Sains Malaysiana 39(6)(2010): 1035–1039

Aliran Lapisan Sempadan Bersebelahan Plat Tegak  dengan Suhu Permukaan Malar

(Boundary Layer Flow Adjacent to a Vertical Plate with Constant Surface Temperature)

Anuar Ishak*

Pusat Pengajian Sains Matematik

Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor, Malaysia

Received: 30 December 2008 / Accepted: 20 May 2010

ABSTRAK

Pembentukan lapisan sempadan halaju dan terma yang dirangsang oleh aliran bebas bersebelahan plat tegak dengan suhu permukaan malar dikaji. Persamaan-persamaan menakluk dalam bentuk persamaan pembezaan separa diturunkan kepada persamaan-persamaan pembezaan biasa dengan penjelmaan keserupaan, sebelum diselesaikan secara berangka. Kedua-dua aliran membantu dan aliran menentang dipertimbangkan. Didapati bahawa penyelesaian adalah unik bagi aliran membantu, manakala penyelesaian dual wujud bagi aliran menentang. Kadar pemindahan haba pada permukaan didapati meningkat dengan peningkatan kedua-dua daya keapungan dan nombor Prandtl.

Kata kunci: Lapisan sempadan; pemindahan haba; penyelesaian dual; penyelesaian keserupaan

ABSTRACT

The development of velocity and thermal boundary layers induced by a free stream adjacent to a vertical plate with constant surface temperature was studied. The governing partial differential equations were reduced to ordinary ones by a similarity transformation, before being solved numerically. Both assisting and opposing flows were considered. It was found that the solution was unique for the assisting flow, while dual solutions were found to exist for the opposing flow. The heat transfer rate at the surface was found to increase with both the buoyancy force and the Prandtl number.

Keywords: Boundary layer; dual solutions; heat transfer; similarity solution

REFERENCES

Ishak, A. 2009a. Mixed convection boundary layer flow over a horizontal plate with thermal radiation. Heat Mass Transfer 46: 147-151.

Ishak, A. 2009b. Radiation effects on the flow and heat transfer over a moving plate in a parallel stream. Chinese Physics Letters 26: 034701.

Ishak, A. 2010. Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect. Meccanica 45: 367-373.

Ishak, A., Merkin, J.H., Nazar, R. & Pop, I. 2008a. Mixed convection boundary layer flow over a vertical permeable surface with prescribed wall heat flux. Z. angew. Math. Phys. 59: 100-123.

Ishak, A., Nazar, R. & Pop, I. 2007. Mixed convection on the stagnation-point flow towards a vertical, continuously stretching sheet. ASME J. Heat Transfer 129: 1087-1090.

Ishak, A., Nazar, R. & Pop, I. 2008b. Local similarity solutions for laminar boundary layer flow along a moving cylinder in a parallel stream. LNCS Comp. Math 5081: 224-235.

Merkin, J.H. 1985. On dual solutions occuring in mixed convection in a porous medium. J. Eng. Math. 20: 171-179.

Merrill, K., Beauchesne, M., Previte, J., Paullet, J. & Weidman, P. 2006. Final steady flow near a stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Transfer 49: 4681-4686.

Merkin, J.H. & Mahmood, T. 1989. Mixed convection boundary-layer similarity solutions: prescribed wall heat flux. Z. angew. Math. Phys. 40: 51-68.

Schlichting, H. 1979. Boundary Layer Theory. 7th Edition. New York: McGraw-Hill.

Schneider, W. 1979. A similarity solution for combined forced and free convection flow over a horizontal plate. Int. J. Heat Mass Transfer 22: 1401-1406.

*Corresponding author; email: anuarishak@yahoo.com

 content