Linear and Nonlinear Stability Analysis of a Horton–Rogers–Lapwood Problem with an Internal Heat Source and Brinkman Effects

Nandal, Reena; Mahajan, Amit

doi:10.1007/s11242-017-0832-1

Cited by 16 publications

(5 citation statements)

References 26 publications

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“…The author considered four different types of heat supply functions, and discussed the results by obtaining the values of the critical Rayleigh number of energy theory Ra E and the critical Rayleigh number of linear instability theory Ra L . Most recently, Nandal and Mahajan [23] studied the effect of internal heat source on the onset of convection in a fluid layer saturated porous medium. The authors considered four different types of internal heat supply functions, and discussed the results for stress-free and isothermal boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Linear Stability Analysis of Penetrative Convection via Internal Heating in a Ferrofluid Saturated Porous Layer

Mahajan

Sunil

Sharma

2017

Fluids

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Penetrative convection due to purely internal heating in a horizontal ferrofluid-saturated porous layer is examined by performing linear stability analysis. Four different types of heat supply functions are considered. The Darcy model is used to incorporate the effect of the porous medium. Numerical solutions are obtained by using the Chebyshev pseudospectral method, and the results are discussed for all three boundary conditions: when both boundaries are impermeable and conducting; when both boundaries are conducting with lower boundary impermeable and free upper boundary; and when both boundaries are impermeable with lower boundary conducting and upper with constant heat flux. The effect of the Langevin parameter, width of ferrofluid layer, permeability parameter, and nonlinearity of the fluid magnetization has been observed at the onset of penetrative convection for water-and ester-based ferrofluids. It is seen that the Langevin parameter, width of ferrofluid layer, and permeability parameter have stabilizing effects on the onset of convection, while the nonlinearity of the fluid magnetization advances the onset of convection.

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Section: Introductionmentioning

confidence: 99%

Linear Stability Analysis of Penetrative Convection via Internal Heating in a Ferrofluid Saturated Porous Layer

Mahajan

Sunil

Sharma

2017

Fluids

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“…These papers represent quite a wide range of different types of boundary condition such as a free upper surface in [4] or the presence of an insulated bounding surface [8,10]. The case where both surfaces are impermeable and are at identical constant temperatures has a critical Darcy-Rayleigh number of 471.38 and a critical wavenumber of 4.6752, values which have been obtained by various authors such as Barletta et al [11], Nandal and Mahajan [12] and Nouri-Borujerdi et al [13,14]. This ten-fold rise in the critical Darcy-Rayleigh number may be explained at least qualitatively by the facts that (i) the internally-heated case admits a destabilising temperature gradient only in the upper half of the layer and (ii) the maximum temperature difference is only 1 8 of that of that of the classical Darcy-Bénard layer.…”

Section: Introductionmentioning

confidence: 93%

Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation

Storesletten

Rees

2019

Fluids

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The onset of convection in an inclined porous layer which is heated internally by a uniform distribution of heat sources is considered. We investigate the combined effects of inclination, anisotropy and internal heat generation on the linear instability of the basic parallel flow. When the Rayleigh number is sufficiently large, instability occurs and a convective motion is set up. It turns out that the preferred motion at convection onset depends quite strongly on the anisotropy ratio, ξ , and the inclination angle. When ξ < 1 the preferred motion is in the form of longitudinal rolls for all inclinations. When ξ > 1 transverse rolls are preferred for small inclinations but, at high inclinations, longitudinal rolls are preferred. At intermediate inclinations the preferred roll orientation varies smoothly between these two extremes.

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“…Results of asymptotic stability in this vein have been the subject of several recent articles using a judicious choice of an energy functional, cf. Amendola & Fabrizio [2], Amendola et al [3], Amendola et al [4], Deepika & Narayana [6], Deseri et al [8], Fabrizio & Lazzari [9], Fabrizio et al [10], Fabrizio et al [11], Franchi & Morro [12], Nandal & Mahajan [15], Straughan [20][21][22].…”

Section: Nonlinear Stabilitymentioning

confidence: 99%

Tridispersive thermal convection

Gentile

Straughan

2018

Nonlinear Analysis: Real World Applications

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We derive the linear instability and nonlinear stability thresholds for a problem\ud of thermal convection in a tridispersive porous medium with a single temperature.\ud Importantly we demonstrate that the nonlinear stability threshold is the same as the\ud linear instability one. The significance of this is that the linear theory is capturing\ud completely the physics of the onset of thermal convection. This result is different to\ud the general theory of thermal convection in a tridispersive porous material where\ud the temperatures in the macropores, mesopores and micropores are allowed to be\ud different. In that case the coincidence of the nonlinear stability and linear instability\ud boundaries has not been proved

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Linear and Nonlinear Stability Analysis of a Horton–Rogers–Lapwood Problem with an Internal Heat Source and Brinkman Effects

Cited by 16 publications

References 26 publications

Linear Stability Analysis of Penetrative Convection via Internal Heating in a Ferrofluid Saturated Porous Layer

Linear Stability Analysis of Penetrative Convection via Internal Heating in a Ferrofluid Saturated Porous Layer

Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation

Tridispersive thermal convection

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