Magnified heat transfer from curved surfaces: A scaling prediction

Abstract

We report the first definitive Nusselt number scale of thermal boundary layers from curved surfaces characterized by the proposed non-dimensional curvature parameter ζ = R 0/(H Ra -1/4), where R 0 denotes the radius of a curved surface, H denotes the corresponding finite height, and Ra denotes the global Rayleigh number of a virtual reference thermal boundary layer on a vertical flat surface. The Nusselt number scale is given by Nu ∼ζ -1/5 Ra 1/4 in which Nu ∼Ra 1/4 is the scale for the flat surface case, revealing that curved thermal boundary layers could present times-of-magnitude larger heat flux with the curvature parameter being ζ ≪ 1. The velocity and thickness scales are also given by V s ∼ R 0 2 / 5 R a 3 / 5 H 7 / 5 κ and Δ T ∼ R 0 1 / 5 H 4 / 5 R a 1 / 5.