Unsteady Boundary Layer Flow Over a Permeable Stretching/Shrinking Cylinder Immersed in Nanofluid

Authors

  • Nor Fadhilah Dzulkifli Faculty of Computer and Mathematics Sciences, Universiti Teknologi MARA Pahang, Jengka Campus, Pahang, Malaysia
  • Norfifah Bachok Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang Selangor, Malaysia
  • Nor Azizah Yacob Faculty of Computer and Mathematics Sciences, Universiti Teknologi MARA Pahang, Jengka Campus, Pahang, Malaysia
  • Norihan Arifin Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang Selangor, Malaysia
  • Haliza Rosali Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang Selangor, Malaysia
  • Ioan Pop Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, 400084, Romania

DOI:

https://doi.org/10.37934/arfmts.85.2.2432

Keywords:

Boundary Layer, Cylinder, Nanofluid, Stretching, Shrinking

Abstract

In this study, the unsteady boundary layer flow over a stretching/shrinking cylinder immersed in nanofluid with the presence of suction effect is analyzed. The governing partial differential equations are converted to ordinary differential equations by introducing similarity transformation variables. The shooting method is applied to solve the system where the numerical solutions are obtained and presented graphically.  The study's objective is to investigate the effect of nanoparticle volume fraction, the unsteadiness parameter, the stretching/shrinking parameter on the velocity and temperature gradients. It is found that the dual solutions are obtained in a specific range of these parameters for both stretching and shrinking cylinders. Besides, a high volume of the nanoparticle in the base fluid increases the velocity gradient and decreases the temperature gradient at the surface. Also, increasing nanoparticle volume fraction in the base fluid expands the solution's range, which denotes the boundary layer separation from the surface has been delayed. The existence of dual solutions allows stability analysis performance by introducing a new dimensionless variable and is solved using bvp4c function in Matlab software. This phase obtains the smallest eigenvalue, showing that the first solution is stable and physically realizable while the second solution is not stable.

Author Biographies

Nor Fadhilah Dzulkifli, Faculty of Computer and Mathematics Sciences, Universiti Teknologi MARA Pahang, Jengka Campus, Pahang, Malaysia

nfd@uitm.edu.my

Norfifah Bachok, Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang Selangor, Malaysia

norfifah@upm.edu.my

Nor Azizah Yacob, Faculty of Computer and Mathematics Sciences, Universiti Teknologi MARA Pahang, Jengka Campus, Pahang, Malaysia

norazizah872@uitm.edu.my

Norihan Arifin , Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang Selangor, Malaysia

norihana@upm.edu.my

Haliza Rosali, Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang Selangor, Malaysia

liza_r@upm.edu.my

Ioan Pop, Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, 400084, Romania

popm.ioan@yahoo.co.uk

References

Tie-Gang, Fang, Zhang Ji, Zhong Yong-Fang, and Tao Hua. "Unsteady viscous flow over an expanding stretching cylinder." Chinese Physics Letters 28, no. 12 (2011): 124707. https://doi.org/10.1088/0256-307X/28/12/124707

Zaimi, WMKA Wan, Anuar Ishak, and Ioan Pop. "Unsteady viscous flow over a shrinking cylinder." Journal of King Saud University-Science 25, no. 2 (2013): 143-148. https://doi.org/10.1016/j.jksus.2012.11.005

Marinca, Vasile, and Remus-Daniel Ene. "Dual approximate solutions of the unsteady viscous flow over a shrinking cylinder with optimal Homotopy Asymptotic Method." Advances in Mathematical Physics 2014 (2014): 1-11. https://doi.org/10.1155/2014/417643

Zaimi, Khairy, Anuar Ishak, and Ioan Pop. "Unsteady flow due to a contracting cylinder in a nanofluid using Buongiorno's model." International Journal of Heat and Mass Transfer 68 (2014): 509-513. https://doi.org/10.1016/j.ijheatmasstransfer.2013.09.047

Mahdy, A., and A. Chamkha. "Heat transfer and fluid flow of a non-Newtonian nanofluid over an unsteady contracting cylinder employing Buongiorno's model." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 4 (2015): 703-723. https://doi.org/10.1108/HFF-04-2014-0093

Abbas, Z., S. Rasool, and M. M. Rashidi. "Heat transfer analysis due to an unsteady stretching/shrinking cylinder with partial slip condition and suction." Ain Shams Engineering Journal 6, no. 3 (2015): 939-945. https://doi.org/10.1016/j.asej.2015.01.004

Azam, M., M. Khan, and A. S. Alshomrani. "Unsteady radiative stagnation point flow of MHD Carreau nanofluid over expanding/contracting cylinder." International Journal of Mechanical Sciences 130 (2017): 64-73. https://doi.org/10.1016/j.ijmecsci.2017.06.010

