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
Diserahkan: 19 Januari
2013/Diterima: 12 Jun 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
RUJUKAN
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.
*Pengarang untuk surat-menyurat; email:
garry_mal@yahoo.com
|