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Research Papers

# Turbulence Modeling of Forced Convection Heat Transfer in Two-Dimensional Ribbed Channels

[+] Author and Article Information

Thermal Processing Laboratory (TPL), Department of Mechanical Engineering, McMaster University, Hamilton, ON, L8S 4L7, Canada

M. S. Hamed1

Thermal Processing Laboratory (TPL), Department of Mechanical Engineering, McMaster University, Hamilton, ON, L8S 4L7, Canadahamedm@mcmaster.ca

1

Corresponding author.

J. Electron. Packag 130(3), 031011 (Aug 05, 2008) (17 pages) doi:10.1115/1.2912182 History: Received February 09, 2007; Revised July 07, 2007; Published August 05, 2008

## Abstract

Although the problem of 2D ribbed channels has been studied heavily in the literature as a benchmark or basic case for cooling of electronic packing, there is still a contradiction in the literature about the suitable turbulence model that should be used in such a problem. The accuracy of the computational predictions of heat transfer rates depends mostly on the choice of the proper turbulence model that is capable of capturing the physics of the problem, and on the corresponding wall treatment. The main objective of this work is to identify the proper turbulence model to be used in thermal analysis of electronic systems. A number of available turbulence models, namely, the standard $k-ε$, the renormalization group $k-ε$, the shear stress transport (SST), the $k-ω$, and the Reynolds stress models, have been investigated. The selection of the most appropriate turbulence model has been based upon comparisons with both direct numerical simulations (DNSs) and experimental results of other works. Based on such comparisons, the SST turbulence model has been found to produce results in very good agreement with the DNS and experimental results and hence it is recommended as an appropriate turbulence model for thermal analysis of electronic packaging.

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## Figures

Figure 1

Major causes of electronic failures (1)

Figure 2

Configuration used for comparison with DNS results

Figure 3

A typical mesh used in the current study

Figure 4

Typical y+ values along the ribbed wall

Figure 5

Streamlines of mean velocity (e∕H=0.1, w∕H=0.1, and s∕H=0.3): (a) DNS (9), (b) k-ε, (c) RNG k-ε, (d) SST, and (e) ω-RSM turbulent models

Figure 6

Streamlines of mean velocity (e∕H=0.05, w∕H=0.1, and s∕H=0.3): (a) DNS (9), (b) k-ε, (c) RNG k-ε, (d) SST, and (e) ω-RSM turbulent models

Figure 7

Streamlines of mean velocity (e∕H=0.025, w∕H=0.1, and s∕H=0.3): (a) DNS (9), (b) k-ε, (c) RNG k-ε, (d) SST, and (e) ω-RSM turbulent models

Figure 8

Contours of mean temperature (e∕H=0.1, w∕H=0.1, and s∕H=0.3): (a) DNS (9), (b) k-ε, (c) RNG k-ε, (d) SST, and (e) ω-RSM turbulent models

Figure 9

Contours of mean temperature (e∕H=0.05, w∕H=0.1, and s∕H=0.3): (a) DNS (9), (b) k-ε (c) RNG k-ε, (d) SST, and (e) ω-RSM turbulent models

Figure 10

Contours of mean temperature (e∕H=0.025, w∕H=0.1, and s∕H=0.3): (a) DNS (9), (b) k-ε, (c) RNG k-ε, (d) SST, and (e) ω-RSM turbulent models

Figure 11

Velocity profiles at the middle of channel (x=36mm): (a) DNS (9), (b) SST model, (c) Case 1 (e∕H=0.1), (d) Case 2 (e∕H=0.05), (e) Case 3 (e∕H=0.025), and (f) Case 4 (e∕H=0)

Figure 12

Turbulent energy profile at the middle of channel (x=36mm): (a) DNS (9), (b) SST model (c) Case 1 (e∕H=0.1), (d) Case 2 (e∕H=0.05), (e) Case 3 (e∕H=0.025), and (f) Case 4 (e∕H=0)

Figure 13

Reynolds shear stress profile at the middle of channel (x=36mm): (a) DNS (9), (b) SST model (c) Case 1 (e∕H=0.1), (d) Case 2 (e∕H=0.05), (e) Case 3 (e∕H=0.025), and (f) Case 4 (e∕H=0)

Figure 14

Mean temperature profile at the middle of channel (x=36mm): (a) DNS (9), (b) SST model, (c) Case 1 (e∕H=0.1), (d) Case 2 (e∕H=0.05), (e) Case 3 (e∕H=0.025), and (f) Case 4 (e∕H=0)

Figure 15

Turbulent heat flux profile at the middle of channel (x=36mm): (a) DNS (9), (b) SST model, (c) Case 1 (e∕H=0.1), (d) Case 2 (e∕H=0.05), (e) Case 3 (e∕H=0.025), and (f) Case 4 (e∕H=0)

Figure 16

The geometry used in the comparison with the experimental data (17)

Figure 17

Wall heat transfer coefficient compared with experimental data (17)

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