Curvature scaling of the transient convective boundary layer flow along a vertical cylinder: An improved explicit form

The scaling method is used to study the transient natural convection boundary layer flow, and the curvature effect is investigated. Important scaling laws, such as boundary layer thickness \ensuremath{\delta}${}_{t}$ and characteristic velocity ${u}_{m\phantom{\rule{0}{0ex}}z}$ of the transient and steady states and cut-off time of the initial growth are determined in the explicit form, where the curvature effect is accurately described by the proposed dimensionless coefficient \ensuremath{\Psi}\ensuremath{'}(A). The present explicit laws provide clearer physical interpretation, make the scaling laws much easier to utilize, and facilitate a better understanding of the underlying physical phenomena governing the curved boundary layer flow.