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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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