Sains Malaysiana 41(9)(2012): 1139–1148

Investigation of Heat Mass Transfer for Combined Convective

Slips Flow: A Lie Group Analysis

(Kajian Pemindahan Haba dan Jisim Bagi Aliran Berolak

Gabungan Gelincir: Analisis Kumpulan Lie)

Md. Jashim Uddin1,*, M. M.Hamad2 & A.I. Md. Ismail1

1School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia

2Mathematics Department, Faculty of Science, Assiut University, Assiut, 71516, Egypt

Diserahkan: 17 November 2011 / Diterima: 21 Mei 2012

ABSTRACT

The steady laminar combined convective flow with heat and mass transfer of a Newtonian viscous incompressible fluid over a permeable flat plate with linear hydrodynamic and thermal slips has been investigated numerically. The velocity of the external flow, the suction/injection velocity and the temperature of the plate surface are assumed to vary nonlinearly following the power law with the distance along the plate from the origin. Lie group analysis is used to develop the similarity transformations and the governing momentum, the energy conservation and the mass conservation equations are converted to a system of coupled nonlinear ordinary differential equations with the associated boundary conditions. The resulting equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method. The effects of hydrodynamic slip parameter (a), thermal slip parameter (b), suction/injection parameter (fw), power law parameter (m), buoyancy ratio parameter (N), Prandtl number (Pr) and Schmidt number (Sc) on the fluid flow, heat transfer and mass transfer characteristics are investigated and presented graphically. We have also shown the effects of the Reynolds number (Re) and the power law parameter (m) on the velocity slip and the thermal slip factors. Good agreement is found between the numerical results of the present paper and published results.

Keywords: Combined convective flow; heat and mass transfer; hydrodynamic and thermal slip; Lie group

ABSTRAK

Aliran berolak tergabung yang mantap dan berlamina dengan pemindahan haba dan jisim bagi suatu bendalir Newtonan likat tak mampat ke atas plat rata yang telap dengan gelinciran linear hidrodinamik dan haba dikaji secara berangka. Halaju aliran luar, halaju sedutan/semburan dan suhu permukaan plat diandaikan berubah terhadap jarak sepanjang plat dari asalan secara tak linear mengikut hukum kuasa. Analisis Kumpulan Lie digunakan untuk memperoleh penjelmaan keserupaan dan persamaan momentum, keabadian tenaga dan keabadian jisim ditukar kepada sistem persamaan pembezaan biasa tak linear dengan syarat sempadan yang sepadan. Persamaan yang terhasil diselesaikan menggunakan kaedah berangka Runge-Kutta-Fehlberg peringkat keempat-kelima. Kesan parameter gelincir halaju a, parameter gelincir haba b, parameter sedutan/semburan (fw), parameter hukum kuasa m, parameter keapungan N, nombor Prandtl (Pr) dan nombor Schmidt (Sc) terhadap aliran bendalir, pemindahan haba dan pemindahan jisim dikaji dan dibentangkan secara bergraf. Kami juga mempamerkan kesan nombor Reynolds Re dan parameter hukum kuasa (m) ke atas faktor gelincir halaju dan faktor gelincir haba. Keputusan berangka dalam makalah ini didapati menepati keputusan yang telah diperoleh dalam penerbitan sebelum ini.

Kata kunci: Gelincir hidrodinamik dan haba; kumpulan Lie; olakan campuran; pemindahan haba dan jisim gabungan

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*Pengarang untuk surat-menyurat; email: jasihim_74@yahoo.com

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