The Nusselt number for two-dimensional Bénard convection with free boundaries at infinite Prandtl number is determined numerically with high precision for Rayleigh numbers in the range 104-1011. The coefficients for the asymptotic dependence of the Nusselt number on the cubic root of the Rayleigh number according to boundary layer theory are also re-evaluated. The numerical data indicate a slow approach to the cubic root law with a deviation of 1% at Ra=1011.
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Ulrich R. Christensen (1989) studied this question.
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