Exact closed form solutions for the mathematical model of unsteady two fluid flow in a circular tube are presented. The pressure gradient is assumed to be oscillatory or exponentially increasing or decreasing in time. The instantaneous velocity prof iles and flow rates depend on the size of the core fluid, the density ratio, the viscosity ratio, and a parameter (e.g. the Womersley number) quantifying time changes. Applications include blood flow in small vessels.
Liu, J. and Wang, C. Y.
Closed Form Solutions of Unsteady Two Fluid Flow in a Tube,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 14,
1, Article 41.
Available at: https://digitalcommons.pvamu.edu/aam/vol14/iss1/41