A dimensionless heat transfer coefficient for free convection that is more appropriate than Nusselt number

Abstract

Heat transfer in flows created by buoyancy, or natural convection, is a widely studied topic across various disciplines spanning natural flows as well as those with engineering applications. The convective heat transfer rate on a surface is commonly represented by the Nusselt number (Nu), a ratio of convective to diffusive transport, expressed often as RanPrm, where Ra is the Rayleigh number, the buoyancy forcing parameter, and Pr the Prandtl number. Motivated by the observation that n∼1/3 for turbulent convection, which implies the heat flux is independent of the length scale (L, characteristic length related to the geometry), we propose an alternate and physically more meaningful non-dimensional heat transfer parameter, denoted by Cq. Cq is derived using only the near wall variables and does not contain L. For n=1/3, Cq is constant. Even for laminar convection, where n∼1/4, Cq∼Ra−1/12, a weak function of Ra. We show that for natural convection over several geometries and a wide range of Ra, the Cq values within a narrow range while the corresponding Nu values span several orders of magnitude. We also show that Cq is akin to the non-dimensional representation of wall shear stress, skin friction coefficient Cf. We believe that just like Cf, Cq will be an equally useful non-dimensional measure of heat transfer in natural convection flows.