The Hydrodynamics of Gravity-Driven Vessel Drainage of Third Order Fluid using Perturbation Method

Azam Ali, K. N. Memon, Syed Feroz Shah, Mohsin Amur, A. M. Siddiqui

Abstract


This work clarifies the tank drainage problem of unsteady, incompressible and isothermal third-order fluid. The analytical solution is obtained from governing continuity and momentum equations for resulting non-linear PDE with no-slip conditions using the perturbation technique. The V(z) velocity profile, flow rate, depth H(t), time efflux, and time depth of the mass relation have been inspected on various parameters. The consequences of the depth H(t), the pipe having radius R, the density of the fluid ρ pipe of length L, dynamic viscosity µ, and small perturbation parameter ϵ on the velocity profile are beheld graphically. Comparison of Analytical result of the special case of third order fluid with existing literature when ϵ = 0 is given.

Full Text:

PDF

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.

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, 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.

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.




DOI: http://dx.doi.org/10.21015/vtm.v10i2.1313

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.