Analysis of Lattice Boltzmann Method for Slip Flow in Trapezoidal Microchannels

Analytical and Numerical Methods in Mechanical Design

دوره 1، شماره 1، شهریور 2022، صفحه 57-69   

نویسندگان

Arman Maroufi^{* 1}؛ Cyrus Aghanajafi²؛ Jamasb Pirkandi³

¹Faculty of Industrial and Mechanical Engineering, Islamic Azad University, Qazvin Branch, Qazvin, Iran

²Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran

³Department of Aerospace Engineering, Malek Ashtar University of Technology, Tehran, Iran

چکیده

Two dimensional analysis of fluid flow and heat transfer through the trapezoidal microchannel has been done. The energy and Nervier stokes equations have been solved considering the wall slip velocity and temperature jump using the Lattice Boltzmann method (LBM). The relation between relaxation times and Knudsen number has been derive in LBM. The effects of Reynolds number, Nusslelt number, temperature jump and velocity slip on different Knudsen number (0.001<Kn<0.1) and different aspect ratios (0.2<AR<1.2) were investigated. The good agreement between results and earlier studies were found. Results show the important effect of AR and Knudsen number on Nusselt number in trapezoidal microchannel. At low Reynolds number the significant influence on Nusselt number has been seen.

کلیدواژه‌ها

Trapezoidal microchannel؛ Lattice Boltzmann method؛ Knudsen number؛ Temperature jump

