Development of Friction Factor-Generalized Equation for Multi-Shapes Microchannel

Abstract

The major goal of this research is to use computational fluid dynamics, CFD to derive a generalized friction factor formula for a smooth micro-size channel in a laminar flow regime. Based on the number of channel sides and the Reynolds number value, this generated formula can be used to precisely calculate the friction factor. The microchannel shapes are correlated to the friction factor constant as a function of the number of channel sides, N, starting from infinity for a circular microchannel, down to 3 numbers of N, for a triangular microchannel. The following microchannel shapes with a constant hydraulic diameter of 104 µm are selected, which are triangle, square, pentagon, hexagonal, octagonal, decagon, and circle. The developed equation works for a fully developed laminar flow range up to Reynolds number of 2000. Moreover, the current work results are further compared with the previous results of microchannels for verification within acceptable value of 0.07% to 0.48%.