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Research Papers: Forced Convection

Numerical Re-examination of Chilton–Colburn Analogy for Variable Thermophysical Fluid Properties

[+] Author and Article Information
Rajan Kumar

School of Engineering,
Indian Institute of Technology,
Mandi, Himachal Pradesh 175001, India
e-mail: rajan.rana9008@gmail.com

Shripad P. Mahulikar

Professor
Department of Aerospace Engineering,
Indian Institute of Technology,
Bombay, P.O. IIT Powai,
Mumbai, Maharashtra 400076, India
e-mail: spm@aero.iitb.ac.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 3, 2015; final manuscript received January 19, 2017; published online March 21, 2017. Assoc. Editor: Laura Schaefer.

J. Heat Transfer 139(7), 071701 (Mar 21, 2017) (10 pages) Paper No: HT-15-1691; doi: 10.1115/1.4035855 History: Received November 03, 2015; Revised January 19, 2017

The Chilton–Colburn analogy is very helpful for evaluating the heat transfer in internal forced flows. The Chilton–Colburn analogy between the Chilton–Colburn j-factor for heat transfer, jH (St·Pr2/3) and the Fanning friction factor (cf) is popularly considered to hold when St·Pr2/3 equals to cf/2, for constant fluid properties. The physical fluid properties, namely, viscosity and thermal conductivity, are generally a function of temperature for microconvective water flow due to a quite steep temperature gradient. Therefore, in present investigation, the validity of Chilton–Colburn analogy between St·Pr2/3 and cf is re-examined for laminar microconvective flow with variable thermophysical fluid properties. It is observed that the Chilton–Colburn analogy is valid only for that portion of the flow regime, where St·Pr2/3 decreases with decreasing cf. The validity of Chilton–Colburn analogy is also verified by the inverse dependence of Reynolds number (Re) with cf. Two modified nondimensional parameters “Π and ΠSk” are emerged from the nondimensional form of 2D, steady-state, incompressible, pure continuum-based, laminar conservation of momentum and energy equations, respectively. These modified nondimensional parameters show the significance of variable fluid properties in momentum transport and energy transport. Additionally, the role of Π and ΠSk in flow friction is also investigated. The higher values of Π and ΠSk indicate the stronger influence on microconvection due to large variations in fluid properties.

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Figures

Grahic Jump Location
Fig. 1

Schematic diagram of a two-dimensional axisymmetric circular microchannel with CWHF boundary condition

Grahic Jump Location
Fig. 2

Computational domain with finer grid spacing in the vicinity of the inlet and the wall

Grahic Jump Location
Fig. 3

Variation of St·Pr2/3 versus cf (examination of Chilton–Colburn analogy): (a) um,in = 0.5 m/s (Chilton–Colburn analogy largely valid), (b) um,in = 2 m/s, and (c) um,in = 3 m/s (Chilton–Colburn analogy largely invalid)

Grahic Jump Location
Fig. 4

Variation of 1/Re versus cf (examination of Chilton–Colburn analogy): (a) um,in = 0.5 m/s (Chilton–Colburn analogy largely valid), (b) um,in = 2 m/s, and (c) um,in = 3 m/s (Chilton–Colburn analogy largely invalid)

Grahic Jump Location
Fig. 5

Variation of cf versus z/D: (a) um,in = 0.5 m/s, (b) um,in = 2 m/s, and (c) um,in = 3 m/s

Grahic Jump Location
Fig. 6

Variation of Po versus z/D: (a) um,in = 0.5 m/s, (b) um,in = 2 m/s, and (c) um,in = 3 m/s

Grahic Jump Location
Fig. 7

Variation of (∂u¯/∂r¯)w versus z/D: (a) um,in = 0.5 m/s, (b) um,in = 2 m/s, and (c) um,in = 3 m/s

Grahic Jump Location
Fig. 8

Variation of Po versus Π, only Chilton–Colburn analogy valid data: (a) um,in = 0.5 m/s, (b) um,in = 2 m/s, and (c) um,in = 3 m/s

Grahic Jump Location
Fig. 9

Variation of Po versus ΠSk, only Chilton–Colburn analogy valid data: (a) um,in = 0.5 m/s, (b) um,in = 2 m/s, and (c) um,in = 3 m/s

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