مراجع

1. Mavriplis, C., J. C. Ahn, and R. Goulard. "Heat transfer and flow fields in short micro channels using direct simulation Monte Carlo." Journal of Thermophysics and Heat Transfer 11.4 (1997): 489-496.
2. Jiang, Pei-Xue, et al. "Thermal–hydraulic performance of small scale micro-channel and porous media heat-exchangers." International Journal of Heat and Mass Transfer 44.5 (2001): 1039-1051.
3. Muzychka, Y. S. "Constructed multi-scale design of compact micro-tube heat sinks and heat exchangers." International journal of thermal sciences 46.3 (2007): 245-252.
4. Srinivasan, Ravi, et al. "Micro machined reactors for catalytic partial oxidation reactions." AIChE Journal 43.11 (1997): 3059-3069.
5. Beskok, Ali, and George E. Karniadakis. Simulation of heat and momentum transfer in complex microgeometries. MS thesis. Princeton University, 1994.
6. Hettiarachchi, HD Madhawa, et al. "Three-dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature." International Journal of Heat and Mass Transfer 51.21 (2008): 5088-5096.
7. Cao, Bin, Guang Wen Chen, and Quan Yuan. "Fully developed laminar flow and heat transfer in smooth trapezoidal microchannel." International communications in heat and mass transfer 32.9 (2005): 1211-1220.
8. Shams, M., et al. "Numerical simulation of slip flow through rhombus microchannels." International Communications in Heat and Mass Transfer36.10 (2009): 1075-1081.
9. Sun, Wei, Sadik Kakac, and Almila G. Yazicioglu. "A numerical study of single-phase convective heat transfer in microtubes for slip flow." International Journal of Thermal Sciences 46.11 (2007): 1084-1094.
10. McHale, John P., and Suresh V. Garimella. "Heat transfer in trapezoidal microchannels of various aspect ratios." International Journal of Heat and Mass Transfer 53.1 (2010): 365-375.
11. Morini, Gian Luca, M. Spiga, and P. Tartarini. "The rarefaction effect on the friction factor of gas flow in microchannels." Superlattices and microstructures 35.3 (2004): 587-599.
12. Hong, Chungpyo, Yutaka Asako, and Jae-Heon Lee. "Heat transfer characteristics of gaseous flows in micro-channel with constant heat flux." International Journal of Thermal Sciences 46.11 (2007):1153-1162.
13. Haddad, O. M., M. M. Abuzaid, and M. A. Al-Nimr. "Developing free-convection gas flow in a vertical open-ended microchannel filled with porous media." Numerical Heat Transfer, Part A: Applications 48.7 (2005): 693-710.
14. Wang, Qiu-Wang, et al. "Numerical investigation of rarefied diatomic gas flow and heat transfer in a microchannel using DSMC with uniform heat flux boundary condition—Part I: numerical method and validation." Numerical Heat Transfer, Part B: Fundamentals 53.2 (2007): 160-173.
15. Aghanajafi, C., V. Vandadi, and M. R. Shahnazari. "Investigation of convection and radiation heat transfer in rhombus microchannels." IJRRAS3.2 (2010): 167-176.
16. Bo, Zheng, et al. "Numerical study on the pressure drop of fluid flow in rough microchannels via the lattice Boltzmann method." International Journal of Numerical Methods for Heat & Fluid Flow 25.8 (2015): 2022-2031.
17. Nayak, Rajlakshmi, et al. "Flow and Thermal Transport Studies in Microchannel Flows using Lattice Boltzmann Method." International Journal of Micro-Nano Scale Transport (2014).
18. Esfahanian, V., E. Dehdashti, and A. M. Dehrouyeh-Semnani. "Fluid-Structure Interaction in microchannel using Lattice Boltzmann method and size-dependent beam element." Advances in Applied Mathematics and Mechanics 6.3 (2014): 345-358.
19. Bakhshan, Younes, and Alireza Omidvar. "Calculation of friction coefficient and analysis of fluid flow in a stepped micro-channel for wide range of Knudsen number using Lattice Boltzmann (MRT) method." Physica A: Statistical Mechanics and its Applications 440 (2015): 161-175.
20. Zarita, Rahouadja, and Madjid Hachemi. "Microchannel fluid flow and heat transfer by lattice boltzmann method." (2014).
21. Karimipour, Arash. "New correlation for Nusselt number of nanofluid with Ag/Al 2 O 3/Cu nanoparticles in a microchannel considering slip velocity and temperature jump by using lattice Boltzmann method." International Journal of Thermal Sciences 91 (2015): 146-156.
22. Maroufi, Arman, and Cyrus Aghanajafi. "Analysis of conduction–radiation heat transfer during phase change process of semitransparent materials using lattice Boltzmann method." Journal of Quantitative Spectroscopy and Radiative Transfer 116 (2013): 145-155.
23. Liou, Tong-Miin, and Chin-Tien Lin. "Three-dimensional rarefied gas flows in constricted microchannels with different aspect ratios: asymmetry bifurcations and secondary flows." Microfluidics and Nanofluidics 18.2 (2015): 279-292.
24. Taher, M. A., L. K. Saha, and Y. W. Lee. "Effects of Circular Riblets Rough Microchannel on Friction and Fluid Flow using LBM." Procedia Engineering105 (2015): 425-430.
25. Kuzmin, A., M. Januszewski, D. Eskin, F. Mostowfi, and J. J. Derksen. "Three-dimensional binaryliquid lattice Boltzmann simulation of microchannels with rectangular cross sections." Chemical engineering journal178 (2011): 306-316.
26. Qian, Y. H., Dominique d'Humières, and Pierre Lallemand. "Lattice BGK models for Navier-Stokes equation." EPL (Europhysics Letters) 17.6 (1992): 479.
27. Zou, Qisu, and Xiaoyi He. "On pressure and velocity boundary conditions for the lattice Boltzmann BGK model." Physics of fluids 9.6 (1997): 1591-1598.
28. Chen, Sheng, and Zhiwei Tian. "Simulation of microchannel flow using the lattice Boltzmann method." Physica A: Statistical Mechanics and its Applications 388.23 (2009): 4803-4810.
29. Guo, Zhaoli, Chuguang Zheng, and Baochang Shi. "An extrapolation method for boundary conditions in lattice Boltzmann method." Physics of Fluids 14.6 (2002): 2007-2010.
30. Renksizbulut, Metin, H. Niazmand, and G. Tercan. "Slip-flow and heat transfer in rectangular microchannels with constant wall temperature." International Journal of Thermal Sciences 45.9 (2006): 870-881.