Abstract
Recently published experimental results [Int. J. Heat Mass Transfer, 23, 738 (1980)] on thermally driven high Rayleigh number turbulent convection have shown that the N∝R2/7 relation (where N is the Nusselt number and R is the Rayleigh number), which is valid up to R≊5×108, is superceded at this point by the relation N=AσR1/3 that holds at least up to R≊1011. For water (Prandtl number σ=6.6), the experimental value for Aσ was found to be Aσ=0.0556±0.001. In the present work, the equations for a turbulent fluid driven by thermal convection are solved using the two-point closure prescription of the direct interaction approximation. The theoretical N vs R relation at high R is found to be of the form N=AσR1/3 and for σ=6.6, and the predicted value of the coefficient Aσ is computed to be Aσ≲0.08, in good agreement with the experimental value. Extension of the model to situations other than convection is discussed.
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