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Research Papers: Heat and Mass Transfer

Effects of Averaging the Heat Transfer Coefficient on Predicted Material Temperature and Its Gradient

[+] Author and Article Information
Chien-Shing Lee

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907
e-mail: cslee@purdue.edu

Tom I-P. Shih

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907
e-mail: tomshih@purdue.edu

Kenneth Mark Bryden

Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: kmbryden@iastate.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 8, 2015; final manuscript received August 26, 2016; published online October 26, 2016. Editor: Dr. Portonovo S. Ayyaswamy.

J. Heat Transfer 139(2), 022002 (Oct 26, 2016) (14 pages) Paper No: HT-15-1586; doi: 10.1115/1.4034698 History: Received September 08, 2015; Revised August 26, 2016

The heat transfer coefficient (HTC) is often averaged spatially when designing heat exchangers. Since the HTC could vary appreciably about a heat transfer enhancement feature such as a pin fin or a rib, it is of interest to understand the effects of averaging the HTC on design. This computational study examines those effects via a unit problem—a flat plate of thickness H and length L, where L represents the distance between pin-fins or ribs. This flat plate is heated on one side, and cooled on the other. Variable HTC is imposed on the cooled side—a higher HTC (hH) over LH and a lower HTC (hL) over LL = L − LH. For this unit problem, the following parameters were studied: abrupt versus gradual transition between hH and hL, hH/hL, LH/L, and H/L. Results obtained show that if the averaged HTC is used, then the maximum temperature in the plate and the maximum temperature gradient in the plate can be severely underpredicted. The maximum temperature and the maximum temperature gradient can be underpredicted by as much as 36.3% and 542%, respectively, if the Biot number is less than 0.1 and as much as 13.0% and 570% if the Biot number is between 0.25 and 0.4. A reduced-order model was developed to estimate the underpredicted maximum temperature.

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Topics: Temperature
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Figures

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Fig. 1

Schematic of the problem studied with abrupt or step change in the HTC

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Fig. 2

Variations in the HTC studied: (a) abrupt or step change and (b) gradual change

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Fig. 3

Temperature and heat flux on the heated and cooled sides of the plate with abrupt change in HTC and imposed heat flux on the heated side: (a) H/L = 0.05 and (b) H/L = 0.25

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Fig. 4

Temperature and heat flux on the heated and cooled sides of the plate with abrupt change in HTC and imposed convective environment on the heated side: (a) H/L = 0.05 and (b) H/L = 0.25

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Fig. 5

∅  as a function of LH/L with hH/hL = 8, abrupt change in HTC, and H/L = 0.05

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Fig. 6

Maximum ∅max as a function of LH/L and hH/hL with abrupt change in HTC: (a) H/L = 0.05 and (b) H/L = 0.25

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Fig. 7

λ  as a function of LH/L for hH/hL = 8 with abrupt change in HTC and H/L = 0.05

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Fig. 8

Maximum λ as a function of LH/L and hH/hL with abrupt change in HTC: (a) H/L = 0.05 and (b) H/L = 0.25

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Fig. 9

Biot number as a function of LH/L for H/L = 0.05 and 0.5 with convective environment imposed on the hot-gas side

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Fig. 10

Temperature on the heated and cooled sides of the plate as a function of H/L with abrupt change in HTC. (a) Imposed heat flux on the heated side and (b) imposed convective environment on the heated side.

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Fig. 11

Maximum ∅max as a function of H/L with LH/L = 0.1 and hH/hL = 8

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Fig. 12

Heat flux on the cooled side of the plate with abrupt and gradual change in HTC

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Fig. 13

Temperature on the heated and cooled sides of the plate with abrupt and gradual change in HTC. (a) Imposed heat flux on the heated side and (b) imposed convective environment on the heated side.

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