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 Pegu

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

Received: 13 June 2012/Accepted: 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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*Corresponding author; email: alassafi2005@yahoo.com