An analytical solution for buoyancy-induced gas microflow in a tall differentially heated enclosure with isothermal vertical walls is presented. The Navier—Stokes system has been solved. The Boussinesq approximation has been employed. Wall—fluid interactions are modelled by first-order velocity slip and temperature jump conditions. The analysis presented covers continuum to slip-flow regime. A functional form for the Nusselt number has been derived analytically. The results indicate that as the Knudsen number increases, the Nusselt number decreases.
WhitesidesG. M., ‘The origins and the future of micro-fluidics’Nature442 (2002): 368–373.
2.
Gad-el-HakM., ‘The fluid mechanics of microdevices - the Freeman scholar lecture’J. Fluids Engng121 (1991): 5–33.
3.
BeskokA.KarniadakisG. E.TrimmerW., ‘Rarefaction and compressibility effects in gas microflows’J. Fluids Engng118 (1991): 448–456.
4.
ZoharY., Heat convection in micro ducts (London: Kluwer Academic Publishers2003).
5.
KandlikarS. G.GarimellaS.LiD.ColinS., Heat transfer and fluid flow in minichannels and microchannels (London: Elsevier Ltd2006).
6.
KarniadakisG.BeskokA.AluruN., Microflows and nanoflows: fundamentals and simulation (New Delhi: Springer (India) Pvt Ltd2005).
7.
LarrodeF. E.HousiadasC.DrossinosY., ‘Slip flow heat transfer in circular microtubes’Int. J. Heat Mass Transf.43 (2002): 2669–2680.
8.
ChenC. H., ‘Slip-flow heat transfer in a microchannel with viscous dissipation’Heat Mass Transf.42 (2002): 853–860.
9.
AydinO.AvciM., ‘Heat and fluid flow characteristics of gases in micropipes’Int. J. Heat Mass Transf.49 (2002): 1723–1730.
10.
SatapathyA. K., ‘Slip flow heat transfer in a semi-infinite microchannel with axial conduction’Proc. IMechE, Part C: J. Mechanical Engineering Science224 (2012): 357–361 DOI: 10.1243/09544062JMES1738.
11.
BatchelorG. K., ‘Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures’Q. Appl. Math.12 (1951): 209–233.
12.
EckertE. R. G.CarlsonW. O., ‘Natural convection in an air layer enclosed between two vertical plates with different temperatures’Int. J. Heat Mass Transf.2 (1961): 106–120.
13.
ElderJ. W., ‘Laminar free convection in a vertical slot’J. Fluid Mech23 (1961): 77–98.
14.
ElderJ. W., ‘Turbulent free convection in a vertical slot’J. Fluid Mech23 (1961): 99–111.
15.
GebhartB.JaluriaY.MahajanR. L.SammakiaB., Buoyancy-induced flows and transport (New York: Hemisphere Publishing Corporation1988).
16.
EckertE. R. G.DrakeR. M., Heat and mass transfer (New York: McGraw-Hill Book Company, Inc.1959).
17.
ChenC.WengH. C., ‘Natural convection in a vertical microchannel’J. Heat Transf.127 (2002): 1053–1056.
18.
WengH. C.ChenC., ‘Variable physical properties in natural convective gas microflows’J. Heat Transf.130 (2002): 082401-1-8.
19.
AungW., ‘Fully developed laminar free convection between vertical plates heated asymmetrically’Int. J. Heat Mass Transf.15 (1971): 1577–1580.
20.
DongariN.AgrawalA.AgrawalA., ‘Analytical solution of gaseous slip flow in long microchannels’Int. J. Heat Mass Transf.50 (2002): 3411–3421.
21.
AminfarH.MohammadpourfardM., ‘Lattice Boltzmann BGK model for gas flow in a microchannel’Proc. IMechE, Part C: J. Mechanical Engineering Science222 (2002):1855–1860 DOI: 10.1243/09544062JMES809.
22.
FingerG. W.KapatJ. S.BhattacharyyaA., ‘Molecular dynamics simulation of adsorbent layer effect on tangential momentum accommodation coefficient’J. Fluids Engng129 (2002): 31–39.
