2016
DOI: 10.1515/jnet-2015-0071
|View full text |Cite
|
Sign up to set email alerts
|

Thermal Convection Induced by an Infinitesimally Thin and Unstably Stratified Layer

Abstract: We examine the linear stability analysis of the equations governing Rayleigh–Bénard convection flows when the basic temperature profile is unstably stratified solely over a thin horizontal slice of the fluid region. We conduct both asymptotic and numerical analyses on three distinct shapes of the basic temperature: (i) a hyperbolic tangent profile, (ii) a piecewise linear profile and (iii) a step-function profile. In the first two cases, the thin unstably stratified layer is centrally located. The presence of … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

0
6
0

Year Published

2016
2016
2017
2017

Publication Types

Select...
2
1

Relationship

2
1

Authors

Journals

citations
Cited by 3 publications
(6 citation statements)
references
References 11 publications
0
6
0
Order By: Relevance
“…Upon relaxing the function f (z) to be constant and applying the substitution, −p 2 = −ξ α 2 − Da, we solve Eqs. (9,10) in the two separate regions, 0 < z < Z 0 and Z 0 < z < 1 which we label with the super scripted variables W − (z),…”
Section: Constant Permeabilitymentioning
confidence: 99%
See 2 more Smart Citations
“…Upon relaxing the function f (z) to be constant and applying the substitution, −p 2 = −ξ α 2 − Da, we solve Eqs. (9,10) in the two separate regions, 0 < z < Z 0 and Z 0 < z < 1 which we label with the super scripted variables W − (z),…”
Section: Constant Permeabilitymentioning
confidence: 99%
“…The constants b and χ are measures of stable and unstable stratification, respectively, with the thickness of the unstably stratified layer getting thinner as χ increases resulting in a situation that mimics Bénard convection without the presence of the horizontal boundaries. Hadji et al [10] considered the case of a step change profile which would correspond to the SB profile in the limits of both b → 0 and χ → ∞, namely, T B (z) = T 1 + (T 2 − T 1 )H (z − Z 0 ), where T 1 and T 2 are the temperature values at the lower and upper plates, respectively, T 1 > T 2 and H (z) denotes the Heaviside function. Such a profile results in a heavy layer on top of a lighter one separated by a horizontal interface z = Z 0 across which diffusion of buoyancy takes place.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Upon relaxing the function f (z) to be constant and applying the substitution, −p 2 = −ξ α 2 − Da, we solve Eqs. (9,10) in the two separate regions, 0 < z < Z 0 and Z 0 < z < 1 which we label with the super scripted variables W − (z), W + (z), S − (z), and S + (z), respectively. With D = d/dz, we have…”
Section: Constant Permeabilitymentioning
confidence: 99%
“…We derive an evolution equation for the leading order concentration profile by making use of long wavelength asymptotics valid in the limit β approaches zero, and as depicted in Fig. (10), the critical wavenumber approaches zero as β approaches zero. We invoke the analysis in [27] which has shown that the scaling of the critical wavenumber with the mass transfer coefficient β takes the form, α 4 C ∼ (β /h) as β → 0, for a dimensionless thickness of the plates of order unity.…”
Section: Weakly Nonlinear Analysismentioning
confidence: 99%