Research Papers: Natural and Mixed Convection

Numerical Investigation of Natural Convection Heat Transfer From an Array of Horizontal Fins in Non-Newtonian Power-Law Fluids

[+] Author and Article Information
Jacob K. Mulamootil

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: jkmkoshy@gmail.com

Sukanta K. Dash

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: sdash@mech.iitkgp.ernet.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 27, 2016; final manuscript received June 8, 2017; published online September 13, 2017. Assoc. Editor: Milind A. Jog.

J. Heat Transfer 140(2), 022501 (Sep 13, 2017) (8 pages) Paper No: HT-16-1829; doi: 10.1115/1.4037537 History: Received December 27, 2016; Revised June 08, 2017

Natural convection heat transfer from an array of horizontal rectangular fins on a vertical flat plate in non-Newtonian power-law fluids has been studied. The underlying physical principles affecting heat transfer were studied using comprehensive solutions obtained from numerical investigations. Heat transfer to the power-law fluid was found to depend on the fluid rheology (power-law index) and significantly on the geometric parameters (interfin spacing, fin length) as well. The dependence was quantified using the Nusselt number (Nu) and fin effectiveness (Q/Q0). The present study shows that compared to a fin analyzed in isolation, the spatial arrangement of multiple fins relative to one another in an array does have a significant effect on the flow field around subsequent fins in power-law fluids. Therefore, the average heat transfer coefficient of the natural convection system is affected significantly. The variation of Nu with the dimensionless fin length (l/L), dimensionless interfin spacing (S/L), and fluid power-law index (n) was plotted. The dependence was found to be counter intuitive to expectations based on studies for natural convection from vertical flat plates to power-law fluids. In the present study involving fins, shear-thinning fluids (n < 1) show a decrease in heat transfer and shear-thickening fluids (n > 1) show an enhancement in heat transfer for higher l/L values. The results of the study may be useful in the design of natural convection systems that employ power-law fluids to enhance or control heat transfer.

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Chhabra, R. P. , and Richardson, J. F. , 2008, Non-Newtonian Flow and Applied Rheology: Engineering Applications, Butterworth-Heinemann, Oxford, UK.
Bird, R. B. , Armstrong, R. C. , and Hassager, O. , 1987, Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics, Wiley, New York.
Acrivos, A. , 1960, “ A Theoretical Analysis of Laminar Natural Convection Heat Transfer to Non-Newtonian Fluids,” AIChE J., 6(4), pp. 584–590. [CrossRef]
Reilly, I. G. , Tien, C. , and Adelman, M. , 1965, “ Experimental Study of Natural Convective Heat Transfer From a Vertical Plate in a Non-Newtonian Fluid,” Can. J. Chem. Eng., 43(4), pp. 157–160. [CrossRef]
Gray, D. D. , and Giorgini, A. , 1976, “ The Validity of the Boussinesq Approximation for Liquids and Gases,” Int. J. Heat Mass Transfer, 19(5), pp. 545–551. [CrossRef]
ANSYS, 2010, “ Ansys 13.0 Help,” ANSYS, Canonsburg, PA.
Tu, J. , Yeoh, G. H. , and Liu, C. , 2012, Computational Fluid Dynamics: A Practical Approach, Butterworth-Heinemann, Oxford, UK.
Irvine, T. F. , Jr., and Capobianchi, M. , 2005, “ Non-Newtonian Fluids—Heat Transfer,” The CRC Handbook of Mechanical Engineering, 2nd ed., F. Kreith and Y. Goswami, eds., CRC Press, Boca Raton, FL, pp. 4–269. [PubMed] [PubMed]
Leung, C. W. , Probert, S. D. , and Shilston, M. J. , 1985, “ Heat Exchanger Design: Optimal Uniform Separation Between Rectangular Fins Protruding From a Vertical Rectangular Base,” Appl. Energy, 19(4), pp. 287–299. [CrossRef]
Senapati, J. R. , Dash, S. K. , and Roy, S. , 2017, “ Numerical Investigation of Natural Convection Heat Transfer From Vertical Cylinder With Annular Fins,” Int. J. Therm. Sci., 111, pp. 146–159. [CrossRef]


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Fig. 1

Schematic of the problem

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Fig. 2

Comparison of Nu predicted by present simulations (l/L = 0) with existing correlations [4,8] for a bare vertical flat plate in power-law fluids

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Fig. 3

Grid independence test: 0 indicates grid with no refinement; 1, 2, 3 indicate levels of refinement

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Fig. 4

Comparison of Nu as a function of l/L for different values of the dimensionless interfin spacing, S/L, at n = 0.3, 0.5, 1.0, and 1.3

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Fig. 5

Vector plots of the dimensionless velocity, U/Vc, for different fin lengths at S/L = 0.13 n = 0.5

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Fig. 6

Comparison of Nu as a function of l/L for different values of the power-law index, n, at S/L = 0.09, 0.13, 0.17, and 0.26

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Fig. 7

Contours of the dimensionless viscosity ηND in the flow field close to the fins for l/L = 0.17 and 0.02; each at S/L = 0.13

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Fig. 8

Variation of Nu with the power-law index, n, at S/L = 0.09 and 0.13

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Fig. 9

Comparison of Q/Q0 as a function of l/L for different values of n, plotted at S/L = 0.09, 0.13, 0.17, and 0.26



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