Precision calculation of the entrance length for laminar flow of Bingham fluid between parallel plates with yield number from 0 to 1000

Abstract

An estimate of the entrance length for a Bingham fluid flowing between parallel plates is needed in engineering applications. The dimensionless entrance length is a function of yield number. The primary objective of this study was to construct plots of dimensionless entrance length vs. yield number that could be used by practitioners for a quick estimation of the entrance length in a Bingham fluid entering between parallel plates, in a range of yield numbers from 0 to 1000. Three well-known calculation methods were used. The methods were found to yield mutually consistent results. A secondary objective of this study was to examine the sensitivity of the calculated entrance length to the value of a dimensionless parameter somewhat arbitrary chosen during the calculations. This parameter specifies the dimensionless value of the unyielded core velocity that is accepted as the core velocity at the end of the entrance region. In all three calculation methods, the entrance length was found to have a noticeable sensitivity to the variation of this parameter. The least sensitive method was the one based on the momentum integral solution. The findings necessitate further, more fundamental research on the entrance length in non-Newtonian fluids.