Critical Rayleigh number of natural convection in high porosity anisotropic horizontal porous layers

Shiina, Yasuaki; Hishida, Makoto

doi:10.1016/j.ijheatmasstransfer.2009.11.045

Cited by 24 publications

(10 citation statements)

References 12 publications

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“…Since many real porous materials display strong anisotropy this focus of attention is natural and is studied by e.g. [176,193,214,226,228,370,387,394,395,398,400,404,439] and [485], and the references therein. These articles concentrate mainly on anisotropy of the permeability tensor or thermal conductivity.…”

Section: Fig 19mentioning

confidence: 99%

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Straughan

2015

Advances in Mechanics and Mathematics

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: Fig 19mentioning

confidence: 99%

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Straughan

2015

Advances in Mechanics and Mathematics

111

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“…As the diameter of the string d is very small, heat conduction rate through the string is small and the heat transfer phenomena in the porous medium is assumed to be isotropic. The permeability of the porous medium k of these conditions is calculated with the following equation (Shiina et al, 2007(Shiina et al, , 2010 to calculate the porous Rayleigh number Ra s :…”

Section: Experimental Apparatus and Conditionsmentioning

confidence: 99%

“…In this work we try to use the critical porous Rayleigh number Ra scritical to discuss experimental results of a high-porosity porous medium. Shiina et al (2007Shiina et al ( , 2010 reported the equation of the critical porous Rayleigh number for the onset of natural convection in an anisotropic porous medium with thin vertical cylindrical rods. When we use a porous medium to reduce the natural convection heat loss of a solar thermal collector, it is necessary to minimize the shading effect of the solar radiation by the porous medium.…”

Section: Introductionmentioning

confidence: 99%

Reduction of heat loss from solar thermal collector by diminishing natural convection with high-porosity porous medium

et al. 2013

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We studied the reduction of natural convection heat loss from a solar thermal collector by placing a high-porosity porous medium above the collector plate in a solar thermal collector system. It is known that natural convection can be diminished in a porous medium. In order to use a porous medium in a solar thermal collector, it is necessary to minimize the shading effect of solar radiation caused by the porous medium. In this work, we used a series of offset wire screens made of fine nylon fishing lines of 0.05 mm in diameter with 2-mm pitch and a porosity of 0.999. The experimental apparatus consisted of a copper 300 mm  300 mm collector plate with a selective absorption film on the surface. We measured the reduction rate of the convection heat loss from the collector plate and the shading effect for actual sun radiation by changing the condition of the porous medium, the temperature of the collector plate, and the inclined angle of the collector plate. Experimental results of the Nusselt number of natural convection in the high-porosity porous medium agreed with the equation proposed by Gupta et al. The effect of the inclined angle on the Nusselt number was small. The net reduction rate of natural convection heat loss was 7% by placing the high-porosity porous medium above the collector plate when the temperature of the collector plate was 100C.

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“…Moreover, anisotropy is a characteristic of artificial porous materials like pelleting used in the chemical engineering process, fiber material used in insulating purpose and in the phase change materials on natural convection. The effect of anisotropy on thermal convection in porous media has gained prime importance in the literature and has been studied extensively 13‐19 . A detailed account on this topic can be found in the book by Nield and Bejan 20 …”

Section: Introductionmentioning

confidence: 99%

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

2020

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By adopting a perturbation method and a local thermal nonequilibrium model, nonlinear thermal convection in an anisotropic porous layer saturated by an elasticoviscous fluid is investigated. An elasticoviscous fluid is modeled by a modified Darcy-Oldroyd-B model, and the fluid and solid phase temperatures are represented using a two-field model for the heat transport equation. Anisotropy in permeability and fluid and solid thermal conductivities are considered. A cubic Landau equation is derived separately to study the stability of bifurcating solution of both stationary and oscillatory convection, and the results of linear instability theory are delineated. The boundary between stationary and oscillatory convection is demarcated by identifying codimensiontwo points in the viscoelastic parameters plane. It is found that the subcritical instability is not possible, and the linear instability analysis itself completely captures the behavior of the onset of convection. Heat transfer is obtained in terms of Nusselt number, and the effect of governing parameters on the same is discussed. The results of the Maxwell fluid are obtained as a particular case from the present study. K E Y W O R D S cubic Landau equation, heat transport, local thermal nonequilibrium, nonlinear convection, Oldroyd-B fluid, porous layer

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Critical Rayleigh number of natural convection in high porosity anisotropic horizontal porous layers

Cited by 24 publications

References 12 publications

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Reduction of heat loss from solar thermal collector by diminishing natural convection with high-porosity porous medium

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

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