Effect of Non-Uniform Inlet Velocity Profile on the Development of a Laminar Flow between Parallel Plates

Abstract

This paper describes a theoretical analysis of a laminar developing flow in the entrance region between parallel plates, when the inlet flow has a constant velocity gradient normal to the channel axis. The analysis is performed within the framework of the boundary layer theory, and governing equations are solved by a finite-difference method. The following results are obtained from the analysis : (1) If the flow rate through the channel is constant, the additional pressure drop in the entrance region is considerably decreased as the normal velocity gradient at the entrance section is increased. (2) As is physically expected, when isothermal walls of the channel are considered, the mean heat transfer rate is much larger at the wall of higher inlet velocity side than at the smaller inlet velocity side. However, an average value of the heat transfer rate on the two walls as a whole is smaller by a few percent than that for the case of a uniform inlet velocity profile. (3) The entrance length shows a significant reduction with the increase of the transverse velocity gradient at the inlet section.