Research Papers: Natural and Mixed Convection

Second-Order Mixed Convective Flow in a Long Vertical Microchannel

[+] Author and Article Information
Huei Chu Weng

Department of Mechanical Engineering,
Chung Yuan Christian University,
Chungli, 32023, Taiwan, ROC

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received April 2, 2012; final manuscript received July 18, 2012; published online January 4, 2013. Assoc. Editor: Bruce L. Drolen.

J. Heat Transfer 135(2), 022506 (Jan 04, 2013) (5 pages) Paper No: HT-12-1148; doi: 10.1115/1.4007423 History: Received April 02, 2012; Revised July 18, 2012

The present investigation is concerned with the role of second-order slip in the mixed convection through a long heated vertical planar microchannel with asymmetric wall temperatures. The fully developed solutions of fields and the corresponding characteristics are analytically derived on the basis of second-order Maxwell–Smoluchowski–Burnett (MSB) slip/jump boundary conditions. Results reveal that second-order slip has an appreciable effect on the flow but a negligible effect on the heat transfer. The effect is to raise the gas motion speeds near the heated walls and to enlarge the pressure gradient required to drive the flow. It then leads to the reduction of local flow drag, except for the case where a reversed flow region exists. The second-order effect could be magnified by increasing the mixed convection number, the ratio of the Grashof number to the Reynolds number.

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Schaaf, S. A., and Chambré, P. L., 1961, Flow of Rarefied Gases, Princeton University Press, Princeton, NJ.
Beskok, A.2001, “Validation of a New Velocity-Slip Model for Separated Gas Microflows,”Numer. Heat Transfer B, 40, pp. 451–471. [CrossRef]
Tunc, G., and Bayazitoglu, Y.2002, “Heat Transfer in Rectangular Microchannels,” Int. J. Heat Mass Transfer, 45, pp. 765–773. [CrossRef]
Renksizbulut, M., Niazmand, H., and Tercan, G., 2006, “Slip-Flow and Heat Transfer in Rectangular Microchannels With Constant Wall Temperature,”Int. J. Therm. Sci., 45, pp. 870–881. [CrossRef]
Shojaeian, M., and Dibaji, S. A. R., 2010, “Three-Dimensional Numerical Simulation of the Slip Flow Through Triangular Microchannels,” Int. Commun. Heat Mass Transfer, 37, pp. 324–329. [CrossRef]
Sadeghi, A., and Saidi, M. H., 2010, “Viscous Dissipation and Rarefaction Effects on Laminar Forced Convection in Microchannels,”ASME J. Heat Transfer, 132, p. 072401. [CrossRef]
Chen, C. K., and Weng, H. C., 2005, “Natural Convection in a Vertical Microchannel,”ASME J. Heat Transfer, 127, pp. 1053−1056. [CrossRef]
Haddad, O. M., Abuzaid, M. M., and Al-Nimr, M. A., 2005, “Developing Free-Convection Gas Flow in a Vertical Open-Ended Microchannel Filled With Porous Media,”Numer. Heat Transfer A, 48, pp. 693–710. [CrossRef]
Biswal, L., Som, S. K., and Chakraborty, S., 2007, “Effects of Entrance Region Transport Processes on Free Convection Slip Flow in Vertical Microchannels With Isothermally Heated Walls,”Int. J. Heat Mass Transfer, 50, pp. 1248−1254. [CrossRef]
Chen, C. K., and Weng, H. C., 2006, “Developing Natural Convection With Thermal Creep in a Vertical Microchannel,”J. Phys. D, 39, pp. 3107−3118. [CrossRef]
Chakraborty, S., Som, S. K., and Rahul, 2008, “A Boundary Layer Analysis for Entrance Region Heat Transfer in Vertical Microchannels Within the Slip Flow Regime,” Int. J. Heat Mass Transfer, 51, pp. 3245–3250. [CrossRef]
Weng, H. C., and Chen, C. K., 2008, “Variable Physical Properties in Natural Convective Gas Microflow,”ASME J. Heat Transfer, 130, p. 082401. [CrossRef]
Weng, H. C., and Chen, C. K., 2009, “Drag Reduction and Heat Transfer Enhancement Over a Heated Wall of a Vertical Annular Microchannel,”Int. J. Heat Mass Transfer, 52, pp. 1075–1079. [CrossRef]
Weng, H. C., and Chen, C. K., 2008, “On the Importance of Thermal Creep in Natural Convective Gas Microflow With Wall Heat Fluxes,”J. Phys. D, 41, p. 115501. [CrossRef]
Buonomo, B., and Manca, O., 2010, “Natural Convection Slip Flow in a Vertical Microchannel Heated at Uniform Heat Flux,”Int. J. Therm. Sci., 49, pp. 1333–1344. [CrossRef]
Avci, M., and Aydin, O., 2007, “Mixed Convection in a Vertical Parallel Plate Microchannel,”ASME J. Heat Transfer, 129, pp. 162–166. [CrossRef]
Avci, M., and Aydin, O., 2007, “Mixed Convection in a Vertical Parallel Plate Microchannel With Asymmetric Wall Heat Fluxes,”ASME J. Heat Transfer, 129, pp. 1091–1095. [CrossRef]
Avci, M., and Aydin, O., 2009, “Mixed Convection in a Vertical Microannulus Between Two Concentric Microtubes,”ASME J. Heat Transfer, 131, p. 014502. [CrossRef]
Weng, H. C., and Jian, S. J., 2012, “Developing Mixed Convection in a Vertical Microchannel,”Adv. Sci. Lett., 9, pp. 908–913. [CrossRef]
Arkilic, E. B., Schmidt, M. A., and Breuer, K. S., 1997, “Gaseous Slip Flow in Long Microchannels,”J. Microelectromech. Syst., 6, pp. 167–178. [CrossRef]
Beskok, A., and Karniadakis, G. E., 1999, “A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales,”Microscale Thermophys. Eng., 3, pp. 43−77. [CrossRef]
Ewart, T., Perrier, P., Graur, I., and Méolans, J. G., 2007, “Mass Flow Rate Measurements in a Microchannel, From Hydrodynamic to Near Free Molecular Regimes,”J. Fluid Mech., 584, pp. 337–356. [CrossRef]
Weng, H. C., and Chen, C. K., 2008, “A Challenge in Navier–Stokes-Based Continuum Modeling: Maxwell–Burnett Slip Law,”Phys. Fluids, 20, p. 106101. [CrossRef]
Perrier, P., Graur, I. A., Ewart, T., and Meolans, J. G., 2011, “Mass Flow Rate Measurements in Microtubes: From Hydrodynamic to Near Free Molecular Regime,”Phys. Fluids, 23, p. 042004. [CrossRef]
Weng, H. C., 2006, “Gas Transport Phenomena in Microfluidic Systems,” Ph.D. thesis, Department of Mechanical Engineering, National Cheng Kung University, Taiwan.
Surana, K. S., Allu, S., Tenpas, P. W., and Reddy, J. N., 2007, “k-Version of Finite Element Method in Gas Dynamics: Higher-Order Global Differentiability Numerical Solutions,”Int. J. Numer. Meth. Eng, 69, pp. 1109−1157. [CrossRef]


Grahic Jump Location
Fig. 2

Velocity distribution for different values of Gr/Re with Kn=0.1

Grahic Jump Location
Fig. 3

Pressure gradient versus Gr/Re with Kn=0.1

Grahic Jump Location
Fig. 4

Local flow drag versus Gr/Re for different values of ξ with Kn=0.1



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