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

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.

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References

D. D. Joye, B. C. Barrett, “The tank drainage problem revisited: Do these equations actually work?”, The Canadian Journal of Chemical Engineering, Vol. 81, No. 5, pp. 1052–1057, 2003

A. N. Hrymak, “Applied fluid mechanics by T. C. Papanastasiou, Prentice-Hall, Englewood Cliffs, NJ, 1994, 520 pp.”, AIChE Journal, Vol. 41, No. 10, pp. 2342–2342, 1995

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport phenomena, John Wiley and Sons, 1961

E. J. Crosby, Experiments in transport phenomena, Wiley, 1961

D. Hanesian, A. Perna, A laboratory manual for fundamentals of engineering design, chemical engineering module: Measurements laboratory, New Jersey Institute of Technology, 1995

N. D. Nevers, Fluid mechanics for chemical engineers, McGraw-Hill Education, 2005

J. O. Wilkes, Fluid mechanics for chemical engineers with microfluidics and CFD, Prentice Hall, 2006

S. Channer, K. N. Memon, A. A. Ghoto, A. M. Siddiqui, S. F. Shah, “Analytical solutionof lift for thin film flow for phan thien tanner fluid”, Sindh University Research Journal, Vol. 51, No. 2, pp. 215–222, 2019

L. K. Forbes, G. C. Hocking, “Unsteady draining flows from a rectangular tank”, Physics of Fluids, Vol. 19, No. 8, Article ID 082104, 2007

L. K. Forbes, G. C. Hocking, “Unsteady draining of a fluid from a circular tank”, Applied Mathematical Modelling, Vol. 34, No. 12, pp. 3958–3975, 2010

G. V. S. K. Reddy, C. V. Subbarao, “Comparison of efflux times between cylindrical and spherical tank through an exit pipe”, International Journal of Engineering and Applied Sciences, Vol. 3, No. 2, pp. 61–68, 2011

C. V. Subbarao, P. S. Rao, G. M. J. Raju, V. S. R. K. Prasad, “Slow draining of large spherical tank under gravity”, Elixir International Journal, Vol. 50, pp. 10346-10348, 2012

C. V. Subbarao, Y. P. Yadav, P. King, “Drag reduction by surfactant solutions in gravity driven flow systems”, Iranian Journal of Chemistry and Chemical Engineering, Vol. 32, No. 2, pp. 119–123, 2013

C. Y. Wang, “On a class of exact solutions of the navier-stokes equations”, Journal of Applied Mechanics, Vol. 33, No. 3, pp. 696–698, 1966

A. A. Mahessar, A. L. Qureshi, A. N. Laghari, S. Qureshi, S. F. Shah, F. A. Shaikh, “Impact of Hairdin, Miro Khan and Shahdad Kot drainage on Hamal dhand, Sindh”, Engineering, Technology & Applied Science Research, Vol. 8, No. 6, pp. 3652–3656, 2018

K. N. Memon, A. M. Siddiqui, S. F. Shah, “Exact solution of tank drainage for Newtonian fluid with slip condition”, Sindh University Research Journal, Vol. 49, No. 2, pp. 283–288, 2017

S. Islam, K. N. Memon, A. M. Siddiqui, S. F. Shah, “Analytical solution of tank drainage for electrically conducting power law fluid”, available at: https://www.preprints.org/manuscript/201802.0033/v1, 2018

K. Afanasiev, A. Munch, B. Wagner, “Landau-Levich problem for non-Newtonian liquids”, Physical Review E, Vol. 76, No. 3, Article ID 036307, 2007

N. Ali, A. Abbasi, I. Ahmad, “Channel flow of Ellis fluid due to peristalsis”, AIP Advances, Vol. 5, No. 9, Article ID 097214, 2015

K. N. Memon, S. F. Shah, A. M. Siddiqui, “Exact solution of unsteady tank drainage for Ellis Fluid”, Journal of Applied Fluid Mechanics, Vol. 11, No. 6, pp. 1629–1636, 2018

M. R. Mohyuddin, T. Gotz, “Resonance behaviour of viscoelastic fluid in Poiseuille flow in the presence of a transversal magnetic field”, International Journal for Numerical Methods in Fluids, Vol. 49, No. 8, pp. 837–847, 2005

J. J. V. Rossum, “Viscous lifting and drainage of liquids”, Applied Scientific Research, Section A, Vol. 7, pp. 121–144, 1958

I. Pop, M. Kumari, G. Nath, “Conjugate MHD flow past a flat plate”, Acta Mechanica, Vol. 106, pp. 215–220, 1994

S. Abel, P. H. Veena, K. Rajgopal, V. K. Pravin, “Non-Newtonian magnetohydrodynamic flow over a stretching surface with heat and mass transfer”, International Journal of Non-Linear Mechanics, Vol. 39, No. 7, pp. 1067–1078, 2004

M. Abdullah, N. Saada, “Free convection MHD couette flow with application of periodic temperature and constant heat flux on walls”, Engineering, Technology & Applied Science Research, Vol. 9, No. 2, pp. 4007–4011, 2019

G. F. Round, V. K. Garg, Applications of fluid dynamics, E. Arnold, 1986

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