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Research Papers

The Effectiveness of the Unit Cell Method in Numerically Modeling and Designing Liquid Cooled Heatsinks

[+] Author and Article Information
Ali C. Kheirabadi

Department of Mechanical Engineering,
Dalhousie University,
Halifax, NS B2V 2W1, Canada
e-mail: ali.cherom.k@dal.ca

Dominic Groulx

Department of Mechanical Engineering,
Dalhousie University,
Halifax, NS B2V 2W1, Canada
e-mail: dominic.groulx@dal.ca

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Thermal Science and Engineering Applications. Manuscript received July 3, 2018; final manuscript received March 9, 2019; published online May 13, 2019. Assoc. Editor: Samuel Sami.

J. Thermal Sci. Eng. Appl 11(6), 061007 (May 13, 2019) (11 pages) Paper No: TSEA-18-1343; doi: 10.1115/1.4043185 History: Received July 03, 2018; Accepted March 10, 2019

This study compares two numerical strategies for modeling flow and heat transfer through mini- and microchannel heatsinks, the unit cell approximation, and the full 3D model, with the objective of validating the former approach. Conjugate heat transfer and laminar flow through a 2 × 2 cm2 copper–water heatsink are modeled using the finite element package COMSOL Multiphysics 5.0. Parametric studies showed that as the heatsink channels’ widths were reduced, and the total number of channels increased, temperature and pressure predictions from both models converged to similar values. Relative differences as low as 5.4% and 1.6% were attained at a channel width of 0.25 mm for maximum wall temperature and channel pressure drop, respectively. Due to its computational efficiency and tendency to conservatively overpredict temperatures relative to the full 3D method, the unit cell approximation is recommended for parametric design of heatsinks with channels’ widths smaller than 0.5 mm, although this condition only holds for the given heatsink design. The unit cell method is then used to design an optimal heatsink for server liquid cooling applications. The heatsink has been fabricated and tested experimentally, and its thermal performance is compared with numerical predictions. The unit cell method underestimated the maximum wall temperature relative to experimental results by 3.0–14.5% as the flowrate rose from 0.3 to 1.5 gal/min (1.1–5.7 l/min).

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Figures

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Fig. 1

Schematic of unit cell geometry for numerically modeling heatsink

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Fig. 2

Schematic of boundary conditions imposed upon the heatsink unit cell model

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Fig. 3

Schematic of the full 3D model geometry and imposed boundary conditions

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Fig. 4

Mesh layout for the unit cell numerical model

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Fig. 5

Distribution of geometric mesh elements

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Fig. 6

Mesh convergence study along channel width, Hch = 4 mm, Lch = 2 cm, Tin = 60 °C, qtotal = 300 W, Qhs = 1 l/min, RTIM′′ = 0.1 K cm2/W

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Fig. 7

Mesh layout for the full 3D numerical model

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Fig. 8

Velocity distribution across heatsinks of varying channel widths

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Fig. 9

Top view velocity profile with varying channel size: (a) 2 mm, (b) 1 mm, (c) 0.5 mm, and (d) 0.25 mm

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Fig. 10

Top view base temperature profile with varying channel size: (a) 2 mm, (b) 1 mm, (c) 0.5 mm, and (d) 0.25 mm

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Fig. 11

Comparison of full 3D and unit cell models: (a) maximum wall temperature and (b) pressure drop

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Fig. 12

Parametric study of heatsink channel width and height, Lch = 2 cm, Tin = 60 °C, qtotal = 300 W, Qhs = 1 l/min, RTIM′′ = 0.1 K cm2/W

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Fig. 13

Heat transfer coefficient of the heatsink for different channel widths and heights, Lch = 2 cm, Tin = 60 °C, qtotal = 300 W, Qin = 1 l/min, RTIM′′ = 0.1 K cm2/W

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Fig. 14

Schematic of experimental test section in collapsed and exploded views

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Fig. 15

Comparison of numerically and experimentally [27] derived wall temperatures, qtotal = 330.4 W, Wch = 0.5 mm, Hch = 2.3 mm, Lch = 2 cm, RTIM′′ = 0.1 K cm2/W

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