Heil, M. (1996) The Stability of Cylindrical Shells Conveying Viscous Flow. Journal of Fluids and Structures 10, 173-196.

This paper examines the stability of cylindrical shells conveying viscous flow. Geometrically non-linear Lagrangian shell theory is used to describe the deformation of the tube wall. The fluid flow is modelled using lubrication theory. The coupled fluid-solid problem is discretised with finite differences and the critical parameter combinations (upstream pressure and volume flux) for which the tube buckles are examined. The most unstable circumferential buckling wavenumber and the buckling modes are determined for an experimental procedure in which the upstream pressure is held at a constant value while the volume flux is increased until buckling occurs. Finally, the effect of variations in the tube's geometry and the effects of the axial pre-stretch are examined.

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