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RESEARCH PAPERS: Forced Convection

# Effects Of Dimple Depth on Channel Nusselt Numbers and Friction Factors

[+] Author and Article Information
N. K. Burgess, P. M. Ligrani

Convective Heat Transfer Laboratory, Department of Mechanical Engineering,  University of Utah, 50 S. Central Campus Drive, Salt Lake City, UT 84112-9208

J. Heat Transfer 127(8), 839-847 (Oct 06, 2004) (9 pages) doi:10.1115/1.1994880 History: Received December 01, 2003; Revised October 06, 2004

## Abstract

Experimental results, measured on dimpled test surfaces placed on one wall of different rectangular channels, are given for a ratio of air inlet stagnation temperature to surface temperature of approximately 0.94, and Reynolds numbers based on channel height from 9940 to 74,800. The data presented include friction factors, local Nusselt numbers, spatially averaged Nusselt numbers, and globally averaged Nusselt numbers. The ratios of dimple depth to dimple print diameter $δ∕D$ are 0.1, 0.2, and 0.3 to provide information on the influences of dimple depth. The ratio of channel height to dimple print diameter is 1.00. At all Reynolds numbers considered, local spatially resolved and spatially averaged Nusselt number augmentations increase as dimple depth increases (and all other experimental and geometric parameters are held approximately constant). These are attributed to (i) increases in the strengths and intensity of vortices and associated secondary flows ejected from the dimples, as well as (ii) increases in the magnitudes of three-dimensional turbulence production and turbulence transport. The effects of these phenomena are especially apparent in local Nusselt number ratio distributions measured just inside of the dimples and just downstream of the downstream edges of the dimples. Data are also presented to illustrate the effects of Reynolds number and streamwise development for $δ∕D=0.1$ dimples. Significant local Nusselt number ratio variations are observed at different streamwise locations, whereas variations with the Reynolds number are mostly apparent on flat surfaces just downstream of individual dimples.

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## Figures

Figure 1

Schematic diagrams of the top and bottom dimpled test surfaces. All dimensions are given in centimeters.

Figure 2

Schematic diagrams of individual dimple geometry details. All dimensions are given in centimeters.

Figure 3

Local Nusselt number ratio data from a channel with shallow dimples on one channel surface and heating on one channel surface, for δ∕D=0.1, H∕D=1, Tu=0.033, and ReH=17,800

Figure 4

Local Nusselt number ratios along the test surface spanwise centerline, Z∕D=0.0, for different Reynolds numbers ReH from a channel with shallow dimples on one channel surface and heating on one channel surface, for δ∕D=0.1, H∕D=1, and Tu=0.033

Figure 5

Local Nusselt number ratios along a line of constant X∕D=23.18 for different Reynolds numbers ReH from a channel with shallow dimples on one channel surface, and heating on one channel surface, for δ∕D=0.1, H∕D=1, and Tu=0.033

Figure 6

Nusselt number ratios spanwise-averaged over one period of dimple surface geometry, for different Reynolds numbers ReH from a channel with shallow dimples on one channel surface and heating on one channel surface, for δ∕D=0.1, H∕D=0.1, and Tu=0.033

Figure 7

Nusselt number ratios streamwise averaged over one period of dimple surface geometry for different Reynolds numbers ReH from a channel with shallow dimples on one channel surface and heating on one channel surface, for δ∕D=0.1, H∕D=1, and Tu=0.033

Figure 8

Nusselt number ratios along the test surface spanwise centerline, Z∕D=0.0, measured at upstream and downstream locations shown in Fig. 1, from a channel with shallow dimples on one channel surface and heating on one channel surface, for δ∕D=0.1, H∕D=1, Tu=0.033, and ReH=49,100

Figure 9

Nusselt number ratios spanwise averaged over one period of dimple surface geometry, measured at upstream and downstream locations shown in Fig. 1, from a channel with shallow dimples on one channel surface and heating on one channel surface, for δ∕D=0.1, H∕D=1, Tu=0.033, and ReH=49,100

Figure 10

Local dimpled channel Nusselt number ratios as dependent on X∕D along the test surface spanwise centerline at Z∕D=0. Data are given for (i) δ∕D=0.1, H∕D=1, and ReH=17,800 from the present study; (ii); δ∕D=0.2, H∕D=1, and ReH=20,000 from Mahmood (1); and (iii) δ∕D=0.3, H∕D=1, and ReH=17,200 from Burgess (2).

Figure 11

Nusselt number ratios spanwise-averaged over one period of dimple surface geometry, as dependent on X∕D. Data are given for (i) δ∕D=0.1, H∕D=1, and ReH=17,800 from the present study; (ii) δ∕D=0.2, H∕D=1, and ReH=20,000 from Mahmood (1); and (iii) δ∕D=0.3, H∕D=1, and ReH=17,200 from Burgess (2).

Figure 12

Globally averaged dimpled channel Nusselt number ratios as dependent on Reynolds number ReH for δ∕D=0.1 and H∕D=1 from the present study. Results from the present study are compared to results from Burgess (2), Mahmood (1), Chyu (12), and Moon (14) for different values of δ∕D, the ratio of dimple depth to dimple print diameter.

Figure 13

Dimpled channel friction factor ratios as dependent on Reynolds number ReH for δ∕D=0.1 and H∕D=1 from the present study. Results from the present study are compared to results from Burgess (2), Mahmood (1), Chyu (12), and Moon (14) for different values of δ∕D, the ratio of dimple depth to dimple print diameter. Symbols are defined in Fig. 1.

Figure 14

Globally averaged dimpled-channel thermal performance parameters as dependent on Reynolds number ReH for δ∕D=0.1 and H∕D=1 from the present study. Results from the present study are compared to results from Burgess (2), Mahmood (1), Chyu (12), and Moon (14) for different values of δ∕D, the ratio of dimple depth to dimple print diameter. Symbols are defined in Fig. 1.

Figure 15

Globally averaged dimpled-channel thermal performance parameters as dependent on Reynolds number ReH for δ∕D=0.1 and H∕D=1 from the present study. Results from the present study are compared to results from Burgess (2), Mahmood (1), Chyu (12), and Moon (14) for different values of δ∕D, the ratio of dimple depth to dimple print diameter. Symbols are defined in Fig. 1.

Figure 16

Globally averaged dimpled-channel Nusselt number ratios as dependent on the ratio of dimple depth to dimple print diameter δ∕D, including comparisons to a correlation equation, for δ∕D=0.1 and H∕D=1 from the present study for δ∕D=0.2 from Mahmood (1), and for δ∕D=0.3 from Burgess (2). Results from Chyu (12) and Moon (14) are included for comparison.

Figure 17

Dimpled channel friction factor ratios as dependent on Reynolds number ReH, including comparisons to correlation equations for δ∕D=0.1 and H∕D=1 from the present study, for δ∕D=0.2 from Mahmood (1), and for δ∕D=0.3 from Burgess (2). Results from Chyu (12) and Moon (14) are included for comparison. Symbols are defined in Fig. 1.

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