Optimal surface fractal dimension for heat and fluid flow in microchannels

The fractal Weierstrass–Mandelbrot function was introduced to characterize the multiscale self-affine rough surface of microchannels. Based on this fractal characterization, the role of the rough surface structure on the thermal and hydrodynamic properties in microchannels was evaluated using a computational fluid dynamic simulation. Once identified, these were used to determine the optimal surface dimension for heat and fluid flow. It was found that, no matter what the Reynolds number and roughness height are, the flow heat transfer performance is being optimized with increasing fractal dimension of the surface until to the dimension value of three (infinitely crumpled).