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

  • M. A. Khaskheli Faculty of Bio-Sciences, Shaheed Benazir Bhutto University of Veterinary and Animal Sciences (SBBUVAS), Pakistan and Department of M&S, QUEST Nawabshah Pakistan
  • K. N. Memon Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology, Pakistan
  • A. H. Sheikh Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology, Pakistan https://orcid.org/0000-0002-8036-1214
  • A. M. Siddiqui Pennsylvania State University, USA
  • S. F. Shah Department of Basic Science & Related Studies, Quaid-e-Awam University of Engineering, Science and Technology, Pakistan

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.

Keywords: tank drainage, Newtonian MHD fluid, analytical solution, series solution

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