Lattice Boltzmann model for thermal transpiration

Abstract

The conventional Navier-Stokes-Fourier equations with no-slip boundary conditions are unable to capture the phenomenon of gas thermal transpiration. While kinetic approaches such as the direct simulation Monte Carlo method and direct solution of the Boltzmann equation can predict thermal transpiration, these methods are often beyond the reach of current computer technology, especially for complex three-dimensional flows. We present a computationally efficient nonequilibrium thermal lattice Boltzmann model for simulating temperature-gradient-induced flows. The good agreement between our model and kinetic approaches demonstrates the capabilities of the proposed lattice Boltzmann method.

Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer

“…Equations (11) and (22) have been further simplified in the literature to simulate micro-and nanoscale heat transfer [21][22][23][24]. For example, the model in Ref.…”

“…The lattice Boltzmann (LB) method is an established numerical scheme for solving the Boltzmann BGK equation [4,5]. Due to this intrinsic link to the kinetic theory of gases, the LB method has been applied to investigate a large number of micro-and nanoscale fluid flows and heat transfer where the gas mean free path λ is comparable to the device dimension L [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], i.e., the finite Knudsen number Kn = λ/L. The LB method was originally applied to simulate flows in the continuum limit, where an exact weakly compressible formulation exists.…”

“…In comparison, little work has been done on the LB method for heat transfer at small length scales. Two approaches were developed to incorporate heat transfer effects into the LB framework: the multispeed approach [17][18][19][20][33][34][35][36] and the double distribution function (DDF) approach [21][22][23][24][37][38][39][40]. The multispeed approach is based on the Boltzmann equation, which defines a single-particle distribution function and uses its second-order velocity moment to describe the temperature field.…”

“…Owing to these features, the DDF approach is very popular in simulating continuum heat transfer problems [37][38][39][40]. Some studies extend these DDF LB models to simulate heat transfer at small length scales while adding heuristic treatments to mimic noncontinuum effects [21][22][23][24]. Nonetheless, such continuumbased DDF LB models lack a rigorous theoretical foundation for modeling noncontinuum heat transfer phenomena, and accuracy of these LB models deteriorates significantly when applied to heat transfer at moderate and large Knudsen numbers.…”

Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows

“…For example, for gaseous flows at the microscale, kinetic effects have to be taken into account as the Knudsen number (Kn, the ratio of the mean free path and the characteristic length) becomes finite (Hadjiconstantinou, 2006). Due to its kinetic origins, the LB method has been shown to be able to describe moderately complex kinetic effects (see, e.g., Zhang et al, 2005;Toschi & Succi, 2005;Sbragaglia & Succi, 2005Tang et al, 2008b;Zhang et al, 2006;Shan et al, 2006;Ansumali et al, 2007;Kim et al, 2008a;Yudistiawan et al, 2008;Guo et al, 2006;Succi, 2002;Kim et al, 2008b;Tang et al, 2008a;Tian et al, 2007). Particularly, as the LB method can be considered as an approximation to the Boltzmann-BGK equation, high-order models should, in principle, be able to go beyond NS hydrodynamics (Shan et al, 2006;Meng & Zhang, 2011a).…”