2013
DOI: 10.1098/rspa.2013.0187
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Porous convection with local thermal non-equilibrium temperatures and with Cattaneo effects in the solid

Abstract: There is increasing interest in convection in local thermal non-equilibrium (LTNE) porous media. This is where the solid skeleton and the fluid may have different temperatures. There is also increasing interest in thermal wave motion, especially at the microscale and nanoscale, and particularly in solids. Much of this work has been based on the famous model proposed by Carlo Cattaneo in 1948. In this paper, we develop a model for thermal convection in a fluid-saturated Darcy porous medium allowing the solid an… Show more

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Cited by 55 publications
(62 citation statements)
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“…From inequality (18), we see that a condition for universal stability is that the coefficients of the last two terms are positive. If we return to the definition of κ 1 and κ 2 , then we find that a sufficient condition for universal stability is that…”
Section: Universal Stabilitymentioning
confidence: 99%
See 1 more Smart Citation
“…From inequality (18), we see that a condition for universal stability is that the coefficients of the last two terms are positive. If we return to the definition of κ 1 and κ 2 , then we find that a sufficient condition for universal stability is that…”
Section: Universal Stabilitymentioning
confidence: 99%
“…In particular, recent attention has often focussed on local thermal non-equilibrium, which is where there is a single porosity but the fluid and solid skeleton have different temperatures (e.g., Banu and Rees [3], Barletta and Rees [4,5], Eltayeb [6], Nield [7,8], Nield and Bejan [1], Nield and Kuznetsov [9,10], Nouri-Borujerdi et al [11], Postelnicu and Rees [12], Rees [13,14], Rees and Bassom [15], Rees et al [16], Straughan [17][18][19]). …”
Section: Introductionmentioning
confidence: 99%
“…For example, thermal waves are important in the study of thermal transport in nanomaterials and nanofluids [6,13], and thermal shocks in solids [14], and for heat transport in biological tissue and surgical operations [8,[15][16][17]. Similarly, thermal relaxation has been shown to impact on flow velocity profiles in Jeffrey fluids [18], and a number of thermal convection problems in fluids and porous media [19][20][21][22] (including thermo-haline convection [23,24]), while type-II flux laws analogous to equation (1.1) have found utility in related contexts involving advection-diffusion systems [25][26][27].…”
Section: Introductionmentioning
confidence: 99%
“…Straughan and colleagues [19][20][21][22][23]), recently we studied the impact of the Cattaneo-Christov heatflow model on the canonical Rayligh-Bénard problem of a Boussinesq fluid layer heated from below [28][29][30]. Our analysis in this earlier context showed that in addition to onset of instability by stationary convection (as predicted classically [29,30]), Cattaneo effects give rise to oscillatory convection as the preferred manner of instability whenever C exceeds some threshold value C T , where C T (P 1 ) is a function of the Prandtl number P 1 [28].…”
Section: Introductionmentioning
confidence: 99%
“…Recently, there has been a great upsurge of interest in understanding this convective instability problem using local thermal non-equilibrium (LTNE) model because of its relevance and applications in many practical situations such as convection in stellar atmospheres, nuclear reactor maintenance, heat exchangers, processing of composite materials, resin flow, fuel cells, tube refrigerators in space, flows in microchannels and porous metallic foams to mention a few [1,2].…”
Section: Introductionmentioning
confidence: 99%