Heat Transport through Rough Channels

TL;DR

This study uses numerical simulations to analyze heat transport in rough channels with fractal interfaces, revealing that roughness minimally affects heat transfer at low Peclet numbers but enhances it at high Peclet numbers due to recirculation zones.

Contribution

It provides new insights into how fractal roughness influences heat transfer efficiency across different flow regimes using direct numerical simulations.

Findings

Roughness has negligible effect at low Peclet numbers.

At high Peclet numbers, roughness increases heat flux and active length.

Recirculation zones in fractal geometries are key to enhanced heat transfer.

Abstract

We investigate the two-dimensional transport of heat through viscous flow between two parallel rough interfaces with a given fractal geometry. The flow and heat transport equations are solved through direct numerical simulations, and for different conduction-convection conditions. Compared with the behavior of a channel with smooth interfaces, the results for the rough channel at low and moderate values of the Peclet number indicate that the effect of roughness is almost negligible on the efficiency of the heat transport system. This is explained here in terms of the Makarov's theorem, using the notion of active zone in Laplacian transport. At sufficiently high Peclet numbers, where convection becomes the dominant mechanism of heat transport, the role of the interface roughness is to generally increase both the heat flux across the wall as well as the active length of heat exchange, when compared with the smooth channel. Finally, we show that this last behavior is closely related with the presence of recirculation zones in the reentrant regions of the fractal geometry.