Provide a suitable range to include the thermal creeping effect on slip velocity and temperature jump of an air flow in a nanochannel by lattice Boltzmann method
Introduction
Micro and NanoElectro Mechanical Systems (MEMS and NEMS) are considered as the one of main favorite research topics nowadays. Flow properties in microscale regimes are different from the macro ones; so that well known Knudsen number (Kn=λ/DH) is used to classify the micro–nanoflows where λ represents the molecular mean free path. The fluid flow is supposed as continuum at Kn<0.001 and Navier–Stokes equations could be used to simulate the flow field at this state [1], [2], [3], [4], [5]. However other regimes as like the slip flow, transient and free molecular can be achieved at 0.001<Kn<0.1, 0.1<Kn<10 and Kn>10, respectively [6], [7], [8], [9], [10], [11].
Navier–Stokes methods with slip velocity boundary condition beside the particle based methods are able to investigate the slip flow regime. The trace and collision between the molecular and particles of a gas flow are the main objects of particle based methods including lattice Boltzmann method (LBM), direct simulation of Monte Carlo (DSMC) and molecular dynamics (MD) [12], [13], [14], [15], [16]. Among them, LBM shows less cost of computation and also works with simpler math equations than MD or DSMC which makes LBM more functional for the microflows [17], [18], [19], [20], [21], [22].
LBM consists of collision and propagation between the particles placed on the specified locations on a lattice. In this approach, the fluid domain is considered by the fictive particles which each one has been made of too many molecular. LBM is almost a new model which deals better with the complex boundaries than the CFD methods. Moreover LBM uses the simple and parallel algorithm that can be used for a wide range of Knudsen number [23], [24], [25], [26], [27], [28]. However it should be mentioned that LBM needed an appropriate collision operation to avoid divergence; in this way, the model of LBM-BGK was developed which showed suitable accuracy and stability [29], [30], [31].
Different models of thermal LBM can be referred for the thermal domains. The internal energy distribution function one is able to consider the pressure work and viscous heat dissipation beside its higher numerical stability. This approach is called thermal lattice Boltzmann method (TLBM) which the both of hydrodynamic (f) and thermal (g) distribution functions are used in together [32], [33], [34], [35], [36], [37], [38].
Provide a suitable formulation for the boundary conditions in terms of distribution functions is one of disadvantages of LBM so that several researchers are trying to develop the useful practical LBM-boundary conditions. Diffuse scattering boundary condition (DSBC) introduced by Niu et al. [39], [40] and Shu et al. [41] represents the relaxation time according to the Knudsen number to determine the slip velocity.
There are several other different models in this way and it is still tried to develop LBM ability at different geometries and conditions [42], [43], [44], [45], [46], [47], [48]. However the effect of thermal creeping has been ignored in the majority of them; hence there is lack of works concerned this phenomenon which means less accuracy in achievements. As a result, the effect of thermal creeping on hydrodynamic and thermal properties of a nanoflow is provided by LBM for the first time at present work.
Section snippets
Problem statement
Forced convection of air (Pr=υ/α=0.7) through a two dimensional nanochannel is studied numerically by using the lattice Boltzmann method (Fig. 1). TLBM-BGK model based on momentum (f) and internal energy (g) distribution functions is chosen to simulate the flow and heat transfer at 0.001≤Kn≤0.1; which implies the slip flow regime at Reynolds number equals to Re=ρiuiDH/μ=10,100,1000. The appropriate hydrodynamic and thermal boundary conditions are used in terms of distribution functions needed
Lattice Boltzmann method
Using density-momentum distribution function, the Boltzmann equation is observed as [33]:
Ω is the collision operation. The internal energy distribution function is written as follows to simulate the thermal domain:which leads to generate the thermal lattice Boltzmann equation according to the internal energy:
Now the collision operations of LBM-BGK model for hydrodynamic and thermal fields are defined:in which
Validations
The flow and heat transfer of the air nanoflow is simulated using the LBM developed computer code in FORTRAN language. Appropriate grid independency study is performed between 1050×35, 1200×40 and 1350×45 lattice nodes; and among them the lattice with 1200×40 nodes shows suitable accuracy and is chosen for the further calculations.
In Fig. 3, the fully developed dimensionless velocity profiles (U=u/ui) through a nanochannel are compared with those of Zhang et al. [31] at Kn=0.05 and Kn=0.1 and
Results and discussions
Forced convection of air in a two dimensional nanochannel is studied numerically by using lattice Boltzmann method (Fig. 1). Nanochannel side walls are kept hot while the cold inlet air streams along them; moreover its aspect ratio is equals to AR=L/H=30.
Conclusion
Forced convection of air in a two dimensional nanochannel was studied numerically by using the lattice Boltzmann method. Nanochannel side walls were kept hot while the cold inlet air streamed along them. The calculations were performed for Re=10,100,1000 and Kn=0.001,0.01,0.1 and Ec=0.1,1,10. The effects of slip flow regime (according to Kn) involved thermal creeping (according to Ec) on hydrodynamic and thermal domains were investigated for the first time by the lattice Boltzmann method and
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