Heat Transfer in Porous Microchannels with Second-Order Slipping Boundary Conditions

Авраменко, А. А.; Kovetska, Yu.Yu.; Shevchuk, Igor V.; Tyrinov, A. I.; Shevchuk, V.I.

doi:10.1007/s11242-019-01300-3

Cited by 16 publications

(3 citation statements)

References 30 publications

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“…( 25)). Like in the previous studies (Dehghan et al 2015(Dehghan et al , 2016Avramenko et al 2018Avramenko et al , 2019, velocity and temperature jumps are governed by the value of the Knudsen number.…”

Section: Problem Statement and Governing Equationsmentioning

confidence: 54%

“…Here, the no-slip conditions on the wall are replaced by the slip conditions expressed in terms of the velocity and temperature jumps quantified using the Knudsen and Prandtl numbers. We have successfully applied these conditions in the calculations of forced and mixed convection (Avramenko et al 2018(Avramenko et al , 2019.…”

Section: Problem Statement and Governing Equationsmentioning

confidence: 99%

“…Dehghan et al (2016) extended their study to cover wide range of different parameters to suggest better designs of micro-heat exchangers to provide heat transfer enhancement at the expense of possible minimal pressure drop. Avramenko et al (2018Avramenko et al ( , 2019 modeled mixed convection in vertical flat and circular porous microchannels using the first-and second-order boundary conditions. The authors studied effects of the Knudsen and Rayleigh numbers, as well as porosity on heat transfer intensity and pressure losses in porous microchannels.…”

Section: Introductionmentioning

confidence: 99%

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Convective Instability in Slip Flow in a Vertical Circular Porous Microchannel

2021

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The paper represents an analysis of convective instability in a vertical cylindrical porous microchannel performed using the Galerkin method. The dependence of the critical Rayleigh number on the Darcy, Knudsen, and Prandtl numbers, as well as on the ratio of the thermal conductivities of the fluid and the wall, was obtained. It was shown that a decrease in permeability of the porous medium (in other words, increase in its porosity) causes an increase in flow stability. This effect is substantially nonlinear. Under the condition Da > 0.1, the effect of the porosity on the critical Rayleigh number practically vanishes. Strengthening of the slippage effects leads to an increase in the instability of the entire system. The slippage effect on the critical Rayleigh number is nonlinear. The level of nonlinearity depends on the Prandtl number. With an increase in the Prandtl number, the effect of slippage on the onset of convection weakens. With an increase in the ratio of the thermal conductivities of the fluid and the wall, the influence of the Prandtl number decreases. At high values of the Prandtl numbers (Pr > 10), its influence practically vanishes.

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Section: Problem Statement and Governing Equationsmentioning

confidence: 54%

Section: Problem Statement and Governing Equationsmentioning

confidence: 99%