New Parametrization for Heat Transport Through Diffusive Convection Interface

A laboratory experiment of two-layer diffusive convection (DC) within a rectangular cell is reported. Heat flux across the interface is respectively evaluated in terms of the heat energy conservation and the assumption of conductive interface. Both of them give the consistent heat flux values. When the 4/3 scaling between heat flux F and ΔT holds (F ~C(R_ρ) ΔT^4/3, where C(Rρ) is function of density ratio Rρ), previous heat flux parameterizations are found to have low coefficient of determination (r²<0.5) with our heat flux data within 1.6<Rρ<13.0. Heat flux is proposed to be a power-law function of Rρ, and the best fitting is C(Rρ)= 0.081(Rρ- 1)^-1.28, resulting in r² as high as 0.74. By using all available heat flux data over a wide Rρ range (1.2 ~27.6), including those collected in previous literatures, C(Rρ) is revised as C(Rρ)= 0.065(Rρ- 1)^-1.20 accompanied by r²=0.70 and reduced chi-square χ² = 0.91. Alternatively, C(Rρ) can be derived from previous DC layer thickness parameterization, which is expressed as C(Rρ)= 0.076(Rρ- 1)^-4/3. This formula is also superior to previous parameterizations in the evaluation of heat flux, indicated by higher r² and lower χ² .