Advertisement

Brazilian Journal of Physics

, Volume 47, Issue 2, pp 182–188 | Cite as

Near Continuum Velocity and Temperature Coupled Compressible Boundary Layer Flow over a Flat Plate

General and Applied Physics
  • 87 Downloads

Abstract

The problem of a compressible gas flows over a flat plate with the velocity-slip and temperature-jump boundary conditions are being studied. The standard single- shooting method is applied to obtain the exact solutions for velocity and temperature profiles when the momentum and energy equations are weakly coupled. A double-shooting method is applied if these two equations are closely coupled. If the temperature affects the velocity directly, more significant velocity slip happens at locations closer to the plate’s leading edge, and inflections on the velocity profiles appear, indicating flows may become unstable. As a consequence, the temperature-jump and velocity-slip boundary conditions may trigger earlier flow transitions from a laminar to a turbulent flow state.

Keywords

Boundary layer Boundary conditions Velocity slip Flow instability 

References

  1. 1.
    H. Blasius, Grenzschichten in flüssigkeiten bei sehr kleiner reibung. Z. Angew. Math. Phys. 56, 1534–1535 (1908)Google Scholar
  2. 2.
    H. Schlichting, K. Gersten, Boundary-layer theory, 8th edn. (Springer) (2003)Google Scholar
  3. 3.
    C.M. Ho, Y.C. Tai, Micro-electro-mechanical-systems (MEMS) and fluid flows. Annu. Rev. Fluid Mech. 30, 579–612 (1998)ADSCrossRefGoogle Scholar
  4. 4.
    M. Gad-el-Hak, The fluid mechanics of microdevices —- the Freeman scholar lecture. J. Fluid. Eng-T. ASME. 121, 5 (1999)CrossRefGoogle Scholar
  5. 5.
    M.J. Martin, I.D. Boyd, Momentum and heat transfer in a laminar boundary layer with slip flow. J. Thermophys Heat Tr. 20(4), 710–719 (2006)CrossRefGoogle Scholar
  6. 6.
    M.H. Yazdi, S. Abdullah, I. Hashim, A. Zaharim, K. Sopian, N.E. Mastorakis, M. Poulos, V. Mladenov, Z. Bojkovic, D. Simian, Friction and heat transfer in slip flow boundary layer at constant heat flux boundary conditions. Math. Comput. Sci. Engin. 10, 207 (2008)Google Scholar
  7. 7.
    J. Lahjomri, A. Oubarra, Hydrodynamic and thermal characteristics of laminar slip flow over a horizontal isothermal flat plate. J. Heat Transf. 135, 021704 (2013)CrossRefGoogle Scholar
  8. 8.
    J.C. Maxwell, On stresses in rarefied gases arising from inequalities of temperature. Proc. Royal Soci London. 27, 185–189 (1878)MATHGoogle Scholar
  9. 9.
    C. Cai, Near continuum boundary layer flows at a flat plate. Theor. Appl. Mech. Lett. 5(8), 134–139 (2015)CrossRefGoogle Scholar
  10. 10.
    A. Aziz, Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition. Commun. Nonlinear Sci. 15(3), 573–580 (2010)CrossRefGoogle Scholar
  11. 11.
    M.R. Safaei, G. Ahmadi, M.S. Goodarzi, A. Kamyar, S.N. Kazi, Boundary layer flow and heat transfer of FMWCNT/water nanofluids over a flat plate. Fluids. 1(4), 31 (2016)CrossRefGoogle Scholar
  12. 12.
    N.K. Vedantam, N. Parthasarathy, N. Ramkumar, Effects of slip on the flow characteristics of laminar flat plate boundary-layer, 2nd US-European Fluids Engineering Meeting. p. 1551 (2006)Google Scholar
  13. 13.
    F.M. White, Viscous fluid flow (McGraw-Hill, 2006)Google Scholar
  14. 14.
    E. Pohlhausen, Wärmeaustausch zwischen festen Körpern und Flüssigkeiten mit kleiner Reibung und kleiner Wärmeleitung, Vol. 1. Wiley (1921)Google Scholar
  15. 15.
    C.R. Illingworth, Some solutions of the equations of flow of a viscous compressible fluids. Proc. Cambridge Pilos. Soc. 46, 469–478 (1950)ADSMathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    C.B. Cohen, E. Reshotko, The compressible laminar boundary layer with heat transfer and arbitrary pressure gradient. Advances Heat Transf. 4, 317 (1967)CrossRefGoogle Scholar
  17. 17.
    L. Rayleigh, Sci. Pap. 1, 474 (1964)MathSciNetGoogle Scholar

Copyright information

© Sociedade Brasileira de Física 2017

Authors and Affiliations

  1. 1.Michigan Technological UniversityHoughtonUSA

Personalised recommendations