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Hybrid Nanofluid Flow Past a Permeable Moving Thin Needle

by Iskandar Waini 1,2, Anuar Ishak 2,* and Ioan Pop 3
Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal 76100, Melaka, Malaysia
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Selangor, Malaysia
Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 612;
Received: 4 March 2020 / Revised: 13 April 2020 / Accepted: 14 April 2020 / Published: 16 April 2020
(This article belongs to the Section Engineering Mathematics)
The problem of a steady flow and heat transfer past a permeable moving thin needle in a hybrid nanofluid is examined in this study. Here, we consider copper (Cu) and alumina (Al2O3) as hybrid nanoparticles, and water as a base fluid. In addition, the effects of thermophoresis and Brownian motion are taken into consideration. A similarity transformation is used to obtain similarity equations, which are then solved numerically using the boundary value problem solver, bvp4c available in Matlab software (Matlab_R2014b, MathWorks, Singapore). It is shown that heat transfer rate is higher in the presence of hybrid nanoparticles. It is discovered that the non-uniqueness of the solutions is observed for a certain range of the moving parameter λ . We also observed that the bifurcation of the solutions occurs in the region of λ < 0 , i.e., when the needle moved toward the origin. Furthermore, we found that the skin friction coefficient and the heat transfer rate at the surface are higher for smaller needle sizes. A reduction in the temperature and nanoparticle concentration was observed with the increasing of the thermophoresis parameter. It was also found that the increase of the Brownian motion parameter leads to an increase in the nanoparticle concentration. Temporal stability analysis shows that only one of the solutions was stable and physically reliable as time evolved. View Full-Text
Keywords: Brownian motion; dual solutions; hybrid nanofluid; stability analysis; thermophoresis; thin needle Brownian motion; dual solutions; hybrid nanofluid; stability analysis; thermophoresis; thin needle
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Waini, I.; Ishak, A.; Pop, I. Hybrid Nanofluid Flow Past a Permeable Moving Thin Needle. Mathematics 2020, 8, 612.

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