Green–Naghdi fluid with non-thermal equilibrium effects

Straughan, Brian

doi:10.1098/rspa.2009.0523

Cited by 27 publications

(28 citation statements)

References 31 publications

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“…The present article is concerned with what happens when the Newtonian fluid is replaced by a power-law fluid. (For completeness it should be noted that Straughan (2010) has developed the theory of Green and Naghdi to describe the convection of nanofluids. The theory involves vorticity and spin of vorticity.…”

Section: Introduction and Discussionmentioning

confidence: 99%

A Note on the Onset of Convection in a Layer of a Porous Medium Saturated by a Non-Newtonian Nanofluid of Power-Law Type

Nield

2010

Transp Porous Med

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Section: Introduction and Discussionmentioning

confidence: 99%

A Note on the Onset of Convection in a Layer of a Porous Medium Saturated by a Non-Newtonian Nanofluid of Power-Law Type

Nield

2010

Transp Porous Med

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“…For example, there are applications in tube refrigerators in space, [19]; in nanofluid flows, 6 Animal fur is a good example of a high porosity material, as seen in this cat. [320,420,425], chapter 8; in fuel cells [102]; in resin flow, important in processing composite materials, [108]; in nuclear reactor maintenance, [137]; in heat exchangers, [107,269]; in microwave ablation of the liver, [208]; in biological tissue analysis, [493]; in flows in microchannels, [215]; in flow and heat transfer in porous metallic foams, [189,240,241,269]; in thermovibrational filtration, [388,389], in textile transport, [486]; and in convection in stellar atmospheres, cf. [425], chapter 8, [426].…”

Section: Applications Examplesmentioning

confidence: 99%

“…In particular, with modern heat transfer devices being increasingly employed on a microscale there is much need to understand penetrative and resonant convection on a nanoscale, cf. [18,118,133,300,303,402,420,425,428,433]. MEMS (microelectro-mechanical-systems) will play an important part in future heat transfer technology, cf.…”

Section: Resonance In Thermal Convectionmentioning

confidence: 99%

“…At about the same time [420] employed an LTNE theory to describe a nanofluid by suitably adapting the thermodynamic analysis of [168]. The theory developed in [420] incorporates higher derivatives of velocity in the momentum equation. This is consistent with what is found experimentally for a suspension where, for example, a non-parabolic profile is found in Couette or Poiseuille flow.…”

Section: Heat Transfer Enhancement In Nanofluidsmentioning

confidence: 99%

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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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“…These include double diffusive convection [13][14][15], ferroconvection [16,17], convection in complex fluids [18,19] and non-uniformly heated fluids [20] and thermovibrational convection [21]. Recent articles have also discussed this situation in vertical porous media [22,23].…”

Section: Introductionmentioning

confidence: 99%

Onset of centrifugal filtration convection: departure from thermal equilibrium

Saravanan

Brindha

2013

Proc. R. Soc. A.

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This paper deals with convective instability in a fluidsaturated, rotating porous layer subject to alternating direction of the centrifugal body force, when the layer fails to exhibit thermal equilibrium. The Darcy model is used to describe the flow, and a twofield model is used to take care of the energy exchange. The normal mode approach of the linear theory and the energy approach of the nonlinear theory are used to find the stability characteristics. Unconditional and sharp nonlinear thresholds are found. The study brings out the failure of the linear theory in describing the instability in most parts of the parameter space of interest where possible subcritical instabilities may arise. The stability boundaries are presented graphically and it is found that the interphase heat transfer coefficient has a significant effect in the thermal non-equilibrium regime.

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Green–Naghdi fluid with non-thermal equilibrium effects

Cited by 27 publications

References 31 publications

A Note on the Onset of Convection in a Layer of a Porous Medium Saturated by a Non-Newtonian Nanofluid of Power-Law Type

A Note on the Onset of Convection in a Layer of a Porous Medium Saturated by a Non-Newtonian Nanofluid of Power-Law Type

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Onset of centrifugal filtration convection: departure from thermal equilibrium

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