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Unsteady axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable stretching/shrinking disc

Najiyah Safwa Khashi'ie (Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Melaka, Malaysia)
Norihan M. Arifin (Department of Mathematics, Universiti Putra Malaysia, Selangor, Malaysia)
Ioan Pop (Facultatea de Matematica si Informatica, Universitatea Babes Bolyai, Cluj-Napoca, Romania)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 9 December 2020

Issue publication date: 24 May 2021




This study aims to analyze the unsteady flow of hybrid Cu-Al2O3/water nanofluid over a permeable stretching/shrinking disc. The analysis of flow stability is also purposed because of the non-uniqueness of solutions.


The reduced differential equations (similarity) are solved numerically using the aid of bvp4c solver (Matlab). Two types of thermophysical correlations for hybrid nanofluid (Type 1 and 2) are adopted for the comparison results. Using correlation Type 1, the heat transfer and flow analysis including the profiles (velocity and temperature) are presented in the figures and tables with different values control parameters. Three sets of hybrid nanofluid are analyzed: Set 1 (1% Al2O3 + 1% Cu), Set 2 (0.5% Al2O3 + 1% Cu) and Set 3 (1% Al2O3 + 0.5% Cu).


The comparison of numerical values between present (Types 1 and 2 correlations) and previous (Type 2 correlations) results are in a good compliance with approximate percent relative error. The appearance of two solutions is noticed when the suction parameter is considered and the unsteady parameter is less than 0 (decelerating flow) for both stretching and shrinking disc while only one solution is possible for steady flow. The hybrid nanofluid in Set 1 can delay the separation of boundary layer but the hybrid nanofluid in Set 3 has the greatest heat transfer rate. Moreover, the inclusion of wall mass suction for stretching case can generate a significant increment of heat transfer rate approximately 90% for all fluids (water, single and hybrid nanofluids).


The present findings are novel and can be a reference point to other researchers to further analyze the heat transfer performance and stability of the working fluids.



The financial support from Ministry of Higher Education (Malaysia) through Fundamental Research Grant Scheme (FRGS)-5540309 are appreciated. The authors also would like to acknowledge Universiti Putra Malaysia, Universiti Teknikal Malaysia Melaka and Babeş-Bolyai University.

Conflict of interest: The authors declare that there is no conflict of interest.


Khashi'ie, N.S., Arifin, N.M. and Pop, I. (2021), "Unsteady axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable stretching/shrinking disc", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 6, pp. 2005-2021.



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