The boundary layer conductance of inclined elliptical leaves under free convection

The efficiency of heat and mass exchange between leaves and their environment under low wind speed is dominated by free convection. This is commonly quantified in terms of the Nusselt number (Nu), the Rayleigh number (Ra) and the boundary layer conductance (gb). The currently available Nu = f(Ra) relations for inclined plates were mostly derived for infinite wide plates or from one-sided heat transfer studies. A comprehensive simulated data set of laminar free convection may be used to derive new Nu relations for elliptical plates at any inclination and for both plate sides. The relevant equations for free convection in 3D are solved numerically using the computational fluid dynamic (CFD) software OpenFOAM. The simulated Nusselt numbers agree very good with previous measurements for vertical and horizontal circular plates having a diameter of 84 mm. Various finite thickness (0.5 mm) elliptical plates (i.e. leaves) having aspect ratios between 1 and 3, plate length ranging from 30 to 160 mm and a range of inclinations are simulated with plate to air differences set to 1-12 K. Simulated heat fluxes from each leaf side are used to parameterize a comprehensive set of Nu relations. The new gb model predicts CFD simulated heat fluxes at both leaf sides (2 - 120 W m-2) with a relative error of 4%, whereas with two tested previous approaches the error is 31-45%.

Automated summary

The study focused on the efficiency of heat and mass exchange between leaves and their environment under low wind speed conditions. Through numerical simulations, a new model of natural convection relationships was derived for different inclinations and elliptical shapes of leaves, with a predicted heat flux error of only 4% for temperature differences of 1-12K.