Objective  To meet the efficient thermal management needs of electronic devices such as ships and underwater vehicles, this study focuses on the constructal design of a tree-shaped microchannel disc heat sink with wavy walls.

  Method  A design prototype of the heat sink with wavy walls is first proposed. Based on constructal theory, the amplitude and wavelength of the wavy walls are designed under the constraints of fixed heat sink volume and fixed microchannel volume by maximizing the comprehensive performance evaluation criteria (PEC) while considering both heat transfer and flow pressure drop.

  Results  The results show that the wavy walls increase the heat transfer surface areas and generate vortices in their cavities, effectively reducing the maximum temperature. When the inlet Reynolds number is fixed at 700, 900 or 1100 respectively, the maximum temperature is reduced by 13.5 K by increasing the amplitude of the wavy walls, while the pressure drop increases significantly; and the maximum temperature is reduced by 4.7 K by reducing the wavelength of the wavy walls, while the pressure drop increases slightly. There are optimal amplitudes that raise the comprehensive performance evaluation criteria to extreme values for given larger wavelengths, while the comprehensive performance evaluation criteria increase monotonously as the amplitude increases for given smaller wavelengths.

  Conclusion  Wavy walls can significantly improve the thermal performance of tree-shaped microchannel disc heat sinks, and the use of constructal design can realize optimal geometric constructs with optimal comprehensive performance evaluation criteria.