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
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
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
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: firstname.lastname@example.org (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,
R.P. Bharti et al. / International Journal of Heat and Mass Transfer 50 (2007) 977–990...
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