Simulation of thermal micro-flow using lattice Boltzmann method with Langmuir slip model

Chen, Sheng; Tian, Zhilong

doi:10.1016/j.ijheatfluidflow.2009.12.006

Cited by 63 publications

(27 citation statements)

References 46 publications

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“…The local Nusselt number (Nu) can be defined [23,[49][50][51][52][53] as, (19) where n is inward direction normal to wall. The local values of the Nusselt number can then be averaged over the surface to determine the overall heat transfer, i.e., average Nusselt number ( ), as (20) Henceforth, the dimensionless variables (u * x , u * y , T * , P * , x * , y * , etc.)…”

Section: Problem Statement and Mathematical Modelingmentioning

confidence: 99%

“…It utilizes the two different distribution functions, one each, for the estimation of flow and thermal fields. It is proven to be much better in terms of numerical stability and efficiency for the wider range of temperature and Prandtl numbers [21][22][23]. It is, however, unfavorable as the simplicity of LBM is lost due to the involvement of compression work done by pressure and viscous heat dissipation [21].…”

Section: Introductionmentioning

confidence: 99%

“…The macroscopic temperature equation is similar to a passive scalar evolution equation, if the viscous heat dissipation and compression work done by pressure are negligible. This approach possesses better numerical stability, over other two approaches, in yielding the efficient solution over the broad range of Prandtl number and the simplicity of LBM is also retained [21][22][23]. The passive scalar thermal lattice Boltzmann method (PS-TLBM) is, therefore, used herein for the estimation of natural convection flow and heat transfer characteristics of a partially heated open ended square cavity.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lattice Boltzmann analysis of effect of heating location and Rayleigh number on natural convection in partially heated open ended cavity

Gangawane

Bharti

Kumar

2015

Korean J. Chem. Eng.

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Natural convection characteristics of a partially heated open ended square cavity have been investigated numerically by using an in-house computational flow solver based on the passive scalar thermal lattice Boltzmann method (PS-TLBM) with D2Q9 (two-dimensional and nine-velocity link) lattice model. The partial part of left wall of the cavity is heated isothermally at either of the three different (bottom, middle and top) locations for the fixed heating length as half of characteristic length (H/2) while the right wall is open to the ambient conditions. The other parts of the cavity are thermally isolated. In particular, the influences of partial heating locations and Rayleigh number (10 3 ≤ Ra≤10 6 ) in the laminar zone on the local and global natural convection characteristics (such as streamline, vorticity and isotherm contours; centerline variations of velocity and temperature; and local and average Nusselt numbers) have been presented and discussed for the fixed value of the Prandtl number (Pr=0.71). The streamline patterns show qualitatively similar nature for all the three heating cases and Rayleigh numbers, except the change in the recirculation zone which is found to be largest for middle heating case. Isotherm patterns are shifted towards a partially heated wall on increasing Rayleigh number and/or shifting of heating location from bottom to top. Both the local and average Nusselt numbers, as anticipated, shown proportional increase with Rayleigh number. The cavity with middle heating location shown higher heat transfer rate than that for the top and bottom heating cases. Finally, the functional dependence of the average Nusselt number on flow governing parameters is also presented as a closure relationship for the best possible utilization in engineering practices and design.

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Section: Problem Statement and Mathematical Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Lattice Boltzmann analysis of effect of heating location and Rayleigh number on natural convection in partially heated open ended cavity

Gangawane

Bharti

Kumar

2015

Korean J. Chem. Eng.

