Scale law analysis of the curved boundary layer flow induced by constant flux heating around a horizontal cylinder for a Prandtl number larger than 1 fluids

Abstract

The convective boundary layer flow on the external surface of an iso-flux heated horizontal cylinder is investigated in this study. Under the premise of a Prandtl number Pr larger than 1, numerical simulations are conducted over a wide range of flow parameters, including variations in Rayleigh and Prandtl numbers. The present simulations demonstrate that similar to the extensively studied flat-plate boundary layer flows, development of the present curved boundary layer also consists of three states: an initial growth state, a transitional state, and a steady state. Scale laws of the characteristic velocity, boundary layer thickness, and Nusselt number Nu describing the initial and steady states are determined based on the calculated cases. The comparison suggests that the proposed scale laws could satisfactorily quantify the boundary layer flow, and the corresponding regression constants R2 are all above 0.995. The results indicate that the present characteristic velocity of the curved boundary layer depends both on time and streamwise location. Hence, the flow of the curved boundary layer follows a two-dimensional initiation, which is different from the one-dimensional growth of the flat-plate boundary layer in the initial state. The obtained scale law also indicates that the characteristic velocity of the boundary layer flow maximizes at π/2, but its thickness is circumferential location independent. In the steady state, the maximum tangential velocity occurs at approximately the central angle θ = 7π/9, and we show that this value is independent of the governing parameters.