Slip boundary conditions and through flow effects on double-diffusive convection in internally heated heterogeneous Brinkman porous media

Harfash, Akil J.; Challoob, Huda A.

doi:10.1016/j.cjph.2017.11.023

Cited by 27 publications

(7 citation statements)

References 44 publications

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“…Vadasz [34] discovered this term has a striking effect on rotating porous convection. Other interesting studies include Altawallbeh et al [35], Bhadauria & Srivastava [36], Deepika [19], Falsaperla et al [37], Harfash & Challoob [38], Straughan [39,40,41]. As far as we are aware, this is the first study of inertia effects via an acceleration coefficient, on convection in a bidisperse porous medium.…”

Section: Introductionmentioning

confidence: 78%

Effect of inertia on double diffusive bidispersive convection

Straughan

2019

International Journal of Heat and Mass Transfer

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Convection thresholds in a saturated bidisperse porous material are calculated in the presence of a non-zero coefficient of inertia, the acceleration coefficient, for the fluid velocity in the macro pores. We concentrate on the case where the layer is heated from below and simultaneously salted from below. The effect of increasing the size of the acceleration coefficient is generally to increase the critical Rayleigh number above which convective motion commences, although the precise values depend on the interaction coefficient between the micro and macro pores, the porosities, and the Lewis number.

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Section: Introductionmentioning

confidence: 78%

Effect of inertia on double diffusive bidispersive convection

Straughan

2019

International Journal of Heat and Mass Transfer

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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%

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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“…Double diffusive convection is a problem with many real-life applications and as such has attracted much attention in the research literature, see, e.g. Barletta and Nield (2011), Deepika (2018), Deepika and Narayana (2016), Harfash and Challoob (2018), Harfash and…”

Section: Introductionmentioning

confidence: 99%

Heated and Salted Below Porous Convection with Generalized Temperature and Solute Boundary Conditions

Straughan

2019

Transp Porous Med

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We address the problem of initiation of convective motion in the case of a fluid saturated porous layer, containing a salt in solution, which is heated and salted below. We amplify the very interesting recent results of Nield and Kuznetsov and examine in detail a whole range of temperature and salt boundary conditions allowing for a combination of prescribed heat flux and temperature. The behaviour of the transition from stationary to oscillatory convection is examined in detail as the boundary conditions vary from prescribed temperature and salt concentration toward those of prescribed heat flux and salt flux.

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Slip boundary conditions and through flow effects on double-diffusive convection in internally heated heterogeneous Brinkman porous media

Cited by 27 publications

References 44 publications

Effect of inertia on double diffusive bidispersive convection

Effect of inertia on double diffusive bidispersive convection

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

Heated and Salted Below Porous Convection with Generalized Temperature and Solute Boundary Conditions

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