Second-Order Slip Flow and Heat Transfer in a Long Isothermal Microchannel

Authors: Huei Chu Weng, Chien-Hung Liu

Abstract:

This paper presents a study on the effect of second-order slip and jump on forced convection through a long isothermally heated or cooled planar microchannel. The fully developed solutions of thermal flow fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and Smoluchowski jump boundary conditions. Results reveal that the second-order term in the Karniadakis slip boundary condition is found to contribute a negative velocity slip and then to lead to a higher pressure drop as well as a higher fluid temperature for the heated-wall case or to a lower fluid temperature for the cooled-wall case. These findings are contrary to predictions made by the Deissler model. In addition, the role of second-order slip becomes more significant when the Knudsen number increases.

Keywords: Microfluidics, forced convection, gas rarefaction, second-order boundary conditions.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1108703

References:

[1] G. Tunc and Y. Bayazitoglu, “Heat transfer in rectangular microchannels,” Int.J. Heat Mass Transfer, vol. 45, pp. 765–773, 2002.
[2] M. Renksizbulut, H. Niazmand, and G. Tercan, “Slip-flow and heat transfer in rectangular microchannels with constant wall temperature,” Int. J. Thermal Sci., vol. 45, pp. 870–881, 2006.
[3] M. Shojaeian and S. A. R. Dibaji, “Three-dimensional numerical simulation of the slip flow through triangular microchannels,” Int. Comm. Heat Mass Transfer, vol. 37, pp. 324–329, 2010.
[4] A. Sadeghi and M. H. Saidi, “Viscous dissipation and rarefaction effects on laminar forced convection in microchannels,” J. Heat Transf.-Trans. ASME, vol. 132, p. 072401, 2010.
[5] B. Çetin, “Effect of thermal creep on heat transfer for a two-dimensional microchannel flow: An analytical approach,” J. Heat Transf.-Trans. ASME, vol. 135, p. 101007, 2013.
[6] H. C. Weng and C.-K. Chen, “A challenge in Navier–Stokes-based continuum modeling: Maxwell–Burnett slip law,” Phys. Fluids, vol. 20, p. 106101, 2008.
[7] H. C. Weng “Second-order slip flow and heat transfer in a long isoflux microchannel,” Int. J. Mech. Aerosp. Ind. Mechatronics Eng., vol. 8, pp. 1422–1425, 2014.
[8] H. C. Weng and C.-K. Chen, “Variable physical properties in natural convective gas microflow,” J. Heat Transf.-Trans. ASME, vol.130, p. 082401, 2008.
[9] H. C. Weng and S. J., Jian, “Developing mixed convection in a vertical microchannel,” Adv. Sci. Lett., vol. 130, pp. 908–913, 2012.
[10] G. E. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation. New York: Springer, 2005, pp. 51–74, 167–172.
[11] R. G. Deissler, “An analysis of second-order slip flow and temperature jump boundary conditions for rarefied gases,” Int. J. Heat Mass Transfer, vol. 7, p. 681–694, 1964.