Fully Developed Transport Constants of Annular Tubes, With Application to the Entrance Region

Abstract

Description of the laminar thermal entry problem in annular tubes has historically been limited to a few geometric cases that require piecing together classical Graetz series and Lévêque series solutions to span all values of the Graetz number. The current work uses a recently developed generalized correlation to describe the full range of Graetz numbers for any annular tube geometry. However, the correlation requires fully developed Nusselt number values that have only been accurately reported in tabular and graphical forms. Exact analytic solutions for the constant wall heat flux condition are developed in this work, and simplified correlations are proposed for all wall conditions that reproduce exact Nusselt number solutions to within ± 0.4%. Using these results, a modified version of the generalized Graetz problem correlation is developed to reproduce the most published Nusselt numbers for the thermal entry problem in an annular tube to be within ± 5%.