Abstract
A theoretical algorithm by united Lagrangian-Eulerian method for the problem in dealing with viscous fluid and a circular cylindrical shell is presented. In this approach, each material is described in its preferred reference frame. Fluid flows are given in Eulerian coordinates whereas the elastic circular cylindrical shell is treated in a Lagrangian framework. The fluid velocity in a two-dimensional uniform elastic circular cylindrical shell filled with viscous fluid is studied under the assumption of low Reynolds number. The coupling between the viscous fluid and the elastic circular cylindrical shell shows kinematic conditions at the shell surface. Also, the radial velocity and axial velocity of the fluid are discussed with the help of graphs.
Highlights
This paper deals with the mathematical analysis of problem for viscous fluid and a circular cylindrical shell by a new theoretical method
Our focus is the velocity of the fluid when the elastic circular cylindrical shell filled with viscous fluid vibrates
The viscous fluid and a circular cylindrical shell are given in different coordinate systems making a common solution
Summary
This paper deals with the mathematical analysis of problem for viscous fluid and a circular cylindrical shell by a new theoretical method. These phenomena are of major importance for aerospace, ocean engineering, mechanical or biomedical applications, etc. Fluid flows are given in Eulerian coordinates whereas the circular cylindrical shell is treated in a Lagrangian framework. United Lagrangian-Eulerian method is used to present the flow velocity of a viscous and incompressible fluid in a circular cylindrical shell. It is a new method of where fluid and circular cylindrical shell equations are given in their preferred reference frames. The two-dimensional problem is that of an elastic circular cylindrical shell in which waves of lateral displacement are propagated
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