Second-Order Slip Flow and Heat Transfer in a Long Isothermal Microchannel
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:70815", author = "Huei Chu Weng and Chien-Hung Liu", title = "Second-Order Slip Flow and Heat Transfer in a Long Isothermal Microchannel", 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.", volume = "9", number = "7", pages = "1352-4", }