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

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.

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

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