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RESEARCH PAPERS: Micro/Nanoscale Heat Transfer

# Nusselt Number and Friction Factor of Staggered Arrays of Low Aspect Ratio Micropin-Fins Under Cross Flow for Water as Fluid

[+] Author and Article Information
Ravi S. Prasher

Intel Corporation, CH5-157, 5000 W. Chandler Blvd., Chandler, AZ 85226 and Department of Mechanical and Aerospace Engineering,  Arizona State University, Tempe, AZ 85287ravi.s.prasher@intel.com

John Dirner, Je-Young Chang, Alan Myers, David Chau, Dongming He, Suzana Prstic

Intel Corporation, CH5-157, 5000 W. Chandler Blvd., Chandler, AZ 85226

J. Heat Transfer 129(2), 141-153 (Apr 13, 2006) (13 pages) doi:10.1115/1.2402179 History: Received August 30, 2005; Revised April 13, 2006

## Abstract

Experimental results of the thermal and hydraulic performances of silicon-based, low aspect ratio micropin-fin cold plates under cross flow conditions are reported. The pins were both circular and square in shape with dimensions (diameter for circular and sides for square) ranging from $50μm$ to $150μm$. The test chip contained 20 integral $75×75μm$ temperature sensors which were used to determine the thermal resistance $(KW−1)$ of the cold plates. The experiments were conducted using water, over a Reynolds number (Re) ranging from 40 to 1000. The data show that the average Nusselt number (Nu) based on the fin diameter varies as $Re0.84$ for $Re<100$ and as $Re0.73$ for $Re>100$, where Re is the Reynolds number based on maximum velocity and the fin diameter. Analysis of the Fanning friction factor $(f)$ data shows that $f$ varies as $Re−1.35$ for $Re<100$ and as $Re−0.1$ for $Re>100$.

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## Figures

Figure 1

Front view of micro-pin fin cold plate

Figure 2

Top view of micropin fin cold plate

Figure 3

Locations of heaters and thermal sensors

Figure 4

SEM picture of RP4 micropin-fin cold plate. (a) Oblique view (b) side view.

Figure 5

Schematic of the experimental test setup

Figure 6

Measured pressure drop versus flow rate for all micropin-fin arrays

Figure 7

Friction factor based on channel approach versus Reynolds number based on hydraulic diameter of the channel

Figure 8

Friction factor based on pin fin approach versus Reynolds number based on pin diameter

Figure 9

Measured thermal resistance versus flow rate for different micropin-fin arrays

Figure 10

Schematic of three-dimensional conduction model to estimate error in assuming one-dimensional heat transfer from the source to the cold plate (assuming h0=2.5×104W∕m2K and h1=1×103W∕m2K)

Figure 11

Nusselt number based on channel approach versus Reynolds number based on hydraulic diameter of the channel

Figure 12

Thermal performance parameter (Eq. 10) versus Reynolds number based on hydraulic diameter of the channel

Figure 13

Nusselt number based on pin fin approach versus Reynolds number based on pin diameter

Figure 14

Ratio of friction factor obtained from experiments and the correlation by Jacob (19) (Eq. 15)

Figure 15

Ratio of friction factor obtained from experiments and the correlations by Armstrong and Winstanley (22) and Damerow (23) (Eq. 16)

Figure 16

Ratio of friction factor obtained from experiments and the correlation by Short (25) (Eq. 17)

Figure 17

Ratio of friction factor obtained from experiments and the correlation (Eq. 19) developed by fitting all data

Figure 18

Comparison between the friction factor obtained from experiments and the correlation (Eq. 19) developed by fitting the data for Re<100 and Re>100 separately

Figure 19

Comparison between the proposed correlation (see text) and data from square pin fin array for friction factor

Figure 20

Ratio of the Nusselt number obtained from experiments and that predicted from long and short fin correlation from the previous literature

Figure 21

Ratio of the Nusselt number obtained from experiments and that predicted from the correlation by Short (39) (Eq. (3029))

Figure 22

Comparison between the Nusselt number obtained from experiments and the correlation developed by fitting the data for Re<100 and Re>100 separately

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