# Exact solution on the impact of slip condition for unsteady tank drainage ﬂow of Ellis ﬂuid

## DOI:

https://doi.org/10.21015/vtm.v10i2.1352## Abstract

In this paper, we look into the effect of slip condition on isothermal and incompressible Ellis fluid of an unsteady tank drainage flow. The non-linear PDE (partial differential equation) is solved exactly by applying the governing continuity and momentum equations, subject to the proper boundary condition, using the separation of variables approach. Unique situations this model put out by Ellis fluid is used to develop concepts like Newtonian, Power law model, and Bingham Plastic model solution. On setting the slip parameterexact solution for Ellis fluid flow is retrivred as well as Newtonian solution is bring back, which was done through Bernoulli's equation. Expressions for velocity field, pipe shear stress, volume flux, velocity average, depth of fluid in the tank at different times and also the relationship between length of the time be different with depth of the tank and the length of time required to complete the drainage is determined. Graphical representation is given of the effects of various development factors on the velocity field *Vz* and fluid depth *H(t*). The tank can empty faster for Ellis fluid compared to its special situations, according to the analogy of Ellis, Power law, Newtonian, and Binghan plastic fluids for the relation of depth with respect to time.

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*VFAST Transactions on Mathematics*,

*10*(2), 201–212. https://doi.org/10.21015/vtm.v10i2.1352

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