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

Abstract

In this study, an unsteady flow for drainage through a circular tank of an isothermal and incompressible Newtonian magnetohydrodynamic (MHD) fluid has been investigated. The series solution method is employed, and an analytical solution is obtained. Expressions for the velocity field, average velocity, flow rate, fluid depth at different times in the tank and time required for the wide-ranging drainage of the fluid (time of efflux) have been obtained. The Newtonian solution is attained by assuming σΒ02=0. The effects of various developing parameters on velocity field υz and depth of fluid H(t) are presented graphically. The time needed to drain the entire fluid and its depth are related and such relations are obtained in closed form. The effect of electromagnetic forces is analyzed. The fluid in the tank will drain gradually and it will take supplementary time for complete drainage.

Analytical solution of tank drainage flow for electrically conducting Newtonian fluid

“…A cylindrical tank, as depicted in fig. 1 and is described in [3], is considered with radius, RT, and diameter, D. The tank contains an isothermal, incompressible electrically conducting Newtonian fluid till height, H0. The radius and length of the pipe, causing drainage under gravity, is R and L. Height of the fluid in tank is function of time and is denoted by H(t).…”

“…It is called attention to that on the off chance that the perturbation parameter is set to be ε = 0in eq. ( 16), we recuperate the answer for the similar problem with Newtonian fluid, which is presented in [3].…”

“…Considering various facts including, precise time and height measurement, friction losses and other end effects, the governing equations model the flow accurately [1,2]. 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.…”

Series Solution of Unsteady Tank Drainage for Third Order Fluid using Adomian Decomposition Method

“…In ancient times this phenomena was manual so that the removal or pouring of the liquid was done with the simple tools like ladles or buckets. In this modern era tank drainage phenomena has gained noteworthy importance and have became simple due to use of advance technologies and engineering [5,9,15]. Now tanks are made with various materials such as cement, plastic and with metals which ensure the efficient distribution and supply of fluid to the desired place.…”

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

“…[ [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. The study of third-order fluid flow problems yields much scientific insight into elastic phenomena and a better knowledge of the mathematical processes needed to solve nonlinear viscoelastic problems.…”