionmentioning

confidence: 99%

Theory of fully developed mixed convection including flow reversal: A nonlinear Boussinesq approximation approach

Jha

Oni

2019

Heat Trans. Asian Res.

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In this article, an exact solution is obtained to investigate the role of nonlinear Boussinesq approximation on mixed convection flow in a vertical channel subject to asymmetric wall heating. The nonlinear density variation with temperature (NDT) in the buoyancy term is introduced to the momentum equation and solved exactly by direct integration. During the course of graphical and numerical computations, results show that the role of NDT is to increase fluid velocity as well as skin-friction while it reduces the rate of heat transfer. In addition, reverse flow formation at the walls is increased due to the inclusion of NDT (nonlinear Boussinesq approximation). K E Y W O R D S flow reversal, mixed convection, nonlinear Boussinesq approximation, nonlinear density variation with temperature (NDT)

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Couple stresses effect on linear instability and nonlinear stability of convection in a reacting fluid

Cited by 20 publications

References 30 publications

Unconditional nonlinear stability for double‐diffusive convection in a porous medium with temperature‐dependent viscosity and density

Unconditional nonlinear stability for double‐diffusive convection in a porous medium with temperature‐dependent viscosity and density

Self-similar analysis of a viscous heated Oberbeck–Boussinesq flow system

Theory of fully developed mixed convection including flow reversal: A nonlinear Boussinesq approximation approach

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