Linear and nonlinear double diffusive convection in a rotating sparsely packed porous layer using a thermal non-equilibrium model

Malashetty, M. S.; Pop, I.; Heera, Rajashekhar

doi:10.1007/s00161-009-0117-1

Cited by 18 publications

(14 citation statements)

References 48 publications

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“…This is effectively analysing the joint effects presented in sections 4.1 and 3.3. The analogous problem of double diffusion with rotation in a Brinkman theory was analysed by [265]. This thus combines the effects of section 4.2 and 3.4.…”

Section: Double Diffusion With Rotationmentioning

confidence: 98%

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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: Double Diffusion With Rotationmentioning

confidence: 98%

“…This thus combines the effects of section 4.2 and 3.4. Both sets of writers [257] and [265] included inertia and studied the heated-salted below problem when the porous layer is undergoing a rotation about the vertical axis with constant angular rotation.…”

Section: Double Diffusion With Rotationmentioning

confidence: 99%

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Straughan

2015

Advances in Mechanics and Mathematics

111

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“…More recently Malashetty and Heera (2008) studied the effect of rotation on the onset of double diffusive convection in a horizontal anisotropic porous layer using a linear and nonlinear theory. The linear and nonlinear double diffusive convection in a rotating sparsely packed porous layer using a thermal non-equilibrium model was investigated by Malashetty et al (2009).…”

Section: L Mmentioning

confidence: 99%

The Effect of Rotation on the Onset of Double Diffusive Convection in a Sparsely Packed Anisotropic Porous Layer

Malashetty

Begum

2011

Transp Porous Med

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The effect of rotation on the onset of double diffusive convection in a sparsely packed anisotropic porous layer, which is heated and salted from below, is investigated analytically using the linear and nonlinear theories. The Brinkman model that includes the Coriolis term is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and a dispersion relation are obtained analytically using linear theory. The effect of anisotropy parameters, Taylor number, Darcy number, solute Rayleigh number, Lewis number, Darcy-Prandtl number, and normalized porosity on the stationary, oscillatory and finite amplitude convection is shown graphically. It is found that contrary to its usual influence on the onset of convection in the absence of rotation, the mechanical anisotropy parameter show contrasting effect on the onset criterion at moderate and high rotation rates. The nonlinear theory based on the truncated representation of Fourier series method is used to find the heat and mass transfers. The effect of various parameters on heat and mass transfer is shown graphically. Some of the convection systems previously reported in the literature is shown to be special cases of the system presented in this study.

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“…An extensive review of work on the LTNE model is given in [1][2][3]. More recent contributions include [5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Double diffusive convection in a viscoelastic fluid-saturated porous layer using a thermal non-equilibrium model

2012

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The stability of a binary viscoelastic fluid-saturated porous layer which is heated from below is studied, where the fluid and solid phases are not in local thermal equilibrium. The modified Darcy-Oldroyd model is employed as a momentum equation, with the fluid and solid phase temperature fields modelled separately. It is found that the inter-phase heat transfer coefficient has a significant effect on the stability of the system. Competition between the processes of viscous relaxation and thermal diffusion cause the convection to set in through oscillatory rather than stationary instability, with the viscoelastic parameters inhibiting the onset of convection. In the case of weakly non-linear theory, both steady and unsteady cases are considered. In the unsteady case the transient behaviour of the Nusselt and Sherwood numbers is investigated. The effect of thermal non-equilibrium on heat and mass transfer is also discussed.

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Linear and nonlinear double diffusive convection in a rotating sparsely packed porous layer using a thermal non-equilibrium model

Cited by 18 publications

References 48 publications

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

The Effect of Rotation on the Onset of Double Diffusive Convection in a Sparsely Packed Anisotropic Porous Layer

Double diffusive convection in a viscoelastic fluid-saturated porous layer using a thermal non-equilibrium model

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