Khan, Ansab Azam, Khairy Zaimi, and Teh Yuan Ying. "Stagnation point flow of Williamson nanofluid towards a permeable stretching/shrinking sheet with a partial slip." CFD Letters 12, no. 6 (2020): 39-56. https://doi.org/10.37934/cfdl.12.6.3956

Awaludin, Izyan Syazana, Rokiah Ahmad, and Anuar Ishak. "On the stability of the flow over a shrinking cylinder with prescribed surface heat flux." Propulsion and Power Research 9, no. 2 (2020): 181-187. https://doi.org/10.1016/j.jppr.2020.03.001

Fang, Tie-gang. "New unsteady boundary layers over a long thin cylinder." Meccanica 50, no. 12 (2015): 2907-2918. https://doi.org/10.1007/s11012-015-0177-1

Yashkun, Ubaidullah, Fatinnabila Kamal, Khairy Zaimi, Nor Ashikin Abu Bakar, and Norshaza Atika Saidin. "Stability analysis on stagnation-point flow and heat transfer towards a permeable stretching/shrinking sheet with heat source in a Casson fluid." CFD Letters 12, no. 6 (2020): 1-15. https://doi.org/10.37934/cfdl.12.6.115

Parvin, Shahanaz, Siti Suzilliana Putri Mohamed Isa, Norihan Md Arifin, and Fadzilah Md Ali. "Dual numerical solutions on mixed convection Casson fluid flow due to the effect of the rate of extending and compressing sheet-Stability analysis." CFD Letters 12, no. 8 (2020): 76-84. https://doi.org/10.37934/cfdl.12.8.7684

Usman , Auwalu Hamisu, Sadiya Ali Rano, Usa Wannasingha Humphries, and Poom Kumam. "Activity of Viscoelastic Nanofluid Film Sprayed on a Stretching Cylinder with Arrhenius Activation Energy and Entropy Generation. " Journal of Advanced Research in Micro and Nano Engineering 3, no. 1 (2020): 12-24.

Rashid, Umair, Haiyi Liang, Hijaz Ahmad, Muhammad Abbas, Azhar Iqbal, and Y. S. Hamed. "Study of (Ag and TiO2)/water nanoparticles shape effect on heat transfer and hybrid nanofluid flow toward stretching shrinking horizontal cylinder. "Results in Physics 21 (2021): 103812. https://doi.org/10.1016/j.rinp.2020.103812

Elsaid , Essam M., and Mohamed S. Abdel-wahed. "Impact of hybrid nanofluid coolant on the boundary layer behavior over a moving cylinder: Numerical case study." Case Studies in Thermal Engineering 25 (2021): 100951. https://doi.org/10.1016/j.csite.2021.100951

Khan , Umair, A. Zaib, and A. Ishak. "Non-similarity solutions of radiative stagnation point flow of a hybrid nanofluid through a yawed cylinder with mixed convection." Alexandria Engineering Journal 60 (2021): 5297-5309. https://doi.org/10.1016/j.aej.2021.04.057

Tiwari, Raj Kamal, and Manab Kumar Das. "Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids." International Journal of Heat and Mass Transfer 50, no. 9-10 (2007): 2002-2018. https://doi.org/10.1016/j.ijheatmasstransfer.2006.09.034

Weidman, P. D., D.G. Kubitschek, and A. M. J. Davis. "The effect of transpiration on self-similar boundary layer flow over moving surfaces." International Journal of Engineering Science 44, no. 11-12 (2006): 730-737. https://doi.org/10.1016/j.ijengsci.2006.04.005

Ismail, Nurul Syuhada, Norihan Md Arifin, Roslinda Nazar, and Norfifah Bachok. "Stability analysis of unsteady MHD stagnation point flow and heat transfer over a shrinking sheet in the presence of viscous dissipation." Chinese Journal of Physics 57 (2019): 116-126. https://doi.org/10.1016/j.cjph.2018.12.005

Oztop, Hakan F., and Eiyad Abu-Nada. "Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids." International Journal of Heat and Fluid Flow 29, no. 5 (2008): 1326-1336. https://doi.org/10.1016/j.ijheatfluidflow.2008.04.009

Downloads

Published

2021-08-05

How to Cite

Dzulkifli, N. F. ., Bachok, N. ., Yacob, N. A. ., Arifin , N. ., Rosali, H. ., & Pop, I. . (2021). Unsteady Boundary Layer Flow Over a Permeable Stretching/Shrinking Cylinder Immersed in Nanofluid. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 85(2), 24–32. https://doi.org/10.37934/arfmts.85.2.2432

Issue

Section

Articles

Most read articles by the same author(s)

1 2 > >>