Thermal-hydraulic performance of flat-plate microchannel with fractal tree-like structure and self-affine rough wall

ABSTRACT

Inspired by the natural bifurcating structures, tree-like microchannels have been applied for microelectronics cooling. In order to understand the thermal-hydraulic performance of a flat-plat tree-like microchannel, successive branching ratios of tree-like structure are optimized based on minimization of flow resistance. It is shown that the optimal successive diameter ratio of symmetrical and dichotomous structures under volume constraint follows Murray’s law, while the optimal successive length ratio under the constraint of fixed channel area follows the power law 2^−2/3. A mathematical model of convection in disc-shaped heat sink composed of a tree-like microchannel with self-affine rough surface is developed by the fractal geometry and finite element method. The flat-plate tree-like micro-channel with optimal successive diameter and length ratio shows enhanced thermal-hydraulic performance. The Nusselt number of the flat-plat tree-like micro-channel increases with the inlet Reynolds number and the self-affine fractal dimension of the rough wall. The present optimization method and mathematical model for the flat-plate tree-like microchannel shed light on the design of flat-plate micro-channel heat sinks and flow channel in fuel cell among other potential cooling applications.

KEYWORDS:

• Tree-like network
• microchannel
• fractal
• rough wall
• Murray's law
• thermal-hydraulic performance

Acknowledgments

This work was jointly supported by the Natural Science Foundation of China [grant numbers 51876196], the Zhejiang Provincial Natural Science Foundation of China [grant numbers LR19E060001], the Fundamental Research Funds for the Provincial Universities of Zhejiang [grant number 2020YW13].

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Zhejiang Provincial Natural Science Foundation of China: [Grant Number LR19E060001]; National Natural Science Foundation of China: [Grant Number 51876196]; Fundamental Research Funds for the Provincial Universities of Zhejiang: [Grant Number 2020YW13].