Sains Malaysiana 46(9)(2017): 1667–1674

http://dx.doi.org/10.17576/jsm-2017-4609-40

 

Unsteady Flow of a Nanofluid Past a Permeable Shrinking Cylinder using Buongiorno’s Model

(Aliran Tak Mantap Nanobendalir melalui Silinder Telap Mengecut menggunakan model Buongiorno)

 

KHAIRY ZAIMI^1*, ANUAR ISHAK² & IOAN POP³

 

¹Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Perlis Indera Kayangan, Malaysia

 

²Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

 

³Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

 

Received: 28 June 2016/Accepted: 18 April 2017

 

ABSTRACT

The unsteady laminar boundary layer flow of a nanofluid and heat transfer over a permeable shrinking cylinder using the Buongiorno’s nanofluid model is investigated. Using a similarity transformation, the governing partial differential equations are transformed into a system of ordinary differential equations and then solved numerically using a shooting method. The numerical results are obtained for velocity, temperature and concentration profiles as well as the skin friction coefficient, the local Nusselt number and the local Sherwood number. Dual solutions are found to exist in a certain range of the suction and unsteadiness parameters. It is observed that suction parameter increase both the skin friction coefficient and the heat transfer rate at the surface, whereas the opposite trend is obtained for the Sherwood number. It is also observed that suction widens the range of the unsteadiness parameter for which the solution exists.

 

Keywords: Nanofluids; shrinking cylinder; suction; unsteady flow

 

ABSTRAK

Aliran lapisan sempadan lamina tak mantap nanobendalir dan pemindahan haba terhadap silinder telap mengecut menggunakan model nanobendalir Buongiorno dikaji. Menggunakan penjelmaan keserupaan, persamaan menakluk dalam bentuk persamaan pembezaan separa dijelmakan kepada persamaan pembezaan biasa dan diselesaikan secara berangka menggunakan kaedah tembakan. Keputusan berangka diperoleh bagi profil-profil halaju, suhu dan pecahan isi padu nanozarah serta pekali geseran kulit, nombor Nusselt setempat dan nombor Sherwood setempat. Penyelesaian dual didapati wujud bagi julat-julat tertentu parameter sedutan dan parameter ketakmantapan. Didapati parameter sedutan meningkatkan pekali geseran kulit dan kadar pemindahan haba pada permukaan, manakala telatah bertentangan diperoleh bagi nombor Sherwood. Didapati juga sedutan meluaskan julat parameter ketakmantapan yang penyelesaian wujud.

 

Kata kunci: Aliran tak mantap; nanobendalir; sedutan; silinder mengecut

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*Corresponding author; email: khairy@unimap.edu.my