Stability of a porous Benard-Brinkman layer in local thermal non-equilibrium with Cattaneo effects in solid

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Abstract

The stability of a porous Benard layer of Brinkman fluid under local thermal non-equilibrium conditions and obeying the Cattaneo flux law in the solid is studied. The preference for stationary and overstable linear motions is examined in the whole parameter space of the problem. It is shown that overstability occupies a region within a branch of a rectangular hyperbola-like curve in the first quadrant of the (τH) plane, where τ,H are the Straughan and thermal inter-phase interaction parameters, respectively, so that overstability persists even when H→∞. The Brinkman effect tends to stabilize the layer but enhances the region of preference of overstability in the parameter space. The influence of the other parameters on the critical mode is also identified. The nonlinear development of the amplitude A of the linear wave motions of both stationary and overstable modes is found to be governed by a first order evolution equation. The analysis of the evolution equation shows that the layer can exhibit supercritical instability for both stationary and overstable modes and subcritical instability and stability for the stationary mode depending on the relative magnitudes of the parameters of the problem. The Brinkman effect is found to reduce the amplitude of the supercritical instability while the porosity modified ratio of thermal conductivities and the ratio of thermal diffusivities tend to promote subcritical instabilities. The implication of these results on the nonlinear global stability of the model is discussed.

Original languageEnglish
Pages (from-to)208-218
Number of pages11
JournalInternational Journal of Thermal Sciences
Volume98
DOIs
Publication statusPublished - Aug 11 2015

Fingerprint

nonequilibrium conditions
Thermal diffusivity
quadrants
thermal diffusivity
Hot Temperature
Thermal conductivity
thermal conductivity
Porosity
Fluxes
porosity
Fluids
fluids
curves
interactions

Keywords

  • Brinkman effect
  • Cattaneo effects
  • Convection
  • Nonlinear evolution
  • Porous layer
  • Stability

ASJC Scopus subject areas

  • Engineering(all)
  • Condensed Matter Physics

Cite this

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title = "Stability of a porous Benard-Brinkman layer in local thermal non-equilibrium with Cattaneo effects in solid",
abstract = "The stability of a porous Benard layer of Brinkman fluid under local thermal non-equilibrium conditions and obeying the Cattaneo flux law in the solid is studied. The preference for stationary and overstable linear motions is examined in the whole parameter space of the problem. It is shown that overstability occupies a region within a branch of a rectangular hyperbola-like curve in the first quadrant of the (τH) plane, where τ,H are the Straughan and thermal inter-phase interaction parameters, respectively, so that overstability persists even when H→∞. The Brinkman effect tends to stabilize the layer but enhances the region of preference of overstability in the parameter space. The influence of the other parameters on the critical mode is also identified. The nonlinear development of the amplitude A of the linear wave motions of both stationary and overstable modes is found to be governed by a first order evolution equation. The analysis of the evolution equation shows that the layer can exhibit supercritical instability for both stationary and overstable modes and subcritical instability and stability for the stationary mode depending on the relative magnitudes of the parameters of the problem. The Brinkman effect is found to reduce the amplitude of the supercritical instability while the porosity modified ratio of thermal conductivities and the ratio of thermal diffusivities tend to promote subcritical instabilities. The implication of these results on the nonlinear global stability of the model is discussed.",
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N2 - The stability of a porous Benard layer of Brinkman fluid under local thermal non-equilibrium conditions and obeying the Cattaneo flux law in the solid is studied. The preference for stationary and overstable linear motions is examined in the whole parameter space of the problem. It is shown that overstability occupies a region within a branch of a rectangular hyperbola-like curve in the first quadrant of the (τH) plane, where τ,H are the Straughan and thermal inter-phase interaction parameters, respectively, so that overstability persists even when H→∞. The Brinkman effect tends to stabilize the layer but enhances the region of preference of overstability in the parameter space. The influence of the other parameters on the critical mode is also identified. The nonlinear development of the amplitude A of the linear wave motions of both stationary and overstable modes is found to be governed by a first order evolution equation. The analysis of the evolution equation shows that the layer can exhibit supercritical instability for both stationary and overstable modes and subcritical instability and stability for the stationary mode depending on the relative magnitudes of the parameters of the problem. The Brinkman effect is found to reduce the amplitude of the supercritical instability while the porosity modified ratio of thermal conductivities and the ratio of thermal diffusivities tend to promote subcritical instabilities. The implication of these results on the nonlinear global stability of the model is discussed.

AB - The stability of a porous Benard layer of Brinkman fluid under local thermal non-equilibrium conditions and obeying the Cattaneo flux law in the solid is studied. The preference for stationary and overstable linear motions is examined in the whole parameter space of the problem. It is shown that overstability occupies a region within a branch of a rectangular hyperbola-like curve in the first quadrant of the (τH) plane, where τ,H are the Straughan and thermal inter-phase interaction parameters, respectively, so that overstability persists even when H→∞. The Brinkman effect tends to stabilize the layer but enhances the region of preference of overstability in the parameter space. The influence of the other parameters on the critical mode is also identified. The nonlinear development of the amplitude A of the linear wave motions of both stationary and overstable modes is found to be governed by a first order evolution equation. The analysis of the evolution equation shows that the layer can exhibit supercritical instability for both stationary and overstable modes and subcritical instability and stability for the stationary mode depending on the relative magnitudes of the parameters of the problem. The Brinkman effect is found to reduce the amplitude of the supercritical instability while the porosity modified ratio of thermal conductivities and the ratio of thermal diffusivities tend to promote subcritical instabilities. The implication of these results on the nonlinear global stability of the model is discussed.

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