An experimental study is presented of the Nusselt-Rayleigh and Sherwood-Rayleigh number relations for water undergoing free-surface natural convection, which is natural convection beneath an air/water interface. The focus of this work is on the Nu-Ra relationship. This relationship is typically studied using the traditional Rayleigh-Be´nard convection experiment where a fluid layer is bounded above and below by solid plates of different, but constant, temperatures. Hence, the boundary conditions are of the no-slip, constant-temperature type. Power laws are typically used in these studies to correlate the Nu-Ra data, and existing studies have given power law exponents that are usually close to 1/3. The experimental data obtained in this study yields a power law relation of the form:
for 107 < Ra < 1011. This result is surprising in that the effect of the free-surface boundary condition on the power law exponent is quite small when compared to the solid plate case. However, the prefactor in Eq. (1) is significantly smaller than for the solid plate case. The Sh-Ra data obtained in this study are also fit to a power law, giving:
where Sh is the dimensionless mass transfer coefficient for evaporation. The exponent of this power law differs from that which has been observed by prior researchers. However, the prior research on evaporation that utilizes this form for scaling the data is considerably smaller than for the heat transfer case. Possible explanations for the observed behavior are presented.
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