Sains Malaysiana 43(3)(2014): 483–489

 

Axisymmetric Slip Flow on a Vertical Cylinder with Heat Transfer

(Aliran Gelincir Simetri Sepaksi pada Silider Menegak dengan Pemindahan Haba)

 

 

GURMINDER SINGH1* & OLUWOLE DANIEL MAKINDE2

1Birla Institute of Technology (Ranchi), Ext. Center Jaipur, 27 Malviya Industrial Area

Jaipur-302017, India

 

2Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395

South Africa

 

Received: 19 January 2013/Accepted: 12 June 2013

 

ABSTRACT

The paper is aimed at studying fluid flow heat transfer in the axisymmetric boundary layer flow of a viscous incompressible fluid, along the axial direction of a vertical stationary isothermal cylinder in presence of uniform free stream with momentum slip. The equations governing the flow i.e. continuity, momentum and energy equation are transformed into non-similar boundary layer equations and are solved numerically employing asymptotic series method with Shanks transformation. The numerical scheme involves the Runge-Kutta fourth order scheme along with the shooting technique. The flow is analyzed for both assisting and opposing buoyancy and the effect of different parameters on fluid velocity, temperature distribution, heat transfer and shear stress parameters is presented graphically.

 

Keywords: Cylindrical surface; heat transfer; non-similarity solution; Runge-Kutta method; shear stress; slip flow

 

ABSTRAK

Makalah ini bertujuan untuk mengkaji pemindahan haba aliran bendalir dalam aliran lapisan sempadan simetri sepaksi bagi suatu bendalir likat tak termampat, sepanjang arah paksi sebuah silinder isoterma pegun tegak yang berdiri dalam kehadiran strim bebas seragam dengan gelincir momentum. Persamaan yang mengawal aliran contohnya persamaan keselanjaran, persamaan momentum dan persamaan tenaga dijelmakan kepada persamaan lapisan sempadan tak serupa dan diselesaikan secara berangka menggunakan kaedah siri berasimptot dengan penjelmaan Shanks. Skim berangka tersebut melibatkan skim tertib keempat Runge-Kutta dan juga teknik penembakan. Aliran dianalisis daripada dua aspek dalam membantu dan melawan keapungan dan kesan ke atas halaju bendalir akibat parameter yang berbeza: Taburan suhu, pemindahan haba dan parameter tegasan ricih dipersembahkan secara grafik.

 

Kata kunci: Aliran gelincir; kaedah Runge-Kutta; pemindahan haba; permukaan silinder; persamaan tak serupa; tegasan ricih

REFERENCES

Aziz, A. & Na, T.Y. 1982. Improved perturbation solutions for laminar natural convection on a cylindrical cylinder. Wärme-und Stoffübertragung 16: 83-87.

Crane, L.J. & McVeigh, A.G. 2010a. Uniform slip flow on a cylinder. Proc. App. Math Mech. 10: 477-478.

Crane, L.J. & McVeigh, A.G. 2010b. Slip flow on microcylinder. ZAMP 61: 579-582.

Conte, S.D. & Boor, C. 1981. Elementary Numerical Analysis. New York: McGraw-Hill Book Co.

Gad-el-Hak, M. 1999. The fluid mechanics of microdevices-The Freeman Scholar Lecture. J. Fluid Engg. 121(1): 5-33.

Glauert, M.B. & Lighthill, M.J. 1955. The axisymmetric boundary layer on a long thin cylinder. Proc. Royal Soc. London A 230: 188-203.

Kelly, H.R.1962. A note on the laminar boundary layer flow on a circular cylinder in axial incompressible flow. J. Aero. Sc. 21(9): 634.

Lin, H.T. & Shih, Y.P. 1980. Laminar boundary layer heat transfer along static and moving cylinders. J. Chinese Inst. Engs. 3: 73-79.

Martin, M.J. & Boyd, D.I. 2006. Momentum and heat transfer in a laminar boundary layer with slip flow. J. Ther. Heat Transfer 20(4): 710-719.

Pop. I., Watanabe, T. & Taniguchi, H. 1995. Laminar boundary layer flow and heat transfer along a moving cylinder with suction and Injection. Technische Mechanik 15(2): 99-106.

Redmond, B. & McDonnell, D. 2004. Heat transfer through the boundary layer on a moving cylindrical fiber. Proc. App. Math. Mech. 10: 475-476.

Redmond, B. & Spillane, S. 2003. Shear stress on the surface of a circular cylinder at rest in a moving fluid in axially symmetric flow using Padé approximation technique. Proc. App. Math Mech. 3: 360-361.

Seban, R.A. & Bond, R. 1951. Skin friction and heat transfer characteristics of a laminar boundary layer on a circular cylinder in axial incompressible flow. J. Aero. Sc. 18: 671- 675.

Sharma, P.R. & Singh, G. 2010. Effects of variable thermal conductivity, viscous dissipation on steady MHD flow natural convection flow of low Prandtl fluid on an inclined porous plate with Ohmic heating. Meccanica 45: 237-247.

Spillane, S. & Redmond, B. 2004. Shear stress analysis in axially symmetric flow using Padé approximation technique. Proc. App. Math. and Mech. 4: 452-453.

 

 

*Corresponding author; email: garry_mal@yahoo.com

 

 

 

previous