In this paper, we propose a lattice Boltzmann BGK model for simulation of micro flows with heat transfer based on kinetic theory and the thermal lattice Boltzmann method (He et al., J. Comp. Phys. 146:282, 1998). The relaxation times are redefined in terms of the Knudsen number and a diffuse scattering boundary condition (DSBC) is adopted to consider the velocity slip and temperature jump at wall boundaries. To check validity and potential of the present model in modelling the micro flows, two two-dimensional micro flows including thermal Couette flow and thermal developing channel flow are simulated and numerical results obtained compare well with previous studies of the direct simulation Monte Carlo (DSMC), molecular dynamics (MD) approaches and the Maxwell theoretical analysis

A lattice boltzmann kinetic model for microflow and heat transfer

In recent years, the lattice Boltzmann method (LBM) has become an alternative and attractive approach to simulate numerous fluid flow problems. A colloidal mixture of nano-sized particles in a base liquid called nanofluid, which is the new generation of heat transfer fluid for various heat transfer applications, has recently been demonstrated to have great potential for improving the heat transfer properties of liquids. This paper intends to provide a brief review of researches on application of lattice Boltzmann method on the prediction of nanofluid and identifies opportunities for future research.

Lattice Boltzmann method for convective heat transfer of nanofluids – A review

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the Lattice Boltzmann method, can provide semi-quantitative results also in the non-hydrodynamic, finite-Knudsen regime, up to $Kn\sim {\cal O}(1)$. This may help the interpretation of recent Lattice Boltzmann simulations of microflows, which show satisfactory agreement with continuum kinetic theory in the moderate-Knudsen regime.

https://arxiv.org/pdf/cond-mat/0509283.pdf

A note on the lattice Boltzmann method beyond the Chapman Enskog limits

Great advances have been made with the lattice Boltzmann (LB) method for complicated fluid phenomena and fundamental thermal processes over the past three decades. This paper presents a systematic overview of the LB method from 1990 to 2018, based on bibliometric analysis and the Science Citation Index Expanded (SCI-E) database. The results show that China took the leading position in this field, followed by the USA and UK. The Chinese Academy of Sciences had the most publications, while the Los Alamos National Laboratory was first as far as highest average citation per paper and h-index are concerned. Physical Review E was the most productive journal and “Mechanics” was the most frequently used subject category. Keyword analysis indicated that recent research has focused on the natural convection and heat transfer of nanofluid or multiphase flow in complex porous media. Hydrothermal treatment of nanofluid with shape factor on the conditions, such as variable magnetic fields, thermal radiation and slipping boundary, were the research hotspots. Further research perspectives mainly explore the multiscale models for coupling multiple transport phenomena, morphology optimization of porous parameters, new nanoparticles with shape factor, multicomponent LB method considering Knudsen diffusion effect, LB-based hybrid methods, radiation performance or boiling-heat transfer of nanofluid, and the active control of droplets, may continue to attract more attention. Moreover, some new applications, such as phase change of metal foam, erosion induced by nanaofluid, anode circulating, 3D modeling in thermal systems with vibration, and magnetohydrodynamics microfluid devices, could be of interest going forward.

/pdf/lattice-boltzmann-method-for-fluid-thermal-systems-status-2a1cetgucv.pdf

Lattice Boltzmann Method for Fluid-Thermal Systems: Status, Hotspots, Trends and Outlook

The flow field in a rough microchannel is numerically analyzed using a hybrid solver, dynamically coupling kinetic and Navier–Stokes solutions computed in rarefied and continuum subareas of the flow field, respectively, and a full Navier–Stokes solver. The rough surface is configured with triangular roughness elements, with a maximum relative roughness of 5 % of the channel height. The effects of Mach number, Knudsen number (or Reynolds number) and roughness height are investigated and discussed in terms of Poiseuille number and mass flow rate. Discrepancies between full Navier–Stokes and hybrid solutions are analyzed, assessing the range of validity of Navier–Stokes equations provided with first-order slip boundary conditions for modeling gas flow along a rough surface. Results indicate that the roughness increases Poiseuille number and decreases mass flux in comparison with those for the smooth microchannel. Increasing rarefaction results in further enhancement of roughness effect. At the same time, the compressibility effect is more noticeable than the roughness one, although the compressibility effect is alleviated by increase in the rarefaction. It was found that, although the Navier–Stokes solution of the flow in a smooth channel is accurate up to Kn = 0.1, when relative roughness height is higher than 1.25 % significant errors already appear at Kn = 0.02.

Numerical simulation of gas flow in rough microchannels: hybrid kinetic–continuum approach versus Navier–Stokes

Poiseuille number of rarefied gas flow in channels with designed roughness is studied and a multiplicative decomposition of Poiseuille number on the effects of rarefaction and roughness is proposed. The numerical methodology is based on the mesoscopic lattice Boltzmann method. In order to eliminate the effect of compressibility, the incompressible lattice Boltzmann model is used and the periodic boundary is imposed on the inlet and outlet of the channel. The combined bounced condition is applied to simulate the velocity slip on the wall boundary. Numerical results reveal the two opposite effects that velocity gradient and friction factor near the wall increase as roughness effect increases; meanwhile, the increments of the rarefaction effect and velocity slip lead to a corresponding decrement of friction factor. An empirical relation of Poiseuille number which contains the two opposite effects and has a better physical meaning is proposed in the form of multiplicative decomposition, and then is validated by available experimental and numerical results.

Yushan Ni

Papers

A multiplicative decomposition of Poiseuille number on rarefaction and roughness by lattice Boltzmann simulation