A Numerical Solution for Laminar Entrance Flow in a Square Duct

Abstract

The laminar entrance flow of an incompressible viscous fluid in a square duct is analyzed numerically. Two approximate mathematical models are considered, with the more exact model including the transverse momentum equations. Finite-difference representations are developed for the equations of both models, and solutions are obtained assuming a uniform inlet velocity distribution. Results are presented for the velocity and pressure distributions in the entrance region, and comparisons made with previous analytical and experimental work. The results provide new insight into the true three-dimensional character of the flow and are more accurate than previously available solutions.