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Effect of a Traveling Thermal Wave on Weakly Nonlinear Convection in a Porous Layer Heated from Below

卷 4, 册 3, 2001, 16 pages
DOI: 10.1615/JPorMedia.v4.i3.30
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摘要

The stability of weakly nonlinear convection in a porous layer heated from below is considered. Much is known about those cases where the boundary temperatures are uniform, or display steady small-amplitude variations about a uniform mean. In this study we consider the effects of small-amplitude traveling thermal waves on the ensuing weakly nonlinear convection. At sufficiently low Rayleigh numbers the induced flow follows the motion of the thermal wave. But at higher Rayleigh numbers this form of convection breaks down and there follows a regime where the flow travels more slowly on average and does not retain the forcing periodicity. It appears that the flow passes through all. multiples of the forcing periodicity as the Rayleigh number increases. At much higher Rayleigh. numbers within the weakly nonlinear regime two very distinct time scales appear in the numerical simulations, and these are described analytically using the method of multiple scales; comparisons with numerical simulations are excellent. A similar scenario exists for large wavespeeds but moderate values of the Rayleigh number.

对本文的引用
  1. Goldstein R.J, Eckert E.R.G, Ibele W.E, Patankar S.V, Simon T.W, Kuehn T.H, Strykowski P.J, Tamma K.K, Heberlein J.V.R, Davidson J.H, Bischof J, Kulacki F.A, Kortshagen U, Garrick S, Heat transfer––a review of 2001 literature, International Journal of Heat and Mass Transfer, 46, 11, 2003. Crossref

  2. Postelnicu Adrian, The effect of a horizontal pressure gradient on the onset of a Darcy–Bénard convection in thermal non-equilibrium conditions, International Journal of Heat and Mass Transfer, 53, 1-3, 2010. Crossref

  3. Jais Ibrahim M., Rees D. Andrew S., Horizontal Cellular Oscillations Caused by Time-Periodic Resonant Thermal Forcing in Weakly Nonlinear Darcy-Bénard Convection, Fluids, 2, 4, 2017. Crossref

  4. Nield Donald A., Bejan Adrian, Internal Natural Convection: Heating from Below, in Convection in Porous Media, 2013. Crossref

  5. Nield Donald A., Bejan Adrian, Internal Natural Convection: Heating from Below, in Convection in Porous Media, 2017. Crossref

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