Prandtl-Number Dependence of Heat Transport in Laminar Horizontal Convection

We report the Prandtl-number (Pr) and Rayleigh-number (Ra) dependencies of the Reynolds number (Re) and mean convective heat transport, measured by the Nusselt number (Nu), in horizontal convection (HC) systems, where the heat supply and removal are provided exclusively through a lower horizontal surface of a fluid layer. For laminar HC, we find that Re~Ra2/5Pr^-4/5, Nu~Ra1/5Pr1/10 with a transition to Re~Ra1/2Pr^-1, Nu~Ra1/4Pr⁰ for large Pr. The results are based on direct numerical simulations for Ra from 3×10⁸ to 5×10¹⁰ and Pr from 0.05 to 50 and are explained by applying the Grossmann-Lohse approach [J. Fluid Mech. 407, 27 (2000)] transferred from the case of Rayleigh-B\'enard convection to the case of laminar HC.