Wavy optimal flows for heat transfer in channels

TL;DR

This paper identifies optimal two-dimensional fluid flows in channels that maximize heat transfer, revealing a transition from unidirectional to wavy patterns at high Péclet numbers, with wavy flows significantly enhancing heat transfer efficiency.

Contribution

It introduces a computational approach combining BFGS and adjoint methods to find flow patterns that optimize heat transfer, discovering a wavy flow regime at high Péclet numbers.

Findings

Wavy flows outperform unidirectional flows in heat transfer rate by 3-30%.

Flow transitions from unidirectional to wavy at Pe ≈ 2^12.

Wavy flows increase interface area between hot and cold fluids.

Abstract

We compute incompressible two-dimensional fluid flows that maximize the rate of heat transfer from the walls of a straight channel given a specified flow input power $Pe^{2}$, where $Pe$ is the P\'{e}clet number. We use the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm together with an adjoint method to compute gradients. The optimal flows are approximately unidirectional up to a critical $Pe \approx 2^{12}$. Above this value the flows assume wavy patterns characterized by finger-like protrusions emanating from both the top and bottom walls of the channel. The rate of heat transfer for these wavy flows is 3% to 30% greater than that of the previously identified unidirectional optima for $2^{13} \leq Pe \leq 2^{17}$. The wavy flows have a much smaller flux through the channel than the unidirectional flows, with regions of slow-moving fluid at nearly homogeneous temperature interspersed with serpentine regions of fast-moving fluid. Consequently, the area of the interface between hot and cold fluid is increased.