Hydrodynamic Entrance Lengths for Incompressible Laminar Flow in Rectangular Ducts

Abstract

The problem of determining the hydrodynamic entrance length in a rectangular channel is solved by the method of linearizing the Navier-Stokes equation. The resulting equation is regarded as an equation to generate a mathematical expression for the axial velocity in the entire region, making smooth transition from a uniform profile to the fully developed one. From this expression, the entrance length, defined as where 99 per cent of the fully developed center-line velocity is attained, is calculated for channels of six aspect ratios. The pressure drops are also calculated and presented herein. A comparison is made with the limited amount of experimental and theoretical data.

A 3D incompressible Navier–Stokes velocity–vorticity weak form finite element algorithm

“…Reducing the size of the time step can improve the condition number of the terminal Newton jacobian matrix for large Reynolds number solutions. The solution-adapted M = 48 × 48 × 48 mesh produced these reported results, following mesh reÿnement studies [25]. This mesh density is able to produce solutions of adequate accuracy for the driven cavity and the thermal cavity benchmarks for the Re and Gr range selected.…”

Disruptive Burning of Aluminum/arbon Slurry Droplets

“…*In fact, the test section lay in the entrance region in which the gas flow was developing. Using the results of Han (1960), the free-stream velocity ncar the centerline ranged from 1.3 to t.6 times the initial average velocity over the lest section presently concerned if the gas temperature were fixed at 2000 K. Since the freestream gas temperature dropped monotonically from about 2000 K to 1600 K over the test section, the free-stream velocity remained approximately constant (i.e., about 1.3 times the initial average velocity). For simplicity, a constant value was assumed.…”

Effects of planar inlet plenums on the hydrodynamically developing flows in rectangular microchannels of complementary aspect ratios

“…Table 2 shows the entrance lengths for several aspect ratios from literatures. Han (1960) provided the approximate analytical solution for the rectangular channel and showed the entrance length to be a function of the channel aspect ratio. The entrance length decreased as the aspect ratio increased such that L e + /Re D decreases from 0.0660 to 0.0427 for the aspect ratios 2.0 and 4.0, respectively.…”