Sains Malaysiana 43(1)(2014): 151-159

Combined Similarity-numerical Solutions of MHD Boundary Layer Slip Flow of

Non-Newtonian Power-law Nanofluids over a Radiating Moving Plate

(Gabungan Penyelesaian Keserupaan Persamaan-berangka Aliran Slip bagi Lapisan Sempadan MHD dengan Nano Bendalir Hukum Kuasa yang Bukan-Newtonian atas Permukaan Beradiasi yang Bergerak)

NUR HUSNA MD. YUSOFF, MD. JASHIM UDDIN* & AHMAD IZANI MD. ISMAIL
School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia

Diserahkan: 24 Ogos 2012/Diterima: 26 Mac 2013

ABSTRACT

A combined similarity-numerical solution of the magnetohydrodynamic boundary layer slip flow of an electrically conducting non-Newtonian power-law nanofluid along a heated radiating moving vertical plate is explored. Our nanofluid model incorporates the influences of the thermophoresis and the Brownian motion. The basic transport equations are made dimensionless first and then suitable similarity transformations are applied to reduce them into a set of nonlinear ordinary differential equations with the associated boundary conditions. The reduced equations are then solved numerically. Graphical results for the non-dimensional flow velocity, the temperature and the nanoparticles volume fraction profiles as well as for the friction factor, the local Nusselt and the Sherwood numbers are exhibited and examined for various values of the controlling parameters to display the interesting aspects of the solutions. It was found that the friction factor increases with the increase of the magnetic field (M), whilst it is decreased with the linear momentum slip parameter (a). The linear momentum slip parameter (a) reduces the heat transfer rates and the nanoparticles volume fraction rates. Our results are compatible with the existing results for a special case.

Keywords: Magnetic field; momentum slip boundary condition; non-Newtonian power–law nanofluids; radiation

ABSTRAK

Gabungan penyelesaian keserupaan-berangka aliran tergelincir bagi lapisan sempadan magnetohidrodinamik nano bendalir hukum kuasa yang bukan-Newtonian yang boleh mengalirkan elektrik atas permukaan bergerak serta beradiasi diterokai. Model nanobendalir kami menggabungkan pengaruh termoforesis dan gerakan Brownian. Persamaan pengangkutan asas dijadikan tidak berdimensi dahulu dan transformasi persamaan yang sesuai digunakan untuk mengurangkan ke satu set persamaan pembezaan biasa tak linear dengan syarat sempadan yang berkaitan. Persamaan yang dikurangkan kemudian diselesaikan secara berangka. Keputusan grafik untuk halaju tidak berdimensi, suhu, profil pecahan isi padu zarah-zarah nano, nombor Nusselt serta Sherwood dipamerkan dan dikaji bagi pelbagai parameter kawalan untuk memaparkan aspek-aspek yang menarik daripada penyelesaian. Kajian mendapati bahawa regangan dinding ricih meningkatkan peningkatan medan magnet M, manakala menurun dengan momentum lelurus slip parameter (a). Momentum lelurus slip parameter a mengurangkan kadar pemindahan haba dan pecahan isi padu zarah nano. Keputusan kami adalah selaras dengan keputusan yang sedia ada bagi kes khas.

Kata kunci: Keadaan sempadan momentum slip; medan magnet; nanobendalir yang bukan Newtonian; radiasi

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*Pengarang untuk surat-menyurat; email: jashim_74@yahoo.com