Impact of round edge on the duct fluid flow: analytical investigation

Abstract

The present study aims to investigate the effect of the round edge on the laminar Newtonian fluid that flows through a channel. As an innovation, the sine and cosine transform functions are employed to solve the momentum governing equation in Cartesian and Cylindrical coordinates. Owing to the duct symmetric, only the quarter of the cross-section (θ = 0 to π/2) is analyzed. The analytical correlations for velocity distribution in both coordinates are provided; afterward, the effect of the round edge on the velocity profile has been investigated. It can be concluded that if a circular cross-section is replaced with a non-circular cross-section, the velocity profile becomes more uniform and less velocity variation is observed. Further, with a constant pressure gradient, among rectangular, round edge and circular cross-sections, the maximum velocity in a circular cross-section becomes minimum. In addition, it is observed that for the same pressure difference, an increase of m value leads to the higher average velocity and mass flow.