Scale law investigation of the curved boundary layer flow around a horizontal cylinder – for Pr

Abstract

In this paper, the convective boundary layer flow that evolves on the external surface of a heated horizontal cylinder is investigated with the scaling analysis. Two thermal boundary conditions at the heated surface are considered: an isothermal and an iso-flux heating condition. The calculated data demonstrate that, similar to the extensively studied flat-plate boundary layer flows, development of the present curved boundary layer also consists of three states, i.e., an initial growth, a transitional state and a steady state. Scale laws of the characteristic velocity and thickness describing the initial and steady states are determined based on the calculated cases. The results show that unlike flat-plate boundary layers, the present characteristic velocity depends on both time and streamwise location and therefore the curved boundary layer flow follows a two-dimensional startup. The obtained scale law also indicates that the maximum characteristic velocity in the initial state is symmetrical about θ = π/2 as it is caused by the tangential component of the buoyancy force. In the steady state, the characteristic velocity occurs at approximately θ = 7π/9 and we show that this value is independent of the governing parameters. Comparison between the proposed scale laws and the calculated cases suggests that the regression constants R2 are above 0.995. Hence, the obtained scale laws could appropriately quantify the present curved boundary layer flow.