Double-diffusive convective motions for a saturated porous layer subject to modulated surface heating

McKay, G.

doi:10.1007/s001610050123

Cited by 4 publications

(2 citation statements)

References 21 publications

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“…[279][280][281][282] and chapter 10 of the book by [414]. In particular, [279,280] investigates the geophysical application to patterned ground formation due to a time-periodic surface flux generated by the Sun.…”

Section: Ltne Thermovibrational Convectionmentioning

confidence: 99%

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Straughan

2015

Advances in Mechanics and Mathematics

113

111

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In this chapter we describe work of [366] and of [393] on thermal convection in a Darcy porous material in a vertical layer subject to different temperatures on the vertical walls.For the case of a single temperature the problem where the porous medium occupies a vertical layer subject to differential heating from one side to the other has attracted much attention. This problem has much application to insulation, such as in the area of building design, and is of importance in window double glazing. For the single temperature situation the first proof that a vertical porous slab of Darcy type which is held at fixed but different temperatures on the vertical walls is stable to perturbations from the equilibrium state is due to [156]. His analysis is based on the linear theory and analyses the two-dimensional problem.[409] further analysed this problem but in three-dimensions and he treated the completely nonlinear situation by employing energy-like integral methods. In particular, [409] produced a threshold for the Rayleigh number which guarantees global nonlinear stability, i.e. regardless of how large the initial perturbation may be. He also employed a generalized energy method to demonstrate that the result of [156] is true in the fully three-dimensional case although the initial data must be restricted. Articles dealing with other interesting aspects of convection in a vertical porous slab or pipe involving effects like double diffusion, and LTNE, include the papers by [32, 33, 36, 46, 211, 220, 221, 329, 330, 362] and [460]. The methods of energy stability techniques applied specifically to convection in a vertical porous slab are addressed in [144, 229] and [356], and these are discussed in detail in the book by [414, pp. 126-134].The analogous problem in LTNE to that of [156] was first addressed by [366]. Specifically [366] dealt with the [156] problem of thermal convection in a vertical porous medium, but he employed the theory of local thermal non-equilibrium, allowing for different fluid and solid temperatures. The interesting work of [366] demonstrates that the vertical configuration is always stable according to linear theory, even with the much more complicated LTNE theory. [393] continued the problem of [366] but they analysed the complete nonlinear three-dimensional situation.

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Section: Ltne Thermovibrational Convectionmentioning

confidence: 99%

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Straughan

2015

Advances in Mechanics and Mathematics

113

111

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“…but with the crucial exception of exploring the model for penetrative convection in a porous medium (see e.g. McKay [68], Carr & de Putter [13]), with boundary surfaces as there would be in the experiment.…”

Section: Introductionmentioning

confidence: 99%

Convection in Porous Media

2004

Fundamentals of the Finite Element Method for Heat and Fluid Flow

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The subject of thermal convection in fluid and porous media is investigated, coupled with the development of efficient spectral finite element methods to improve on the more commonly used techniques for these types of problems. Convection induced by the selective absorption of radiation in a porous medium is investigated in the first four chapters. For the Darcy and Brinkman models for fluid flow the thresholds of the linear and nonlinear theories are shown to be extremely close, demonstrating that the linear theory is accurate enough to predict the onset of convective motion. The exploration of a quadratically modelled internal heat source is discussed next. It is shown that the linear and nonlinear thresholds are close unless the quadratic term becomes dominant over the linear term. Developing a doublediffusive model yields a critical parameter for which no oscillatory convection occurs when it is exceeded. This is an unobservea phenomenon in the present literature. Thermal convection in a linearly viscous fluid in a finite box is also explored. It is demonstrated that the linear and nonlinear thresholds do not coincide, which contradicts results by Georgescu & Mansutti [25]. Legendre and Chebyshev polynomial based spectral methods are also developed for the evaluation of eigenvalues and eigenfunctions inherent in stability analysis in porous media, drawing on the experience of the implementation of the well established techniques in the previous work. These generate sparse matrices, where the standard homogeneous boundary conditions for both porous and fluid media problems are contained within the method.

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Double-Diffusive Convection

Nield

Bejan

2012

Convection in Porous Media

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Double-diffusive convective motions for a saturated porous layer subject to modulated surface heating

Cited by 4 publications

References 21 publications

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Convection in Porous Media

Double-Diffusive Convection

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