-----------------------------------------------------------

Joint Fluid Dynamics Seminar/Chemical Engineering Seminar

Monday, Nov 5th, 2007, 4:00 PM
Cullimore Hall, Room 611
New Jersey Institute of Technology

Two problems in the dynamics of thermal feedback

Bin Liu

Courant Institute of Mathematical Sciences, New York University

Abstract

In this talk, I will first focus on the dynamics of a thermally convecting fluid as it interacts with freely moving solid objects, here, simple spheres. It gives rise to surprisingly robust oscillations between different, large-scale circulation patterns. Once begun, this process repeats cyclically. The spheres are unpacked, entrained by the fluid, move from one side of the convection cell to the other, and repacked. The frequency of this cycle is highest when the spheres occupy about half of the cell bottom area and their size coincides with the thickness of the thermal boundary layer. This phenomenon shows that a deformable mass can drive a turbulent, thermally convecting fluid into robust oscillation.

Time permitting, I will discuss another example that also deals with thermal feedback in a spatially extended system -- the influence of air conditioners on the urban heat island (UHI). The relation between air conditioning and the heat island effect is studied with an explicit mathematical model that bears a strong resemblance to a mean-field neural network model. In this model system, I show how large-scale spatial temperature fluctuations and dynamic hysteresis emerge even with an isotropic distribution of air conditioners.