Exact Solution of Unsteady Tank Drainage for Ellis Fluid

Abstract

In this work, we investigate the the problem of an unsteady tank drainage while considering an isothermal and incompressible Ellis fluid. Exact solution is gotten for a resulting non-linear PDE (partial differential equation)-subject to proper boundary conditions-. The special cases such as Newtonian, Power law, and as well as Bingham solution are retrieved from this suggested model of Ellis fluid. Expressions for velocity profile, shear stress on the pipe, volume flux, average velocity, and the relationship between the time vary with the depth of a tank and the time required for complete drainage are obtained. Impacts of different developing parameters on velocity profile vz and depth H(t) are illustrated graphically. The analogy of the Ellis, power law, Newtonian, and Bingham Plastic fluids for the relation of depth with respect to time, unfold that the tank can be empty faster for Ellis fluid as compared to its special cases.

Keywords

• Tank drainage
• Ellis fluid; Exact solution.