Optimal heat transfer and optimal exit times

TitleOptimal heat transfer and optimal exit times
Publication TypeJournal Article
Year of Publication2018
AuthorsMarcotte F., Doering C.R, Thiffeault J.L, Young W.R
JournalSiam Journal on Applied Mathematics
Date Published2018/03
Type of ArticleArticle
ISBN Number0036-1399
Accession NumberWOS:000426747800027
Keywordsexit time distribution; heat transfer; Mathematics; mixing enhancement; rayleigh-benard convection; transport; ventilation

A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls. Starting from a positive initial temperature distribution in the interior, the goal is to flux the heat through the walls as efficiently as possible. Here we consider a distinct but closely related problem, that of the integrated mean exit time of Brownian particles starting inside the domain. Since flows favorable to rapid heat exchange should lower exit times, we minimize a norm of the exit time. This is a time-independent optimization problem that we solve analytically in some limits and numerically otherwise. We find an (at least locally) optimal velocity field that cools the domain on a mechanical time scale, in the sense that the integrated mean exit time is independent on molecular diffusivity in the limit of large-energy flows.

Short TitleSIAM J. Appl. Math.
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