Unsteady flow in a flattened tube

Abstract

The study of the flow in a tube flattened by parallel plates is important in the transport of fluids in laterally restricted conduits. The unsteady (starting and oscillatory) flows are solved using the method of eigenfunction superposition. The necessary eigenvalues and eigenfunctions of the Helmholtz equation are determined, for the first time, by accurate one-region or two-region point match collocations. The starting times for the starting transient depends on the aspect ratio of the duct. For oscillatory flows, the velocity maximum shifts towards the walls at higher normalized frequencies.