Numerical simulation of heat transfer in a micro-cavity

Baliti, Jamal; Hssikou, Mohamed; Alaoui, Mohammed

doi:10.1139/cjp-2016-0528

Cited by 7 publications

(8 citation statements)

References 19 publications

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“…While for Kn = 10, the slip flow is from the hot to the cold end. It is noted that such opposite results have been observed in previous two-dimensional configurations [18][19][20], and is explained by the balance between the shear stress and tangential heat flux induced driven mechanisms [18,20,26]. We denote the vortex ring in the case of Kn = 0.01 as type-I and in the case of Kn = 10 as type-II for convenience in the following discussions [see the labels in Fig.…”

Section: A General Flow Patternsmentioning

confidence: 89%

“…benchmark problem for evaluating more efficient novel numerical methods such as the octant flux splitting information preservation (IP) DSMC method [24], the low-variance Monte Carlo simulation method [25], the regularized-13 (R13) equations method [18,26], the (discrete) unified gas kinetic scheme (UGKS, DUGKS) [19,27] and the fast spectral method for full Boltzmann equation [21,28].…”

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confidence: 99%

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Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

2017

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Rarefied gas flow in a three-dimensional enclosure induced by nonuniform temperature distribution is numerically investigated. The enclosure has a square channel-like geometry with alternatively heated closed ends and lateral walls with a linear temperature distribution. A recently proposed implicit discrete velocity method with a memory reduction technique is used to numerically simulate the problem based on the nonlinear Shakhov kinetic equation. The Knudsen number dependencies of the vortexes pattern, slip velocity at the planar walls and edges, and heat transfer are investigated. The influences of the temperature ratio imposed at the ends of the enclosure and the geometric aspect ratio are also evaluated. The overall flow pattern shows similarities with those observed in two-dimensional configurations in literature. However, new features due to the three-dimensionality are observed with new types of vortexes that are not identified in previous studies on similar twodimensional enclosures at high Knudsen and small aspect ratios.

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Section: A General Flow Patternsmentioning

confidence: 89%

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confidence: 99%

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

2017

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“…In addition to the three Equations 7 to 9, there are two other equations characterizing the Newtonian fluids given by the right‐hand side of the Equation and the Fourier law, which gives the heat flux vector in the NSF. The two stress tensor and heat transfer vector are then:

σ_{ij} = - 2 μ \frac{\partial v_{true〈 i}}{\partial x_{j true〉}},

q_{i} = - \frac{15}{4} μ \frac{\partial θ}{\partial x_{i}} .

…”

Section: Macroscopic Methodsmentioning

confidence: 99%

Rarefaction and external force effects on gas microflow in a lid‐driven cavity

Baliti

Hssikou

Alaoui

2018

Heat Trans. Asian Res.

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In this paper, the regularized 13‐moment approach (R13) is used to investigate the rarefaction effect on rarefied gas flow within a lid‐driven cavity. We will discuss the validity domain of the Navier‐Stokes and Fourier (NSF) solutions using the first order of velocity slip and temperature jump boundary conditions (NSF) and the regularized 10‐moments (R10) in slip and early transition regime. The effect of an external body force is examined in different directions according to the cavity inclination angle. A Maxwell monatomic gas is considered to study the flow and thermal characteristics within the lid‐driven cavity. The NSF method correctly describes the velocity profiles, but it captures only the trend of other macroscopic parameters. The NSF heat flux, which is found to be from the hot regions to the cold ones, loses its validity in the slip regime and beyond to predict an inverted heat flux predicted by both regularized models. Contrary to the R10, which can capture the rarefaction effect in the whole slip regime. The dimensionless shear stress tends to grow by increasing the rarefaction along the moving wall. The external body force affects the shear stress and velocity streamlines symmetry and creates an additional vortex, depending on the inclination angle.

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“…The effect of such coefficient on thermal transpiration phenomena is evaluated using velocity dependent Maxwell (VDM) boundary condition, and by means of DSMC method . A heated microcavity with specular walls is also treated by means of NSF and moments theories (Baliti et al 2017(Baliti et al , 2016.…”

Section: Continuum Model Based Descriptionmentioning

confidence: 99%

Continuum Analysis of Rarefaction Effects on a Thermally Induced Gas Flow

Hssikou

Baliti

Alaoui

2019

Mathematical Problems in Engineering

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A Maxwell gas confined within a micro cavity with non-isothermal walls is investigated in the slip and early transition regimes using the classical and extended continuum theories. The vertical sides of the cavity are kept at the uniform and environmental temperature 0 , while the upper and bottom ones are linearly heated in opposite directions from the cold value 0 to the hot one . The gas flow is, therefore, induced only by the temperature gradient created along the longitudinal walls. The problem is treated from a macroscopic point of view by solving numerically the so-called regularized 13-moment equations (R13) recently developed as an extension of Grad 13-moments theory to the third order of the Knudsen number powers in the Chapman-Enskog expansion. The gas macroscopic properties obtained by this method are compared with the classical continuum theory results (NSF) using the first and second order of velocity slip and temperature jump boundary conditions. The gas flow behavior is studied as a function of the Knudsen number ( ), nonlinear effects, for different heating rates 0 ⁄ . The micro cavity aspect ratio effect is also evaluated on the flow fields in this study.

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Numerical simulation of heat transfer in a micro-cavity

Cited by 7 publications

References 19 publications

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

Rarefaction and external force effects on gas microflow in a lid‐driven cavity

Continuum Analysis of Rarefaction Effects on a Thermally Induced Gas Flow

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