Analysis of Aspect Ratio in a Miniature Rectangle Channel for Low Frictional Resistance

We conducted a theoretical investigation of the cross-sectional aspect ratio of a rectangular channel to have sufficiently low frictional resistance under less than 150 of the Reynolds number. From the theoretical consideration, it was clarified that 3.40 or more is recommended as a criterion for determining the aspect ratio. This addresses the problem of determining the interval of rectangle channels, installed in a plate reactor. There is a concern that the real system does not follow the analytical solution, assuming laminar flow, since the higher aspect ratio leads to disturbances of the flow such as the emergence of vortices. However, in the channel's volume range of (W × H × L) = (7.0 mm × 0.38 mm × 0.26 m), such a turbulence was not observed in the detailed numerical calculation by CFD, where both calculation results were in agreement to within 3% accuracy. Moreover, even in an experimental system with a surface roughness of ca. 7%, friction resistance took agreement within an accuracy of ±30%.