Gradients on boundaries, slip conditions, and Rayleigh-Bénard convection

Fabian Bleitner (McMaster)

Monday, January 26, 11:30 (HH403)

We first introduce the Rayleigh-Bénard problem and briefly review scaling laws for heat transfer, with a special focus on boundary conditions. In particular, we justify the use of slip boundary conditions. Using energy methods, boundary gradients naturally emerge for these conditions. Recently, a more refined treatment of these gradients showed an improvement in the bounds for scaling laws. Based on these findings, we discuss ideas and challenges associated with further exploiting this technique.