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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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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