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Efficient thermal conductivity for horizontal layer cooled both from top and bottom

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Old   March 1, 2014, 13:14
Default Efficient thermal conductivity for horizontal layer cooled both from top and bottom
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Nikolay Vinnichenko
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I'm trying to simulate cooling of horizontal water layer with heat fluxes specified at top and bottom with a simple engineering model of 1D thermal conduction equation. So, I need an empirical expression for efficient thermal conductivity coefficient. I suppose, it is different for the upper sublayer with unsteady stratification (temperature has maximum at some depth) and for the lower stably-stratified sublayer. I tried using molecular heat conductivity for the lower sublayer and the standard Nusselt-Rayleigh relation for two horizontal plates for the upper one, but the result was unsatisfactory. I guess, this is because there is penetrative convection in the lower sublayer, since the bound between the sublayers is fluid, not a wall. Has anybody encountered relations for efficient thermal conductivity or Nusselt number in such configuration?
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