Effect of Slip Condition on Unsteady Tank Drainage Flow of third Order Fluid

Authors

  • Muneer Ahmed Mahar Department of Basic Science and Related Studies, Mehran University of Engineering and Technology Jamshoro, Pakistan
  • Kamran Nazir Memon *Department of Mathematics and Statistics, QUEST, Nawabshah, Pakistan;
  • Syed Feroz Shah Department of Basic Science and Related Studies, Mehran University of Engineering and Technology Jamshoro, Pakistan
  • Azam Ali Amur Department of Basic Science and Related Studies, Mehran University of Engineering and Technology Jamshoro, Pakistan
  • A. M. Siddiqui Pennsylvania State University, York Campus, Edgecombe 17403, USA

DOI:

https://doi.org/10.21015/vtm.v10i2.1338

Abstract

Unsteady, isothermal, and incompressible third-order fluid is considered in the tank, cylindrical coordinates are taken into account and the flow of the fluid is considered in the z-direction. The behavior of viscoelastic fluid is analyzed with slip conditions. Velocity profile, flow rate, and mathematical relation between time depth of mass and time efflux, etc. are calculated with the perturbation method. Perturbation is a suitable technique for nonlinear partial differential equations because it converts them into the linear form which is easy to solve. Different physical flow parameters are inspected graphically. A comparison of slip and no-slip is presented also Newtonian and third-order fluids are compared too.

References

M Kamran Alam, KN Memon, AM Siddiqui, SF Shah, Muhammad Farooq, Muhammad Ayaz, Taher A

Nofal, and Hijaz Ahmad. Modeling and analysis of high shear viscoelastic ellis thin liquid film phenomena.

Physica Scripta, 96(5):055201, 2021.

Lawrence K Forbes and Graeme C Hocking. Unsteady draining of a fluid from a circular tank. Applied

mathematical modelling, 34(12):3958–3975, 2010.

Vijay K Garg. Applied computational fluid dynamics. CRC Press, 1998.

T Hayat, Naveed Ahmed, and M Sajid. Analytic solution for mhd flow of a third order fluid in a porous

channel. Journal of Computational and Applied Mathematics, 214(2):572–582, 2008.

Tasawar Hayat and AH Kara. Couette flow of a third-grade fluid with variable magnetic field. Mathe-

matical and Computer Modelling, 43(1-2):132–137, 2006.

Saeed Islam, Kamran Nazir Memon, Abdul Majeed Siddiqui, and Syed Feroz Shah. Analytical solution

of tank drainage for electrically conducting power law fluid. 2018.

Mansoor Ali Khaskheli, Kamran Nazir Memon, Abdul Hanan Sheikh, Abdul Majeed Siddiqui, and

Syed Feroz Shah. Tank drainage for an electrically conducting newtonian fluid with the use of the

bessel function. Eng. Technol. Appl. Sci. Res, 10(2), 2020.

Mansoor Ali Khaskheli, Kamran Nazir Memon, Abdul Hanan Sheikh, Abdul Majeed Siddiqui, and

Syed Feroz Shah. Tank drainage for an electrically conducting newtonian fluid with the use of the

bessel function. Eng. Technol. Appl. Sci. Res, 10(2), 2020.

Kamran Nazir Memon, Muhammad Kamran Alam, Jamel Baili, Zeeshan Nawaz, Abdul Hanan Shiekh,

and Hijaz Ahmad. Analytical solution of tank drainage flow for electrically conducting newtonian fluid.

Thermal Science, 25(Spec. issue 2):433–439, 2021.

KN Memon, S Islam, AM Siddiqui, Sher Afzal Khan, Nazir Ahmad Zafar, and MAkram. Lift and drainage

of electrically conducting power law fluid on a vertical cylinder. Applied Mathematics & Information

Sciences, 8(1):45, 2014.

KN Memon, Sher Afzal Khan, S Islam, Nazir Ahmad Zafar, Syed Feroz Shah, and AM Siddiqui. Unsteady

drainage of electrically conducting power law fluid. Applied Mathematics & Information Sciences,

(5):2287, 2014.

KN Memon, SF Shah, and AM Siddiqui. Exact solution of unsteady tank drainage for ellis fluid. Journal

of Applied Fluid Mechanics, 11(6):1629–1636, 2018.

KN Memon, AM Siddiqui, and SF Shah. Exact solution of tank drainage for newtonian fluid with slip

condition. Sindh University Research Journal-SURJ (Science Series), 49(2), 2017.

Melvin Mooney. Explicit formulas for slip and fluidity. Journal of Rheology (1929-1932), 2(2):210–222,

Syed Asad Raza Shah, KN Memon, SF Shah, AH Sheikh, and AM Siddiqui. Delta perturbation method

for thin film flow of a third grade fluid on a vertical moving belt. STATISTICS, COMPUTING AND INTERDISCIPLINARY

RESEARCH, 4(1):61–73, 2022.

Syed Mansoor Shah, KN Memon, Syed Feroz Shah, Abdul Hanan Sheikh, Abbas Ali Ghoto, and AM Siddiqui.

Exact solution for ptt fluid on a vertical moving belt for lift with slip condition. Indian Journal of

Science and Technology, 12:30, 2019.

AM Siddiqui, M Akram, KN Memon, and S Islam. Khalid khan, withdrawal and drainage of thin film

flow on a vertical cylinder. Scientific Research and Essays, 7(41):3554–3565, 2012.

RH SOLANGI, SF SHAH, AM SIDDIQUI, and KN MEMON. Effect of slip condition on thin layer flow on

an upright cylinder for drainage of electrically conducting power law fluid. Sindh University Research

Journal-SURJ (Science Series), 48(4), 2016.

Downloads

Published

2022-12-31

How to Cite

Mahar, M. A., Memon, K. N., Shah, S. F., Amur, A. A., & Siddiqui, A. M. (2022). Effect of Slip Condition on Unsteady Tank Drainage Flow of third Order Fluid. VFAST Transactions on Mathematics, 10(2), 189–200. https://doi.org/10.21015/vtm.v10i2.1338

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