The effect of gaseous slip on microscale heat transfer: An extended Graetz problem

International Journal of Heat and Mass Transfer

Volumn 49, Issue 15-16, 2006, Pages 2502-2513

  Myong, R S ^a,b   Lockerby, D A ^c   Reese, J M ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b Gyeongsang National University   (South Korea)

^c BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

Extended Graetz problem; Langmuir adsorption; Microfluidics; Rarefied gas dynamics; Reynolds analogy; Slip flow; Temperature jump

Indexed keywords

ADSORPTION; FLUIDICS; GAS DYNAMICS; HEAT CONDUCTION; MATHEMATICAL MODELS; REYNOLDS NUMBER; THERMAL EFFECTS;

EXTENDED GRAETZ PROBLEMS; LANGMUIR ADSORPTION; MICROFLUIDICS; RAREFIED GAS DYNAMICS; REYNOLDS ANALOGY; SLIP FLOW; TEMPERATURE JUMP;

HEAT CONVECTION;

ADSORPTION; FLUIDICS; GAS DYNAMICS; HEAT CONDUCTION; HEAT CONVECTION; MATHEMATICAL MODELS; REYNOLDS NUMBER; THERMAL EFFECTS;

EID: 33646553624     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2005.11.035     Document Type: Article

References (39)

1. Arkilic E.B., Schmidt M.A., and Breuer K.S. Gaseous slip flow in long microchannels. J. Microelectromech. Syst. 6 2 (1997) 167-178
2. Reese J.M., Gallis M.A., and Lockerby D.A. New directions in fluid dynamics: non-equilibrium aerodynamic and microsystem flows. Phil. Trans. Roy. Soc. Lond. A 361 (2003) 2967-2988
3. Chapman S., and Cowling T.G. The Mathematical Theory of Non-uniform Gases. third ed. (1970), Cambridge University Press, Cambridge
4. Bird G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows (1994), Clarendon Press, Oxford, England
5. Eu B.C. Kinetic Theory and Irreversible Thermodynamics (1992), John Wiley & Sons Inc., New York
6. Myong R.S. Thermodynamically consistent hydrodynamic computational models for high-Knudsen-number gas flows. Physics of Fluids 11 9 (1999) 2788-2802
7. Barron R.F., Wang X., Ameel T.A., and Warrington R.O. The Graetz problem extended to slip-flow. Int. J. Heat Mass Transfer 40 8 (1997) 1817-1823
8. Larrodé F.E., Housiadas C., and Drossinos Y. Slip-flow heat transfer in circular tubes. Int. J. Heat Mass Transfer 43 (2000) 2669-2680
9. Mikhailov M.D., and Cotta R.M. Mixed symbolic-numerical computation of convective heat transfer with slip flow in microchannels. Int. Commun. Heat Mass Transfer 32 3-4 (2005) 341-348
10. Hadjiconstantinou N.G., and Simek O. Constant-wall-temperature Nusselt number in micro and nanochannels. Trans. ASME 124 (2002) 356-364
11. Yan F., and Farouk B. Computations of low pressure fluid flow and heat transfer in ducts using the direct simulation monte carlo method. J. Heat Transfer 124 (2002) 609-616
12. Mikhailov M.D., and Cotta R.M. Eigenvalues for the Graetz problem in slip-flow. Int. Commun. Heat Mass Transfer 24 3 (1997) 449-451
13. Millikan R.A. The general law of fall of a small spherical body through a gas, and its bearing upon the nature of molecular reflection from surfaces. Phys. Rev. 22 1 (1923) 1-23
14. Eu B.C., Khayat R.E., Billing G.D., and Nyeland C. Non-linear transport coefficients and plane couette flow of a viscous, heat-conducting gas between two plates at different temperatures. Can. J. Phys. 65 (1987) 1090-1103
15. R.S. Myong, Velocity-slip effect in low-speed microscale gas flows, AIAA Paper No. (2001) 2001-3076.
16. Myong R.S. Gaseous slip model based on the Langmuir adsorption isotherm. Phys. Fluids 16 1 (2004) 104-117
17. Myong R.S., Reese J.M., Barber R.W., and Emerson D.R. Velocity slip in microscale cylindrical couette flow: the Langmuir model. Phys. Fluids 17 (2005) 087105
18. Choi H.L., Lee D., and Maeng J.S. Computation of slip flow in microchannels using Langmuir slip condition. Numer. Heat Transfer Part A-Appl. 44 1 (2003) 59-71
19. Langmuir I. Surface chemistry. Chem. Rev. 13 (1933) 147
20. Adamson A.W. Physical Chemistry of Surfaces (1982), John Wiley & Sons, New York
21. Gombosi T.I. Gaskinetic Theory (2002), Cambridge University Press, Cambridge
22. Yu S., and Ameel T.A. Slip-flow heat transfer in rectangular microchannels. Int. J. Heat Mass Transfer 44 (2001) 4225-4234
23. Burmeister L.C. Convective Heat Transfer (1993), John Wiley & Sons, New York
24. Graetz L. Uber die Warmeleitungsfahigheit von Flussigkeiten. Annalen der Physik und Chemie 18 (1883) 79-94 Part 1
25. Graetz L. Uber die Warmeleitungsfahigheit von Flussigkeiten. Annalen der Physik und Chemie 25 (1885) 337-357 Part 2
26. Sellars J.R., Tribus M., and Klein J.S. Heat transfer to laminar flow in a round tube or flat conduit-the Graetz problem extended. Trans. ASME 78 (1956) 441-448
27. Lebedev N.N. Special Functions and their Applications (1972), Dover Pub, New York
28. Abramowitz M., and Stegun C.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1972), Dover Pub, New York
29. Mikhailov M.D., and Özisik M.N. Unified Analysis and Solutions of Heat and Diffusion (1984), John Wiley & Sons, New York
30. Slater L.J. Confluent Hypergeometric Functions (1960), Cambridge University Press, Cambridge
31. Bayazitoĝlu Y., and Özisik M.N. On the solution of Graetz type problems with axial conduction. Int. J. Heat Mass Transfer 23 (1980) 1399-1402
32. Cotta R.M. Integral Transforms in Computational Heat and Transfer (1993), CRC Press, Boca Raton
33. Grosjean C.C., Pahor S., and Strnad J. Heat transfer in laminar flow through a gap. Appl. Sci. Res. 11 (1963) 292-294
34. Pahor S., and Strnad J. A note on heat transfer in laminar flow through a gap. Appl. Sci. Res. 10 (1961) 81-84
35. S.N. Singh, Heat transfer by laminar flow in a cylindrical tube, Appl. Sci. Res. 7 (1957-58) 325-340.
36. Maxwell J.C. On stresses in rarefied gases arising from inequalities of temperature. Phil. Trans. Roy. Soc. London 170 (1879) 231
37. von Smoluchowski M. Uber den Temperauresprung bei Warmeleitung in Gasen. Sitzungsberichte Wiene Akademie 107 (1898) 304
38. Wolfram S. The Mathematica Book (1999), Cambridge University Press, Cambridge
39. Housiadas C., Larrodé F.E., and Drossinos Y. Numerical Evaluation of the Graetz Series. Int. J. Heat Mass Transfer 42 (1999) 3013-3017