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.

Analytical solution of tank drainage flow for electrically conducting Newtonian fluid

“…The flow rate expression, per unit width is denoted by Q, average velocity,  , and mass balance over the entire tank formula is given in [1,5,7] by using these formulas in after using (26), we obtain:…”

“…Some outstanding --------------reviews concerning series solutions and exact solutions have been given by Khaskheli et al [3]. The Newtonian, power law and couple stress fluids have been used for tank drainage flow by [4][5][6][7] to study and analyze the problem for exact solution.…”

Tank Drainage for an Electrically Conducting Newtonian Fluid with the use of the Bessel Function

“…In [17], an analytical solution approach of the tank drainage problem for an electrically conducting power law fluid is presented. In [18][19][20], the Ellis fluid has been studied regarding the tank drainage problem with the special cases of Newtonian, power law and Bingham plastic fluid.…”

The hydrodyanamics of gravity-driven vessel drainage of third order fluid using perturbation method

“…Velocity profile temperature distribution are studied in Refs. [ [5] , [6] , [7] ].Using tank drainage flow rate and time efflux are obtained for Ellis fluid [ 8 ]. There is no one model can define all characteristics of Non-Newtonian fluid but in recent times ordered as “n” fluids have picked up remarkable attention among the Non-Newtonian fluids that almost complete the requirements of being a pure Non-Newtonian fluid, one subclass is second-grade, however this fluid lacks the shear thickening and thinning properties, in that case Fosdick and Raja Gopal established a theory regarding constancy and thermodynamics of third-grade fluids that encompasses all Non-Newtonian fluid characteristics including both properties shear thickening and shear thinning [ [9] , [10] , [11] ].Dealing with the third-order flow was a challenging task, but successfully it is done theoretically nowadays so that the third-order fluid model is well thought-out in this study because no one has study it till today in this geometry with perturbation technique.…”