Sains Malaysiana 42(6)(2013):
855–862
Heat Transfer Analysis for Falkner-Skan Boundary Layer Flow
Past a Stationary Wedge with Slips Boundary Conditions Considering
Temperature-dependent Thermal Conductivity
(Analisis Pemindahan Haba bagi Aliran Lapisan Sempadan
Falkner-Skan Melintasi Suatu Baji Pegun dengan Syarat Sempadan Gelinciran serta
Keberaliran Haba Bersandar-Suhu)
A.A. Mutlag*, Md. Jashim Uddin & Ahmad Izani Ismail
School of Mathematical Sciences, Universiti Sains Malaysia
11800 Penang, Malaysia
A.A. Mutlag*
Mathematics Department, College of Education for Pure
Science
AL- Anbar University, AL- Anbar, Iraq
Md. Jashim Uddin
Mathematics Department, American International
University-Bangladesh
Banani, Dhaka 1213, Bangladesh
M.A.A. Hamad4
Mathematics Department, Faculty of Science, Assiut
University, Assiut 71516
Egypt
Diserahkan: 13 Jun 2012/Diterima: 27 September 2012
ABSTRACT
We studied the problem of heat transfer for Falkner-Skan boundary
layer flow past a stationary wedge with momentum and thermal slip boundary
conditions and the temperature dependent thermal conductivity. The governing
partial differential equations for the physical situation are converted into a
set of ordinary differential equations using scaling group of transformations.
These are then numerically solved using the Runge-Kutta-Fehlberg fourth-fifth
order numerical method. The momentum slip parameter d leads to increase in the
dimensionless velocity and the rate of heat transfer whilst it decreases the
dimensionless temperature and the friction factor. The thermal slip parameter
leads to the decrease rate of heat transfer as well as the dimensionless
temperature. The dimensionless velocity, rate of heat transfer and the friction
factor increase with the Falkner-Skan power law parameter m but the
dimensionless fluid temperature decreases with m. The dimensionless fluid
temperature and the heat transfer rate decrease as the thermal conductivity
parameter A increases. Good agreements are found
between the numerical results of the present paper with published results.
Keywords: Falkner-Skan; momentum slip; thermal slip; scaling group
of transformation; temperature dependent thermal conductivity
ABSTRAK
Kami mengkaji permasalahan pemindahan haba bagi
aliran lapisan sempadan Falkner-Skan melintasi suatu baji pegun dengan syarat
sempadan gelinciran momentum dan haba serta kekonduksian haba bersandar-suhu. Persamaan pembezaan separa menakluk bagi
situasi fizik dijelmakan kepada suatu set persamaan pembezaan biasa menggunakan
penjelmaan kumpulan penskalaan. Set persamaan pembezaan biasa tersebut
kemudiannya diselesaikan secara berangka menggunakan kaedah berangka
Runge-Kutta-Fehlberg keempat-kelima. Parameter gelinciran momentum δ
didapati meningkat terhadap halaju tak berdimensi dan kadar pemindahan haba. Parameter gelinciran momentum didapati
berkurang terhadap suhu tak berdimensi dan juga tegasan ricih. Halaju
tak berdimensi, kadar pemindahan haba dan pekali
tegasan ricih meningkat terhadap parameter hukum kuasa Falkner-Skan m, tetapi
suhu bendalir menurun dengan m. Suhu bendalir tak berdimensi dan kadar
pemindahan haba menurun apabila parameter konduktiviti haba A meningkat. Didapati keputusan berangka dalam kertas ini menepati keputusan
yang telah diterbitkan sebelum ini.
Kata kunci: Falkner-Skan; gelinciran haba; gelinciran momentum; kekonduksian
haba bersandar suhu; penjelmaan kumpulan penskalaan
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*Pengarang
untuk surat-menyurat; email: alassafi2005@yahoo.com