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Hybrid nanofluid flow on a shrinking cylinder with prescribed surface heat flux

Iskandar Waini (Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Melaka, Malaysia)
Anuar Ishak (Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi, Malaysia)
Ioan Pop (Faculty of Mathematics and Computer Science, Babes Bolyai University, Cluj Napoca, Romania)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 14 October 2020

Issue publication date: 24 May 2021




This study aims to investigate the flow impinging on a stagnation point of a shrinking cylinder subjected to prescribed surface heat flux in Al2O3-Cu/water hybrid nanofluid.


Using similarity variables, the similarity equations are obtained and then solved using bvp4c in MATLAB. The effects of several physical parameters on the skin friction and heat transfer rate, as well as the velocity and temperature profiles are analysed and discussed.


The outcomes show that dual solutions are possible for the shrinking case, in the range λc<λ<1, where λc is the bifurcation point of the solutions. Meanwhile, the solution is unique for λ1. Besides, the boundary layer is detached on the surface at λc, where the value of λc is affected by the hybrid nanoparticle φhnf and the curvature parameter γ. Moreover, the friction and the heat transfer on the surface increase with the rising values φhnf and γ. Finally, the temporal stability analysis shows that the first solution is stable in the long run, whereas the second solution is not.


The present work considers the problem of stagnation point flow impinging on a shrinking cylinder containing Al2O3-Cu/water hybrid nanofluid, with prescribed surface heat flux. This paper shows that two solutions are obtained for the shrinking case. Further analysis shows that only one of the solutions is stable as time evolves.



The authors would like to thank the anonymous reviewers for their constructive comments and suggestions which led to the improvement of this paper. The financial supports received from the Universiti Kebangsaan Malaysia (Project Code: DIP-2020–001) and the Universiti Teknikal Malaysia Melaka are gratefully acknowledged.

Competing interests: The authors declare no competing interests.


Waini, I., Ishak, A. and Pop, I. (2021), "Hybrid nanofluid flow on a shrinking cylinder with prescribed surface heat flux", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 6, pp. 1987-2004.



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