## View abstract

### Session S37 - New Developments in Mathematical Fluid Dynamics

Friday, July 16, 11:00 ~ 11:25 UTC-3

## Bounds on the heat transfer rate via passive advection

### Gautam Iyer

#### Carnegie Mellon University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak42799d1af9717a46a5c760e3043155ec').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy42799d1af9717a46a5c760e3043155ec = 'g&#97;&#117;t&#97;m' + '&#64;'; addy42799d1af9717a46a5c760e3043155ec = addy42799d1af9717a46a5c760e3043155ec + 'm&#97;th' + '&#46;' + 'cm&#117;' + '&#46;' + '&#101;d&#117;'; var addy_text42799d1af9717a46a5c760e3043155ec = 'g&#97;&#117;t&#97;m' + '&#64;' + 'm&#97;th' + '&#46;' + 'cm&#117;' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak42799d1af9717a46a5c760e3043155ec').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy42799d1af9717a46a5c760e3043155ec + '\'>'+addy_text42799d1af9717a46a5c760e3043155ec+'<\/a>';

In heat exchangers, an incompressible fluid is heated initially and cooled at the boundary. The goal is to transfer the heat to the boundary as efficiently as possible. In this talk we study a related steady version of this problem: Consider the steady state temperature of in a fluid that is stirred, uniformly heated and cooled on the boundary. For a given large P\'eclet number, how should one stir to minimize the total heat? This problem was studied by Marcotte, Doering, Thiffeault and Young in '18, where the authors provided upper bounds using matched asymptotics. In this talk we will discuss how these upper bounds can be rigorously proved using large deviations, prove an almost matching lower bound in one case.

Joint work with Son Van (Carnegie Mellon University).