A transient intrusion flow on a cooled horizontal surface

Abstract

We investigate the dynamical evolution and thermal processes of a fluid on a suddenly cooled horizontal surface subjected to an isothermal or an isoflux condition. A simple scaling analysis is performed to study an intrusion flow induced by a suddenly cooled surface. Analytical results demonstrate that there exist two scenarios for the dynamical evolution and thermal processes of such an intrusion flow for Prandtl numbers smaller than unity. In a typical case, the intrusion flow could travel under different regimes such as the “conduction regime,” “accelerating convection–inertial regime,” “steady convection–inertial regime,” and “decelerating convection–viscous regime,” respectively. A set of scaling laws under different regimes have been presented based on scaling analysis. In addition, a two-dimensional numerical simulation is conducted to validate the scaling laws. The scaling laws are in agreement with our numerical results.