Discovering scaling laws for heat transport with convex optimization

Date: Thu. November 10, 2022
Event: FAU DCN-AvH Seminar
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Title: FAU DCN-AvH Seminar “Discovering scaling laws for heat transport with convex optimization”

Speaker: Prof. Dr. Giovanni Fantuzzi
Affiliation: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

Abstract. When a fluid (air, water, etc.) is subject to strong temperature variations, ensuing density differences drive the fluid in motion. This phenomenon is observed at all scales, from thin films of drying paint to the atmosphere and oceans. By how much does convection enhance the transport of heat compared to pure diffusion? How does this enhancement depend on the strength of the heating? This talk will demonstrate that answers to these fundamental questions can be searched for using tools from convex optimization. I will show that “a priori” estimates on the heat transport can be obtained with computer assistance by solving semidefinite programs, a well-known type of convex optimization problem. I will then demonstrate how these computational estimates have inspired the proof of new rigorous scaling laws for the heat transport in fluid with internal sources of heat. Remaining challenges and open questions will be discussed if time allows.

Slides

Strong heating (large $R$ ) = turbulence
Video courtesy of John Craske