Development of Unsteady Flow in a Wavy Minichannel System

Flow through a minichannel with a square cross-sectional shape whose center-line follows a wavy path has been numerically studied. The wavy center-line path is defined by a series of circular arcs. Now when a fluid flows through such a wavy channel unsteady flow can develop at Reynolds numbers that are far below the value at which transition to turbulence occurs. The development of this unsteadiness can lead to increases in the pressure losses in the channel and to significant increases in the heat transfer rate when the channel wall is heated or cooled. To study the conditions under which unsteady flow develops with a wavy, circular arc center-line shape attention has been given to flow through a channel system in which there is a short straight entrance section followed by a wavy channel section with four full waves followed by a short straight outlet section. It has been assumed that the flow is incompressible and that there is no slip at the channel walls. The unsteady form of the governing equations have been written in dimensionless form and solved using a commercial finite-element based software package, FIDAP. The solution has the following parameters: the Reynolds number, the Prandtl number, and the dimensionless radius of the wavy portion of the channel system. Results have only been obtained for a Prandtl number 0.7 for Reynolds numbers of between 10 and 500 for various dimensionless wave radii. The solution shows that steady exists at low Reynolds numbers but that at a critical Reynolds unsteady flow exists, this critical Reynolds number depending on the dimensionless wave radius. The major concern in this work is with defining the conditions under which this unsteady flow develops and with the effect of the development of this unsteadiness on the pressure drop in the channel system.