Sains Malaysiana 43(8)(2014): 1249-1257

 

Scaling Transformation for Free Convection Flow of a Micropolar Fluid along a Moving Vertical Plate in a Porous Medium with Velocity and Thermal Slip Boundary Conditions

(Transformasi Penskalaan untuk Aliran Olakan Bebas Bendalir Mikropolar Sepanjang Plat Menegak dalam Medium Berliang dengan Syarat Sempadan Slip Halaju dan Haba)

 

A.A. Mutlag1,2*, Md. Jashim Uddin1,2 & Ahmad Izani Md. Ismail1

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

 

2Mathematics Department, College of Education for Pure Science, AL- Anbar University, ALAnbar Iraq

 

3Mathematics Department, American International University-Bangladesh, Banani Dhaka, 1213

Bangladesh

 

Diserahkan: 11 Januari 2013/Diterima: 9 Disember 2013

 

Abstract

We study and discuss the effect of thermal slip on steady free convection flow of a viscous, incompressible micropolar fluid past a vertical moving plate in a saturated porous medium. The effect of viscous dissipation is incorporated in the energy equation. The associated partial differential equations are transformed into a system of ordinary differential equations using similarity transformations generated by a group method and this system is then solved numerically. The effect of controlling parameters on the dimensionless velocity, angular velocity and temperature as well as friction factor, couple stress factor and heat transfer rate are shown graphically and discussed in detail. It is found that the dimensional velocity and angular velocity decrease whilst the temperature increases with velocity slip parameter. It is further found that thermal slip decreases the dimensional velocity and temperature but increases the dimensional angular velocity. Data from published work and our results are found to be in good agreement.

 

Keywords: Free convection; micropolar fluid; moving plate; porous medium; scaling group; velocity and thermal slip boundary conditions

 

Abstrak

 

Kami mengkaji dan membincangkan kesan slip haba pada aliran olakan bebas tak mampat bendalir mikro-kutub likat yang mantap melalui plat menegak yang bergerak dalam medium berliang tepu. Kesan penghambaran likat dimasuk ke dalam persamaan tenaga. Persamaan pembezaan separa bersekutu dijelmakan kepada sistem persamaan pembezaan biasa menggunakan penjelmaan keserupaan yang dijanakan menggunakan kaedah kumpulan dan sistem ini kemudiannya diselesaikan secara berangka. Kesan parameter pengawal halaju tak berdimensi, halaju sudut dan suhu serta faktor geseran, faktor regangan pasangan dan kadar pemindahan haba ditunjukkan secara grafik dan dibincangkan secara terperinci. Didapati bahawa halaju berdimensi dan halaju sudut menurun manakala suhu naik dengan slip halaju. Adalah selanjutnya didapati bahawa slip haba menurun halaju berdimensi dan suhu tetapi meningkatkan halaju sudut berdimensi. Data daripada kerja yang telah diterbitkan dan keputusan kami didapati mempunyai persamaan.

 

Kata kunci: Bendalir mikropolar; kumpulan penskalaan; medium berliang; perolakan bebas; plat bergerak; syarat sempadan slip termal halaju dan termal

 

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*Pengarang untuk surat-menyurat; email: alassafi2005@yahoo.com

 

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