Local thermal non-equilibrium effects in the Horton-Rogers-Lapwood problem with a free surface

Celli, Michele; Lagziri, Hajar; Bezzazi, Mohammed

doi:10.1016/j.ijthermalsci.2017.03.001

Cited by 15 publications

(14 citation statements)

References 11 publications

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“…Nouri-Borujerdi et al [20] studied the consequence of having internal heat generation within the layer, while a very recent work by Lagziri and Bezzazi [21] considers a case which effects a transition between cases studied by Banu and Rees [15] and Barletta and Rees [19] by employing thermal boundary conditions of the third kind. Celli et al [22] have also considered the effect of an open upper surface. The work of Banu and Rees [15] has also been re-examined by Straughan [23] using an energy stability theory and this work confirms the absence of subcritical instabilities.…”

Section: Nomenclaturementioning

confidence: 99%

Pattern selection for Darcy-Bénard convection with local thermal nonequilibrium

Bidin

Rees

2020

International Journal of Heat and Mass Transfer

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Section: Nomenclaturementioning

confidence: 99%

Pattern selection for Darcy-Bénard convection with local thermal nonequilibrium

Bidin

Rees

2020

International Journal of Heat and Mass Transfer

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“…From a practical standpoint, the local thermal non-equilibrium (LTNE) model has a vital effect on the cooling process of countless engineering devices [10,17]. On the other hand, the approach of the LTNE can highlight difficulties in the modelling of thermal boundaries, especially in the case of isoflux [18][19][20]. The objective behind this work is to analyze the convective instability in the case where two impermeable walls are supposed to be modelled in the form of Newton's cooling law equation for Robin (third-kind) thermal conditions and uniform heat flux (Model A) for Neumann (second-kind) thermal conditions.…”

Section: Introductionmentioning

confidence: 99%

Effects of Neumann and Robin boundaries on the thermal instability

Lagziri

Fakiri

Bouardi

2023

IRASE

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The thermo convective instability of the Darcy-Benard problem (DB) using Robin (third-kind) thermal conditions is investigated here. We consider a viscous Newtonian fluid saturating a porous layer in which the layer is sandwiched between two impermeable boundaries. The upper and the lower walls are modelled in the form of the Neumann (second-kind) and the Robin (third-kind) thermal conditions, respectively. The difference in the temperature distribution between both phases allows the lack of a local thermal equilibrium model to be present. As a consequence, the third kind of thermal condition brings about one extra dimensionless parameter of the Biot number to the usual one of the inter-heat transfer coefficient and the thermal conductivity ratio. The normal modes method adopted in a linear stability analysis gives rise to perturbed governing equations. The eigenvalue problem is handled numerically as a result of the perturbed governing equations leading to the marginal stability condition.

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“…In a detailed manner, Banu and Rees [5] studied buoyancy-driven convection in a layer of Darcy porous medium. Subsequently, many researchers extended this study under various additional effects [6][7][8][9][10][11][12][13]. An exhaustive bibliography on this topic can be found in the review article by Rees and Pop [14] and in the book by Neild and Bejan [15].…”

Section: Introductionmentioning

confidence: 99%

Thermal instability of an Oldroyd-B fluid-saturated porous layer: implications of pressure gradient and LTNE temperatures

Hemanthkumar

Shivakumara

2020

SN Appl. Sci.

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A local thermal nonequilibrium model is used to investigate the instability of an Oldroyd-B fluid-saturated horizontal layer of porous medium by imposing a constant pressure gradient in the horizontal direction and maintaining a constant temperature difference between the boundaries. The flow in the porous medium is studied by a modified Darcy-Oldroyd-B model. The problem has been transformed into a generalized complex eigenvalue problem and solved numerically by utilizing the Galerkin method. The pressure gradient and/or the viscoelasticity of the fluid instill oscillatory instability. The influence of constant horizontal pressure gradient is to hasten the onset of oscillatory convection: a result of contrast noticed in Newtonian fluids. The impact of constant horizontal pressure gradient is to increase the critical frequency of oscillations and to increase the size of convection cells. Besides, the effect of viscoelastic parameters on the oscillatory onset diminishes in the presence of pressure gradient. For the Maxwell fluid, instability sets in earlier compared to an Oldroyd-B fluid. The numerical results obtained under the limiting case are shown to be in excellent agreement with the published ones.

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Local thermal non-equilibrium effects in the Horton-Rogers-Lapwood problem with a free surface

Cited by 15 publications

References 11 publications

Pattern selection for Darcy-Bénard convection with local thermal nonequilibrium

Pattern selection for Darcy-Bénard convection with local thermal nonequilibrium

Effects of Neumann and Robin boundaries on the thermal instability

Thermal instability of an Oldroyd-B fluid-saturated porous layer: implications of pressure gradient and LTNE temperatures

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