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“…Slit type microchannels were taken into experimental investigation by Almeida et al (2010); their measurements for wide ranges of Reynolds number, hydraulic diameter and surface roughness proposed the systematic variation of frictional activity with micro structure and flow characteristics. Velocity slip and temperature jump phenomena in micro-flows were numerically investigated by Chen & Tian (2010). Wen et al (2003) experimentally inspected the augmentation characteristics of heat transfer and pressure drop by the imposed wall heat flux, mass flux and different strip-type inserts in small tubes.…”

Section: Introductionmentioning

confidence: 99%

Fluid Mechanics, Heat Transfer and Thermodynamic Issues of Micropipe Flows

Ozalp¹

2011

Evaporation, Condensation and Heat Transfer

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“…Essentially, the gas molecules are assumed to interact with the surface via a long range attractive force, as a result the molecules can be adsorbed onto the surface and then desorbed some time later. The situation can be modelled by assuming a number of 'sites' that are available for a molecule to bond to and, from the percentage of sites occupied, the velocity slip and temperature jump conditions can be calculated [126]. This method was rst proposed in a practical sense by Myong [127] and implemented with promising results thereafter [126,128,129].…”

Section: 5mentioning

confidence: 99%

Numerical investigation of gaseous heat and mass transfer: the effect of rarefaction

Bond¹

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Recent advances in micro-scale fabrication have uncovered the limitations of classical uid dynamics analysis techniques. The current status of numerical techniques for micro-ows is found to be highly varied with no accepted best-practice. This situation encourages investigation of new and improved methods in the eld. In this work a new numerical method based upon the solution of the model Boltzmann equation using arbitrary order polynomials is presented. The S-model is solved by a discrete ordinate method with velocity space discretized with a truncated Hermite polynomial expansion. Physical space is discretized according to the Conservative Flux Approximation scheme with extension to allow non-uniform grid spacing. This approach, which utilizes Legendre polynomials, allows the spatial representation and ux calculation to be of arbitrary order. High order boundary conditions are implemented. Various results are shown to demonstrate the utility and limitations of the method with comparison to solutions of the Euler and Navier-Stokes equations and from the Direct Simulation Monte Carlo and Uni ed Gas Kinetic schemes. The e ect of both the velocity space discretization and Knudsen number on the convergence properties of the scheme are also investigated.Due to limitations in the geometric adaptability of the new method an implementation of the Uni ed Gas Kinetic Scheme with a variety of enhancements is also presented. These enhancements include internal degree of freedom handling and advanced gas-surface interaction mechanisms including a model of the adsorption and desorption of gas molecules by a surface.The numerical methods developed are used to investigate physical ow phenomena including rare ed e ects such as thermal creep. Pressure gradient inducing thermal creep driven ows in microchannels, commonly referred to as Knudsen pumps, are investigated across a range of rarefaction with particular focus on the e ects of realistic gas coe cients and geometric con guration on performance.A range of geometries are investigated consisting of a previously proposed curved-straight channel and three newly developed channels including a novel two dimensional matrix pump arrangement and classical linear designs. Use of the S-model kinetic equations enables investigation with realistic values of the Prandtl number and viscosity index for argon and nitrogen as well as for Maxwell molecules. The pumping performance and ow structure of each geometry is investigated for a range of channel aspect ratios and Knudsen numbers where the Knudsen numbers are nely spaced between 0.1 and 2.0 to allow approximate performance extrema to be identi ed. The in uence of Prandtl number is found to be signi cant with increased maximum mass ow rates for argon and nitrogen of 5.5-6% when compared to a gas with Maxwellian molecular model. The impact of speci c heat ratio is found to be comparatively minor with a di erence of 0.5% between the argon and nitrogen. The two new channel designs are found to lie between the classical and existing ...

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Simulation of thermal micro-flow using lattice Boltzmann method with Langmuir slip model

Cited by 63 publications

References 46 publications

Lattice Boltzmann analysis of effect of heating location and Rayleigh number on natural convection in partially heated open ended cavity

Lattice Boltzmann analysis of effect of heating location and Rayleigh number on natural convection in partially heated open ended cavity

Fluid Mechanics, Heat Transfer and Thermodynamic Issues of Micropipe Flows

Numerical investigation of gaseous heat and mass transfer: the effect of rarefaction

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