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Research Papers: Heat Transfer Enhancement

Thermal Characteristics in a Curved Rectangular Channel With Variable Cross-Sectional Area

[+] Author and Article Information
Avijit Bhunia, C. L. Chen

 Teledyne Scientific Company, 1049 Camino Dos Rios, MC A10, Thousand Oaks, CA 91360abhunia@teledyne.com

J. Heat Transfer 133(12), 121901 (Oct 03, 2011) (10 pages) doi:10.1115/1.4004390 History: Received December 31, 2009; Revised April 21, 2011; Published October 03, 2011; Online October 03, 2011

Heat transfer due to steady, laminar air flow through a curved rectangular channel with a variable cross-sectional (c/s) area is investigated computationally. Such a flow passage is formed between two fin walls of a curved fin heat sink with a 90 deg bend, used in avionics cooling. Simulations are carried out for two different configurations: (a) a variable c/s area curved channel with inlet and outlet sections (entry and exit lengths) that are straight and constant c/s area—termed as the long channel and (b) a variable c/s area curved channel with no entry and exit lengths—termed as the short channel. Multiple secondary flow patterns develop in the curved section of the channel, which in conjunction with the bulk axial flow, lead to the formation of multiple vortices and separation bubbles. The complex 3-D flow structures, as well as the variable c/s area of the curved channel (diverging–converging) significantly alter the heat transfer characteristics, compared to the straight fin heat sink. Secondary flow strengthens with increasing axial (bulk) flow velocity, or Dean number in dimensionless form. This in turn improves heat transfer from all walls, particularly, the outer curvature (concave) wall and the heat sink base. At the highest Dean number condition, the local heat transfer coefficient at certain locations of the outer curvature wall is augmented by as much as 3.5 times, compared to the straight fin walls. The overall channel average heat transfer coefficient is improved by about 40% for the long channels, and about 10% for the short ones. However, the heat transfer enhancement is associated with a penalty of higher pressure drop, compared to the straight channels. To quantify the effectiveness of thermal performance enhancement a system Figure of Merit (FOM) is defined. A greater than unity FOM value is observed for all curved channel geometries and flow rate conditions. This indicates that heat transfer enhancement in the variable c/s area curved channel outweighs the penalty of additional pressure drop, compared to a straight channel of similar length.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

A schematic of curved fin heat sink. Representative air flow paths in two passages are shown by red arrows. The flow cross-section (c/s) area in the curved section of each flow passage varies along the length.

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Figure 2

Schematic of an individual flow passage between two fins: the long channel shown in Fig. 1 and the numerical simulation

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Figure 3

Schematics of various 3-D flow patterns in the curved section (90 deg bend) of a long, VACC as observed at the highest axial flow velocity condition [3]. Re = 2017 and De = 1008. AR = 2.3, CR = 5.6, Lav /Dh  = 39.6, Lentry /Dh  = 16.1, and Lexit /Dh  = 16.1. Only the top half of the channel is shown.

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Figure 4

Dimensionless temperature contours at various angular positions along a 90 deg bend of a long, VACC(diverging–converging). Re = 2017, and De = 1008, based on uniform flow velocity (Vi ) and hydraulic diameter (Dh ) at channel inlet and properties at average temperature [Tav  = (Ti  + Tw )/2]. Lav /Dh  = 39.6, Lentry /Dh  = 16.1, and Lexit /Dh  = 16.1. AR = 2.3, CR = 5.6. (a) Angular position 0 deg or curvature inlet; (b) angular position 22.5 deg; (c) angular position 45 deg; (d) angular position 67.5 deg; and (e) angular position 90 deg, outlet from the curved portion of the channel or beginning of the straight constant c/s area exit channel.

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Figure 5

Variation of spanwise averaged local Nusselt number (Nuloc ) at various dimensionless axial locations along channel walls: ICW and OCW of VACC (diverging–converging), and side walls for a CASC. (a) Long channel with constant c/s area, straight entry and exit lengths (Lentry and Lexit ); (b) short channel with no entry and exit length (Lentry  = Lexit  = 0). Lw  = LICW for ICW of VACC, Lw  = LOCW for OCW of VACC, and Lw  = Lav for side walls of CASC. Lav is the same for VACC and CASC. Re = 2017, and De = 1008, based on uniform flow velocity (Vi ) and hydraulic diameter (Dh ) at channel inlet and properties at average temperature [Tav  = (Ti  + Tw )/2]. Lav /Dh  = 39.6, Lentry /Dh  = 16.1, and Lexit /Dh  = 16.1. AR = 2.3, CR = 5.6.

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Figure 6

Variation of spanwise averaged local Nusselt number (Nuloc ) with dimensionless axial locations (l+ ) or inverse of Graetz number (1/Gz) along the OCW. Re and De values are based on uniform flow velocity (Vi ) and hydraulic diameter (Dh ) at channel inlet and properties at average temperature [Tav  = (Ti  + Tw )/2]. Lav /Dh  = 39.6, Lentry /Dh  = 16.1, and Lexit /Dh  = 16.1. AR = 2.3, CR = 5.6. Inset A: Schematic of base vortex for Re < 366. Inset B: Schematic of base and split base vortex for Re > 366.

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Figure 7

Variation of wall averaged Nusselt number (Nuw ) with dimensionless axial flow velocity (Reynolds number) at various channel walls of a long, VACC and CASC. Re values are based on uniform flow velocity (Vi ) and hydraulic diameter (Dh ) at channel inlet, and properties at average temperature [Tav  = (Ti  + Tw )/2]. Lav /Dh  = 39.6 for both VACC and CASC. For VACC − Lentry /Dh  = 16.1 and Lexit /Dh  = 16.1. AR = 2.3, CR = 5.6.

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Figure 8

Variation of heat transfer enhancement in a CC compared to a CASC with axial flow velocity (Reynolds number Re in dimensionless form). Heat transfer enhancement is characterized as the ratio of average Nusselt number in the curved channel (Nuav, CC ) to that in the CASC (Nuav, CASC ). Two types of curved channel considered: VACC and CACC. Re values are based on uniform flow velocity (Vi ) and hydraulic diameter (Dh ) at channel inlet and properties at average temperature [Tav  = (Ti  + Tw )/2]. Curved channels AR = 2.3, CR = 5.6. Long channels (VACC, CACC, and CASC) average length Lav /Dh  = 39.6. Long VACC and CACC Lentry /Dh  = 16.1 and Lexit /Dh  = 16.1. Short channels (VACC, CACC, and CASC) average length Lav /Dh  = Lcurv /Dh  = 6.8, no entry or exit length.

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Figure 9

Variation of system FOM for heat transfer enhancement in a CC compared to a CASC with axial flow velocity (Reynolds number Re in dimensionless form). Heat transfer enhancement is characterized as the ratio of average Nusselt number in the curved channel (Nuav, CC ) to that in the CASC (Nuav, CASC ). Pressure drop increase is defined as the ratio of dimensionless pressure drop in the curved channel (,fCC ) to that in the CASC (fCASC ). Two types of curved channel considered: VACC and CACC. Re values are based on uniform flow velocity (Vi ) and hydraulic diameter (Dh ) at channel inlet and properties at average temperature [Tav  = (Ti  + Tw )/2]. Curved channels AR = 2.3, CR = 5.6. Long channels (VACC, CACC, and CASC) average length Lav /Dh  = 39.6. Long VACC and CACC Lentry /Dh  = 16.1 and Lexit /Dh  = 16.1. Short channels (VACC, CACC, and CASC) average length Lav /Dh  = Lcurv /Dh  = 6.8, no entry or exit length.

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