# 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

## 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

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

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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

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