Thermal Lattice Boltzmann Simulation of Rarefied Gas Flows in Nanochannels for Wide Range of Knudsen Number

Abstract:

Using a modified Lattice Boltzmann Method (LBM), developing thermal flow through micro and nano channels has been modeled. Based on the improving of the dynamic viscosity and thermal conductivity, an effective relaxation time formulation is proposed which is able to simulate wide range of Knudsen numbers, Kn,. The results show that in spite of the standard LBM, the temperature distributions and the local Nusselt number obtained from this modified thermal LBM, agree well with the other numerical and empirical results in a wide range of Knudsen numbers.

• Periodical: Advanced Materials Research (Volumes 403-408)
• Pages: 5313-5317
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.403-408.5313
• Online since: November 2011
• Authors: A.H. Meghdadi Isfahani, A. Soleimani
• Keywords: Convection, Lattice Boltzmann Method, Micro-Flow, Nano Flows, Rarefaction

References

[1] G. Karniadakis, A. Beskok, N. Aluru, Microflows and nanoflows fundamentals and simulation, Springer Inc., USA. (2005).

[2] X. Shan, X. -F. Yuan, H. Chen, Kinetic theory representation of hydrodynamics: a way beyond Navier-Stokes equation, J. Fluid Mechanics. 550 (2006) 413-441.

DOI: 10.1017/s0022112005008153

[3] S.S. Chikatamarla, I.V. Karlin, Entropy and Galilean invariance of lattice Boltzmann theories, Phys. Rev. Lett. 97 (2006) 190601.

DOI: 10.1103/physrevlett.97.190601

[4] S. Ansumali, I.V. Karlin, S. Arcidiacono, A. Abbas, N.I. Prasianakis, Hydrodynamics beyond Navier-Stokes: Exact solution to the lattice Boltzmann hierarchy, Phys. Rev. Lett. 98 (2007) 124502.

DOI: 10.1103/physrevlett.98.124502

[5] S.H. Kim, H.P. Pitsch, I.D. Boyd, Accuracy of higher-order lattice Boltzmann methods for microscale flows with finite Knudsen numbers, J. computational Physics, 227 (2008) 8655-8671.

DOI: 10.1016/j.jcp.2008.06.012

[6] Y.H. Zhang, X.J. Gu, R.W. Barber, D.R. Emerson, Capturing Knudsen layer phenomena using a lattice Boltzmann model, Phys. Rev. E. 74 (2006) 046704.

DOI: 10.1103/physreve.74.046704

[7] G.H. Tang, Y.H. Zhang, D.R. Emerson, Lattice Boltzmann models for nonequilibrium gas flows, Phys. Rev. E. 77 (2008) 046701.

DOI: 10.1103/physreve.77.046701

[8] G.H. Tang, Y.H. Zhang, X.J. Gu, D.R. Emerson, Lattice Boltzmann modeling Knudsen layer effect in non-equilibrium flows, EPL, 83 (2008) 40008.

DOI: 10.1209/0295-5075/83/40008

[9] S. Succi, I.V. Karlin, H. Chen, Role of the H theorem in lattice Boltzmann hydrodynamic simulations, Rev. Mod. Phys. 74, (2002) 1203.

DOI: 10.1103/revmodphys.74.1203

[10] Y. Peng, Thermal Lattice Boltzmann Two-Phase Flow Model for Fluid Dynamics, PhD Thesis, University of Pittsburgh (2005).

[11] C. Cercignani, The Boltzmann Equations and its Applications, Springer-Verlag, New York (1988).

[12] X.Y. He, S.Y. Chen, G.D. Doolen, A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys. 146 (1998) 282-300.

DOI: 10.1006/jcph.1998.6057

[13] S. Succi, The lattice Boltzmann Equation: for Fluid Dynamics and Beyond, Oxford University Press (2001).

[14] A. Homayoon, A.H. Meghdadi Isfahani, E. Shirani, M. Ashrafizadeh, A novel modified lattice Boltzmann method for simulation of gas flows in wide range of Knudsen number, int. communications heat mass transfer, article in press (2011).

DOI: 10.1016/j.icheatmasstransfer.2011.03.007

[15] W.G. Polard, R.D. Present, On gaseous self-diffusion in long capillary tubes, Phys. Rev. 73 (7), (1948) 762-774.

DOI: 10.1103/physrev.73.762

[16] X.D. Niu, Y.T. Chew, C. Shu, A lattice Boltzmann BGK model for simulation of micro flows. Europhys Lett 2004; 67(4); 600.

DOI: 10.1209/epl/i2003-10307-8

[17] X.D. Niu, C. Shu, Y.T. Chew, A thermal lattice Boltzmann model with diffuse scattering boundary condition for micro thermal flows, computer & fluids, 36 (2007) 273-281.

DOI: 10.1016/j.compfluid.2005.11.007

[18] N.G. Hadjiconstantinou, O. Simek, Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels, J. heat transfer, 124, (2002), 356-364.

DOI: 10.1115/1.1447931

[19] H.P. Kavehpour, M. Faghri, Y. Asako, Effect of compressibility and rarefaction on gaseous flows in microchannels, J. numerical heat transfer A, 32: 677-696, (1997).

DOI: 10.1080/10407789708913912