Optimal Flows for Thermal Transport

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

Thermal transport by forced convection is ubiquitous in residential, commercial, and industrial settings, for example in the heating and cooling of buildings and the cooling of power equipment, vehicles, and cloud-computing data centers. Improved thermal transport technologies are an important part of efforts to improve overall energy efficiency. Common methods of thermal transport enhancement involve inserting passive or active obstacles in flows or increasing the roughness of walls. These methods can enhance mixing of fluid both near and away from heated surfaces but also increase the power needed to drive the flow, so the net gain in efficiency is often limited. New ways of manipulating flows may yield superior heat transfer efficiency. This project will develop a systematic approach to identify useful flows and the forcing that generates them. The approach adapts constrained optimization methods for partial differential equations (PDE) that have been used recently to estimate upper bounds on rates of heat transfer by natural convection. By modifying the flow domain geometries, boundary conditions, constraints, and numerical methods, this project will identify effective flows in new settings relevant to engineering applications and understand the physical mechanisms underlying their effectiveness. In addition, this project will provide support and research training for graduate students and summer research experiences for undergraduate students, and outreach activities for middle and high school students. This project will discover improved flows for thermal transport enhancement in four fundamental areas. It will extend the existing steady 2D method to efficiently compute optimal unsteady 2D flows in benchmark geometries such as channel flows and closed and open domains between hot and cold surfaces. It will also develop computational methods for optimal flows in 3D domains that are analogous to the 2D domains we have studied and determine the gains from 3D flows relative to 2D flows in comparable domains. In model heat sink arrays, the heat transferred by Navier-Stokes flows with oscillatory driving to that for the optimal steady and unsteady flows will be compared. In addition, this project will also characterize the optimal flows for “hot spots,” relevant to processor cooling, by changing the objective function to an approximation of the maximum temperature in the domain. Finally, the search for optimal channel flows will be extended to multiple initial optimal modes in straight channels and to channels with rough walls. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.