Date: Friday, September 22, 2017
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: The optimal design of wallbounded heat transport
Abstract: Flowing a fluid is a familiar and efficient way to cool: fans cool electronics, water cools nuclear reactors, and the atmosphere cools the surface of the Earth. In this talk, we discuss a class of problems from fluid dynamics which ask for the design of incompressible wallbounded flows achieving optimal rates of heat transport for a given flow intensity budget. Guided by a perhaps unexpected connection between this optimal design problem and various "energydriven pattern formation" problems from materials science, we construct flows achieving nearly optimal rates of heat transport in their scaling with respect to the intensity budget. The resulting flows share striking similarities with selfsimilar elastic wrinkling patterns, such as can be seen in the shape of a hanging drape or nearby the edge of a torn plastic sheet. They also remind of (carefully designed versions) of the complex multiscale patterns seen in turbulent fluids. Nevertheless, we prove that in certain cases natural buoyancydriven convection is not capable of achieving optimal rates of cooling. This is joint work with Charlie Doering.
Files:
Speaker: Ian Tobasco
Institution: University of Michigan
Event Organizer: AIM seminar organizers
