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

Authors

  • Naina Salar Shaikh Department of Mathematics and Statistics, Quaid e Awam University of Engineering Science and Technology, Nawabshah, SBA, Sindh Province, Pakistan
  • Kamran Nazir Memon Department of Mathematics and Statistics, Quaid e Awam University of Engineering Science and Technology, Nawabshah, SBA, Sindh Province, Pakistan
  • Muhammad Suleman Sial Department of Basic Sciences and Related Studies, MUET, Jamshoro, Sindh, Pakistan
  • A. M. Siddiqui York Campus of Pennsylvania State University, Edgecombe 17403, United States of America

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.

References

fanasiev, K., Münch, A. and Wagner, B., 2007. Landau-Levich problem for non-Newtonian liquids. Physical Review E, 76(3), p.036307.

Ali, N., Abbasi, A. and Ahmad, I., 2015. Channel flow of Ellis fluid due to peristalsis. AIP Advances, 5(9), p.097214.

Agnes Serawa Anak Jutang, Noorhelyna Razali, Haliza Othman, Hawa Hishamuddin, 2020. International Journal of Recent Technology and Engineering (IJRTE), Volume-8 Issue-5, p. 2342- 2348

Bird, R.B., Stewart, W.E., Lightfoot, E.N. and Meredith, R.E., 1961. Transport phenomena. Journal of The Electrochemical Society, 108(3), p.78C.

Bird, R.B., Stewart, W.E. and Lightfoot, E.N., 2002. Transport Phenomena. John Wiley & Sons, Inc. New York, NY, 1.

Chhabra, R.P. and Richardson, J.F., 1999. Non-Newtonian Flow: Fundamentals and Engineering Applications. Elsevier.

Memon, K.N., Alam, M.K., Baili, J., Nawaz, Z., Shiekh, A.H. and Ahmad, H., 2021. Analytical solution of tank drainage flow for electrically conducting Newtonian fluid. Thermal Science, 25(Spec. issue 2), pp.433-439.

Alam, M.K., Memon, K.N., Siddiqui, A.M., Shah, S.F., Farooq, M., Ayaz, M., Nofal, T.A. and Ahmad, H., 2021. Modeling and analysis of high shear viscoelastic Ellis thin liquid film phenomena. Physica Scripta, 96(5), p.055201.

Kumar, G.S., Subbarao, C.V. and King, P., 2011. Efflux time for two exit pipe system. International Journal of Applied Science and Engineering, 9(4), pp.277-286.

Dunn, J.E. and Rajagopal, K.R., 1995. Fluids of differential type: critical review and thermodynamic analysis. International Journal of Engineering Science, 33(5), pp.689-729.

Elgamal, M., Kriaa, K. and Farouk, M., 2021. Drainage of a Water Tank with Pipe Outlet Loaded by a Passive Rotor. Water, 13(13), p.1872.

Forbes, L.K. and Hocking, G.C., 2007. Unsteady draining flows from a rectangular tank. Physics of Fluids, 19(8), p.082104.

Forbes, L.K. and Hocking, G.C., 2010. Unsteady draining of a fluid from a circular tank. Applied mathematical modelling, 34(12), pp.3958-3975.

Hanesian, D., 1984. Chemical Engineering Laboratory Manual. NJIT, Newark.

Memon, K.N., Siddiqui, A.M. and Shah, S.F., 2017. Exact Solution of Tank Drainage through the Circular Pipe for Couple Stress Fluid. J. Appl. Environ. Biol. Sci, 7(12), pp.27-34.

Memon, K.N., Shah, S.F. and Siddiqui, A.M., 2018. Exact solution of unsteady tank drainage for Ellis Fluid. Journal of Applied Fluid Mechanics, 11(6), pp.1629-1636.

Memon, K.N., Khan, S.A., Islam, S., Zafar, N.A., Shah, S.F. and Siddiqui, A.M., 2014. Unsteady Drainage of Electrically Conducting Power Law Fluid. Applied Mathematics & Information Sciences, 8(5), p.2287.

Memon, K.N., Siddiqui, A.M. and Shah, S.F., 2017. Exact solution of tank drainage for Newtonian fluid with slip condition. Sindh University Research Journal-SURJ (Science Series), 49(2).

Papanastasiou, T.C., 1994. Applied fluid mechanics. Prentice Hall.

Khaskheli, M.A., Memon, K.N., Sheikh, A.H., Siddiqui, A.M. and Shah, S.F., 2020. Tank Drainage for an Electrically Conducting Newtonian Fluid with the use of the Bessel Function. Eng. Technol. Appl. Sci. Res, 10(2).

Reddy, G.V.S.K. and Subbarao, C.V., 2011. Comparison of Efflux Times between cylindrical and spherical tank through an exit pipe. International Journal of Engineering and Applied Sciences, 3(2), pp.61-68.

Islam, S., Memon, K.N., Siddiqui, A.M. and Shah, S.F., 2018. Analytical solution of tank drainage for electrically conducting power law fluid.

Van Dongen, D.B. and Roche, E.C., 1999. Efflux time from tanks with exit pipes and fittings. International Journal of Engineering Education, 15(3), pp.206-212.

Wang, C.Y., 1991. Exact solutions of the steady-state Navier-Stokes equations. Annual Review of Fluid Mechanics, 23(1), pp.159-177.

Round, G.R. and Garg, V.K., 1986. Applications of fluid dynamics.

Downloads

Published

2022-12-31

How to Cite

Shaikh, N. S., Memon, K. N., Sial, M. S., & Siddiqui, A. M. (2022). Exact solution on the impact of slip condition for unsteady tank drainage flow of Ellis fluid. VFAST Transactions on Mathematics, 10(2), 201–212. https://doi.org/10.21015/vtm.v10i2.1352

Issue

Vol. 10 No. 2 (2022): July-December

Section

Articles

License

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC-By) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

                                      

This work is licensed under a Creative Commons Attribution  License CC BY