Scale law investigation of the curved boundary layer flow around a horizontal cylinder - for Pr <1 fluids

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 theta = pi/2 as it is caused by the tangential component of the buoyancy force. In the steady state, the characteristic velocity occurs at approximately theta = 7 pi/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 R-2 are above 0.995. Hence, the obtained scale laws could appropriately quantify the present curved boundary layer flow.