The hydrodyanamics of gravity-driven vessel drainage of third order fluid using perturbation method

Azam Ali Amur; K N Memon; Syed Feroz Shah; Mohsin Amur; Hijaz Ahmad; A M Siddiqui; Dilber Uzun Ozsahin; Sameh Askar

doi:10.1016/j.heliyon.2023.e20196

The hydrodyanamics of gravity-driven vessel drainage of third order fluid using perturbation method

Heliyon. 2023 Sep 21;9(10):e20196. doi: 10.1016/j.heliyon.2023.e20196. eCollection 2023 Oct.

Authors

Azam Ali Amur¹, K N Memon^{1

2}, Syed Feroz Shah¹, Mohsin Amur³, Hijaz Ahmad^{4

5}, A M Siddiqui⁶, Dilber Uzun Ozsahin^{7

8}, Sameh Askar⁹

Affiliations

¹ Department of Basic Science, Mehran University of Engineering Technology Jamshoro, Pakistan.
² Department of Mathematics and Statistics, QUEST, Nawabshah, Pakistan.
³ Gernal Faculty Shaheed Benazir Bhutto University Shaheed Banzir Abad, Pakistan.
⁴ Near East University, Operational Research Center in Healthcare, Nicosia, 99138, TRNC Mersin 10, Turkey.
⁵ Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
⁶ Pennsylvania State University, York Campus, Edgecombe, 17403, USA.
⁷ Department of Medical Diagnostic Imaging, College of Health Science, University of Sharjah, Sharjah, United Arab Emirates.
⁸ Research Institute for Medical and Health Sciences, University of Sharjah, Sharjah, United Arab Emirates.
⁹ Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia.

Abstract

In this work, tank drainage phenomena for in-compressible and isothermal fluid having unsteady fluid flow for third order fluid is studied. Analytical solution of the proposed problem is obtained using perturbation method subject to proper boundary conditions. No-slip condition is used because of fluid will have zero velocity relative to a solid boundary. Object of this work is to find out the velocity profile, flow rate, time required to empty a tank (time efflux) and mathematical relation of time and depth of the tank. Influence of different parameter over velocity profile, effect of radius of the tank over depth, effect of radius of piper over flow rate and effect of depth over flow rate are examined graphically using mathematica. Velocity profile of this model is compared with newtonian fluid's while assuming epsilon as a zero using graph and table from which it is clear that third order fluid posses greater velocity then Newtonian fluid.

Keywords: Perturbation method; Tank drainage; Third- order fluid.