Microscale Flow and Heat Transfer

Agrawal, Amit; Kushwaha, Hari Mohan; Jadhav, Ravi Sudam

doi:10.1007/978-3-030-10662-1

Cited by 27 publications

(47 citation statements)

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“…Next, using (28)- (30) and Table 6 in "Appendix A," we can write up to nonlinear quadratic order ψ = ψ(ρ, θ, r j , R jk , g j , G jk , A (1) jk , θ, θ, j ), (40)…”

Section: Resultsmentioning

confidence: 99%

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Second-order constitutive theory of fluids

Paolucci

2021

Continuum Mech. Thermodyn.

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A fully second-order continuum theory of fluids is developed. The conventional balance equations of mass, linear momentum, energy and entropy are used. Constitutive equations are assumed to depend on density, temperature and velocity, and their derivatives up to second order. The principle of equipresence is used along with the Coleman-Noll procedure to derive restrictions on the constitutive equations by utilizing the second law. The entropy flux is not assumed to be equal to the heat flux over the temperature. We obtain explicit results for all constitutive quantities up to quadratic nonlinearity so as to satisfy the Clausius-Duhem inequality. Our results are shown to be consistent but more general than other published results. KeywordsConstitutive equations • Second order • Quadratic nonlinearity • Coleman-Noll procedure Communicated by Andreas Öchsner.

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“…Next, using (28)- (30) and Table 6 in "Appendix A," we can write up to nonlinear quadratic order ψ = ψ(ρ, θ, r j , R jk , g j , G jk , A (1) jk , θ, θ, j ), (40)…”

Section: Resultsmentioning

confidence: 99%

“…ν (9) β (4) − β (5) ,θ − (ρ β (6) ) ,ρ /ρ ν (1) −ν ν (12) −β (9) ν (2) −β (1) ,θ ν (13) −β (7) ,θ ν (3) −β (1) ν (14) −β…”

Section: Resultsmentioning

confidence: 99%

Second-order constitutive theory of fluids

Paolucci

2021

Continuum Mech. Thermodyn.

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“…The effect of ridges therefore cannot be neglected especially in rarefied gas flows. Most of the analytical, experimental and computational work deals with randomly distributed rough micro-structures, micro-cavities, textured, furrowed or wavy microchannels, but work on structured micro-ridges protruding outward from the channel wall surface is minimal [1]. In the current numerical investigation, it is found that the influence of ridges and rarefaction on Poiseuille number (fRe where f is friction factor and Re is Reynolds number) on gas flow in microchannels is vigorously coupled.…”

Section: Introductionmentioning

confidence: 83%

Influence of three-dimensional transverse micro-ridges on the Poiseuille number in a gaseous slip flow

Garg

Agrawal

2019

SN Appl. Sci.

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Micro-ridges are regular micro-engineering structures protruding outward from the microchannel wall surface. The role of these micro-ridges in changing the friction factor (f) of a microchannel with internal rarefied gas flows is not explored in the literature. In this work, we present three-dimensional numerical simulations in a microchannel containing ridges arranged transverse to the flow direction. The length of the ridges is varied with respect to the pitch of the ridges; this ratio being christened as ridge fraction (δ). The effect of δ, ridge height ratio (h/H), Reynolds number (Re), Knudsen number (Kn) and Tangential momentum accommodation coefficient (α v) on the flow friction in terms of Poiseuille number (fRe) is investigated. In the continuum and slip regimes, it is found that fRe decreases with an increase in δ and h and a significant reduction in flow friction was shown with respect to a straight microchannel. There exists a critical height after which decrease in fRe does not occur. Further, fRe was observed to be a strong function of Re at high δ, which is attributed to the intensity of acceleration-deceleration experienced by the gas during the flow. Also, fRe is established to be directly proportional to α v. The various flow characteristics are scrutinised where vortices are found trapped inside the ridge affecting the dynamics of flow in the ridges, whose size increases on increasing the gas rarefaction. This comprehensive investigation of behaviour of slip flow in complex microchannels will be useful in designing micro-devices with reduced friction.

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“…The Knudsen number is defined as the ratio Kn ≡ λ f ree /L c , with L c the characteristic length of the flow problem at hand. Situations with Kn > 10 are said to be in the molecular flow regime, a situation commonly encountered in MEMS devices even at moderate vacuum levels because of the typically small characteristic lengths [10]. In the molecular flow regime, interactions between gas molecules can be neglected.…”

Section: Damping Contributionsmentioning

confidence: 99%

“…All relevant surface areas of the MEMS accelerometer for calculating the damping contributions are listed in Table 1. Using these parameters together with the estimates for τ obtained through Monte-Carlo simulation, the total expected gas damping as a function of pressure can be calculated through Equations ( 4) and (10). The relative contributions of both kinetic damping and squeezed-film damping from distinct regions in the accelerometer are listed in Table 2, as well as the corresponding damping coefficient at a reference pressure of 0.1 mbar.…”

Section: Pressure Dependence Of the Quality Factormentioning

confidence: 99%

Gas Damping in Capacitive MEMS Transducers in the Free Molecular Flow Regime

Boom

Bertolini

Hennes

et al. 2021

Sensors

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We present a novel analysis of gas damping in capacitive MEMS transducers that is based on a simple analytical model, assisted by Monte-Carlo simulations performed in Molflow+ to obtain an estimate for the geometry dependent gas diffusion time. This combination provides results with minimal computational expense and through freely available software, as well as insight into how the gas damping depends on the transducer geometry in the molecular flow regime. The results can be used to predict damping for arbitrary gas mixtures. The analysis was verified by experimental results for both air and helium atmospheres and matches these data to within 15% over a wide range of pressures.

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Microscale Flow and Heat Transfer

Cited by 27 publications

References 0 publications

Second-order constitutive theory of fluids

Second-order constitutive theory of fluids

Influence of three-dimensional transverse micro-ridges on the Poiseuille number in a gaseous slip flow

Gas Damping in Capacitive MEMS Transducers in the Free Molecular Flow Regime

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