Effect of Prandtl Number on Natural Convection Heat Transfer from a Heated Semi-Circular Cylinder

Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number. The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number, . The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. The resulting flow and temperature fields are visualized in terms of the streamline and isotherm patterns in the proximity of the cylinder. The flow remains attached to the cylinder surface over the range of conditions spanned here except that for and ; at these conditions, a separated flow region is observed when the condition of the constant wall temperature is prescribed on the surface of the cylinder. The heat transfer characteristics are analyzed in terms of the local and average Nusselt numbers. The maximum value of the local Nusselt number always occurs at the corner points whereas it is found to be minimum at the rear stagnation point on the flat surface. Overall, the average Nusselt number increases with Grashof number and/ or Prandtl number in accordance with the scaling considerations. The numerical results are used to develop simple correlations as functions of Grashof and Prandtl number thereby enabling the interpolation of the present numerical results for the intermediate values of the Prandtl or Grashof numbers for both thermal boundary conditions.

Authors:

• Avinash Chandra
• R. P. Chhabra

Keywords:

• Constant heat flux
• Constant surface temperature
• Grashof number
• natural convection
• Prandtl number
• Semi-circular cylinder

References:

[1] J. E. Hesselgreaves, Compact Heat Exchangers: Selection, Design and
Operation, Pergamon, Oxford, 2001.
[2] S. Kakac and H. Liu, Heat Exchangers: Selection, Rating, and Thermal
Design, Second ed., CRC Press, Boca Raton, FL, 2002.
[3] M. M. Zdravkovich, Flow Around Circular Cylinders, Volume 1:
Fundamentals, Oxford University Press, New York, 1997.
[4] M. M. Zdravkovich, Flow Around Circular Cylinders, Volume 2:
Applications, Oxford University Press, New York, 2003.
[5] O. G. Martynenko and P. P. Khramstov, Free Convective Heat Transfer,
Springer, New York, 2005.
[6] F. Kreith, The CRC Handbook of Thermal Engineering, CRC Press,
Boca Raton, FL, 2000.
[7] V. T. Morgan, The overall convective heat transfer from smooth circular
cylinders, Advances in Heat Transfer 11 (1975) 199-264.
[8] M. Coutanceau and J. R. Defaye, Circular cylinder wake configurations:
A flow visualization survey, Applied Mechanics Reviews 44 (1991)
255-305.
[9] A. K. De and A. Dalal, A numerical study of natural convection around
a square, horizontal, heated cylinder placed in an enclosure,
International Journal of Heat and Mass Transfer 49 (2006) 4608-4623.
[10] C. Sasmal and R. P. Chhabra, Laminar natural convection from a heated
square cylinder immersed in power-law fluids, Journal of Non-
Newtonian Fluid Mechanics 166 (2011) 811-830.
[11] A. O. Elsayed, E. Z. Ibrahim and S. A. Elsayed, Free convection from a
constant heat flux elliptic tube, Energy Conversion and Management 44
(2003) 2445-2453.
[12] R. P. Bharti, P. Sivakumar and R. P. Chhabra, Forced convection heat
transfer from an elliptical cylinder to power-law fluids, International
Journal of Heat and Mass Transfer 51 (2008) 1838-1853.
[13] A. K. De and A. Dalal, Numerical study of laminar forced convection
fluid flow and heat transfer from a triangular cylinder placed in a
channel, Journal of Heat Transfer 129 (2007) 646-656.
[14] A. Prhashanna, A. K. Sahu and R. P. Chhabra, Flow of power-law fluids
past an equilateral triangular cylinder: Momentum and heat transfer
characteristics, International Journal of Thermal Sciences 50 (2011)
2027-2041.
[15] S. A. Nada, H. El-Batsh and M. Moawed, Heat transfer and fluid flow
around semi-circular tube in cross flow at different orientations, Heat
and Mass Transfer 43 (2007) 1157-1169.
[16] S. A. Nada and M. Mowad, Free convection from a vertical and inclined
semicircular cylinder at different orientations, Alexandria Engineering
Journal 42 (2003) 273-283.
[17] A. Chandra and R. P. Chhabra, Flow over and forced convection heat
transfer in Newtonian fluids from a semi-circular cylinder, International
Journal of Heat and Mass Transfer 54 (2011) 225-241.
[18] A. Chandra and R. P. Chhabra, Momentum and heat transfer
characteristics of a semi-circular cylinder immersed in power-law fluids
in the steady flow regime, International Journal of Heat and Mass
Transfer 54 (2011) 2734-2750.
[19] A. Chandra and R. P. Chhabra, Mixed convection from a heated semicircular
cylinder to power-law fluids in the steady flow regime,
International Journal of Heat and Mass Transfer (2011) In press.
[20] A. Chandra and R. P. Chhabra, Laminar free convection from a
horizontal semi-circular cylinder to power-law fluids, Submitted for
publication (2011).
[21] A. Chandra and R. P. Chhabra, Influence of power-law index on
transitional Reynolds numbers for flow over a semi-circular cylinder,
Applied Mathematical Modelling 35 (2011) 5766-5785.
[22] S. W. Churchill, Laminar free convection from a horizontal cylinder
with a uniform heat flux density, Letters in Heat and Mass Transfer 1
(1974) 109-112.
[23] S. W. Churchill and H. H. S. Chu, Correlating equations for laminar and
turbulent free convection from a horizontal cylinder, international
Journal of Heat and Mass Transfer 18 (1975) 1049- 1053.
[24] S. O. Atayilmaz and I. Teke, Experimental and numerical study of the
natural convection from a heated horizontal cylinder, International
Communications in Heat and Mass Transfer 36 (2009) 731- 738.
[25] A. Prhashanna and R. P. Chhabra, Laminar natural convection from a
horizontal cylinder in power-law fluids, Industrial and Engineering
Chemistry Research 50 (2011) 2424-2440.