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

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.

Automated summary

Inspired by natural bifurcating structures, tree-like microchannels have been utilized for microelectronics cooling. The thermal-hydraulic performance of a flat-plate tree-like microchannel is investigated through the optimization of successive branching ratios based on flow resistance minimization. The study reveals that the optimal successive diameter ratio follows Murray's law and the optimal successive length ratio follows the power law 2(-2/3). A mathematical model is developed for convection in a disc-shaped heat sink with a self-affine rough surface. The optimized flat-plate tree-like microchannel demonstrates enhanced thermal-hydraulic performance and sheds light on the design of micro-channel heat sinks and flow channels in cooling applications.