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Convection Problems in a Half-Space

  • Brian Straughan
Part of the Applied Mathematical Sciences book series (AMS, volume 91)

Abstract

It is often useful to define a convection problem on a half space. For example, Hurle, Jakeman & Wheeler (1982) use the velocity in a phase change problem to transform their stability analysis to one on a half-space; also Hurle, Jakeman & Pike (1967) have heat conducting half-spaces bounding a fluid layer to investigate the effects of finite conductivity at the boundary. While it may offer some simplicity to deal with a half-space configuration, from the mathematical point of view it does introduce new complications. In particular, Galdi & Rionero (1985) derive a very sharp result on the asymptotic behaviour of the base solution for which the energy maximum problem for R E admits a maximizing solution. Roughly speaking, either the base solution must decay at least linearly at infinity, or the gradient of the base solution must decay at least like 1/z 2 (if z > 0 is the half-space.) To describe this result and related ones in geophysics it is convenient to return to the general equations for a heat conducting linearly viscous fluid.

Keywords

Rayleigh Number Half Space Maximum Problem Convection Problem Finite Conductivity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Brian Straughan
    • 1
  1. 1.Department of MathematicsUniversity of GlasgowGlasgowUK

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