The rate of heat transfer due to natural convection in confined, horizontal, fluid layers can be expressed by equations involving the dimensionless parameters Nusselt No., Rayleigh No., and Prandtl No., where Rayleigh No. equals the product of Grashof and Prandtl Nos.
Statistical correlation by stepwise multiple regression of experimental data obtained from four different investigators, on both gases and liquids, yields three separate equations corresponding to three distinct regimes of convection. The total range spanned by the data is from the onset of convection to Rayleigh = 109.
The equations are
Regime |
Ra Range |
Equation |
Std. Error of Estimate |
Initial |
1600-3000 |
Nu = 0.00238(ra).816 |
± 4% |
Laminar |
3000-105 |
Nu = 0.221 (ra).256 |
± 7% |
Turbulent |
105-109 |
Nu = 0.0891(ra).316 (pr).0853 |
± 12% |
The standard error of estimate, which is the probable error in the prediction of Nu from a regression equation, is obtained for each regime. A very high degree of accuracy was obtained for all correlations.
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