Steady forced convection heat transfer from a heated circular cylinder to power-law fluids

Topics: Convection, Fluid dynamics, Heat transfer Pages: 47 (7818 words) Published: February 28, 2014
International Journal of Heat and Mass Transfer 50 (2007) 977–990 www.elsevier.com/locate/ijhmt

Steady forced convection heat transfer from a heated
circular cylinder to power-law fluids
Ram Prakash Bharti a, R.P. Chhabra a,*, V. Eswaran b
a
b

Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India Received 12 January 2006

Available online 12 October 2006

Abstract
Forced convection heat transfer to incompressible power-law fluids from a heated circular cylinder in the steady cross-flow regime has been investigated numerically by solving the momentum and thermal energy equations using a finite volume method and the QUICK scheme on a non-uniform Cartesian grid. The dependence of the average Nusselt number on the Reynolds number (5 6 Re 6 40), power-law index (0.6 6 n 6 2) and Prandtl number (1 6 Pr 6 1000) has been studied in detail. The numerical results are used to develop simple correlations as functions of the pertinent dimensionless variables. In addition to the average Nusselt number, the effects of Re, Pr and n on the local Nusselt number distribution have also been studied to provide further physical insights. The role of the two types of thermal boundary conditions, namely, constant temperature and uniform heat flux on the surface of the cylinder has also been presented. Ó 2006 Elsevier Ltd. All rights reserved.

Keywords: Steady flow; Power-law fluids; Shear-thinning; Shear-thickening; Circular cylinder; Nusselt number; Constant wall temperature; Uniform heat flux

1. Introduction
The steady cross-flow past a circular cylinder represents
an idealization of many industrially important processes.
Typical examples include the flow on the shell side of tubular heat exchangers, pin fins, the use of thin wires as measuring sensors and probes, the use of screens to filter polymer melts and sewage sludges, etc. In addition to such

an overwhelming pragmatic significance, this flow is also
regarded to be one of the classical problems of fluid
mechanics. Consequently, a voluminous body of information on a variety of flow phenomena associated with this configuration has accumulated over the years, albeit most
of it relates to the Newtonian fluids. Several excellent survey articles and books summarizing the current state of the art for Newtonian fluid flow past a circular cylinder are
now available [1–11]. Hence, adequate information is
*

Corresponding author. Tel.: +91 512 2597393; fax: +91 512 2590104. E-mail address: chhabra@iitk.ac.in (R.P. Chhabra).

0017-9310/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2006.08.008

now available on most aspects of flow and heat transfer
for Newtonian fluid flow past a circular cylinder. Suffice it to say here that even for Newtonian fluids, the flow characteristics have been studied much more extensively than the corresponding heat or mass transfer problems.

On the other hand, many materials of industrial significance exhibit a range of non-Newtonian fluid behaviour features. For instance, most polymeric systems (melts and
solutions) and slurries exhibit shear dependent viscosity
thereby displaying shear-thinning or shear-thickening, or
both, under appropriate conditions. Despite their wide
occurrence in fiber reinforced resin processing, in the handling of paper pulp suspensions, fluidization of fibrous materials, etc., very little work is currently available on
the cross-flow of shear-thinning and shear-thickening fluids which are frequently modelled by the simple power-law
model [12,13] over a circular cylinder. The available literature for the flow past a single cylinder and across a periodic array of cylinders [2,14,15] seems to suggest the viscoelastic effects to be minor in this flow configuration. Furthermore,

978

R.P. Bharti et al. / International Journal of Heat and Mass Transfer 50 (2007) 977–990...

References: R.P. Bharti et al. / International Journal of Heat and Mass Transfer 50 (2007) 977–990
[2]
R.P. Chhabra, Bubbles, Drops and Particles in Non-Newtonian
Fluids, second ed., CRC Press, Boca Raton, FL, 2006.
Dekker, New York, 1996, Chapter 1.
the Rheology and Flow of Non-Newtonian Fluids, Elsevier, Amsterdam, 1999, Chapter 39.
R. Clift, J. Grace, M.E. Weber, Bubbles, Drops and Particles,
Academic Press, New York, USA, 1978.
Transfer 41 (1998) 3409–3430.
Fluid Mech. 28 (1996) 477–539.
M.M. Zdravkovich, Flow Around Circular Cylinder vol. 1, Fundamentals, Oxford University Press, New York, USA, 1997.
M.M. Zdravkovich, Flow Around Circular Cylinder vol. 2, Applications, Oxford University Press, New York, USA, 2003.
P.J. Carreau, D. De Kee, R.P. Chhabra, Rheology of Polymeric
Systems, Hanser-Gardner: Munich, Germany, 1997.
R.P. Chhabra, J.F. Richardson, Non-Newtonian Flow in the Process
Industries: Fundamentals and Engineering Applications, Butterworth-Heinemann, Oxford, 1999.
and elasticity effects, J. Non-Newtonian Fluid Mech. 57 (1995) 177–
202.
comparisons of predictions for microstructure and flow field, J. NonNewtonian Fluid Mech. 77 (1998) 153–190.
Non-Newtonian Fluid Mech. 50 (1993) 217–224.
Angew. Math. Mech. 81 (2001) 31–36.
fluids, Int. J. Non-Linear Mech. 36 (2001) 947–953.
Chem. Res. 43 (2004) 3439–3450.
(2004) 1–16.
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • Forced Convection Heat Transfer Essay
  • Essay about Free & Forced Convection Heat Transfer
  • Free & Forced Convection Heat Transfer Essay
  • Convection: Surface Heat Transfer Essay
  • Numerical Study of Laminar Mixed Convection Heat Transfer of Power-Law Non-Newtonian Fluids in Square Enclosures by Finite Volume Method Essay
  • Forced Convection (in a cross flow heat exchanger) Essay
  • find the convection heat transfer coefficient in a heat exchanger Essay
  • Heat Transfer Essay

Become a StudyMode Member

Sign Up - It's Free