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RESEARCH PAPERS

# Numerical Simulation of Laminar Flow and Heat Transfer Inside a Microchannel With One Dimpled Surface

[+] Author and Article Information
X. J. Wei

IBM Systems and Technology, 2070 Route 52, Hopewell Junction, NY 12533 and G W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332xwei@us.ibm.com

Y. K. Joshi

G W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

P. M. Ligrani

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, England, UK

J. Electron. Packag 129(1), 63-70 (Mar 02, 2006) (8 pages) doi:10.1115/1.2429711 History: Received November 01, 2005; Revised March 02, 2006

## Abstract

Steady, laminar flow and heat transfer, inside a rectangular microchannel with a dimpled bottom surface, are numerically studied. The microchannel is $50×10−6m$$(50μm)$ deep and $200×10−6m$$(200μm)$ wide. The dimples are placed in a single row along the bottom wall with a pitch of $150×10−6m$$(150μm)$. The dimple depth is $20×10−6m$$(20μm)$, and the dimple footprint diameter is $98×10−6m$$(98μm)$. Fully developed periodic velocity and temperature boundary conditions are used at the inlet and outlet of one unit cell of the dimpled microchannel. Key flow structures such as recirculating flow and secondary flow patterns and their development along the flow directions are identified. The impact of these flow structures on the heat transfer is described. Heat transfer augmentations (relative to a channel with smooth walls) are present both on the bottom-dimpled surface, and on the sidewalls of the channel. The pressure drops in the laminar-microscale flow are either equivalent to, or less than, values produced in smooth channels with no dimples. It is concluded that dimples, proven to be an effective passive heat transfer augmentation for macroscale channels, can also be used to enhance heat transfer inside microchannels.

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## Figures

Figure 16

Thermal performance parameter for different Reynolds numbers, η=(Str∕Sts)∕(fr∕fs). The microscale-laminar results from the present study are compared with macroscale turbulent results from Mahmood and Ligrani (9) for a channel with a staggered array of macroscale dimples with a ratio of dimple depth to dimple print diameter of 0.2, Hc∕D=0.5, and D=5.08cm.

Figure 15

Normalized average Nusselt number and friction factor as dependent upon Reynolds number. The microscale-laminar results from the present study are compared with macroscale turbulent results from Mahmood (9) for a channel with a staggered array of macroscale dimples with a ratio of dimple depth to dimple print diameter of 0.2, Hc∕D=0.5, and D=5.08cm.

Figure 14

Normalized Nusselt number for individual walls for ReDh=274 and laminar microscale dimples. The numerically predicted value is normalized to the average Nusselt number for corresponding wall of a rectangular channel with smooth walls with same boundary conditions (constant heat flux) and aspect ratio (0.25).

Figure 13

Normalized spanwise-averaged Nusselt numbers over all walls for ReDh=274 and laminar microscale dimples. The numerically predicted value is normalized to the average Nusselt number for rectangular channels with smooth walls with same boundary conditions (constant heat flux) and aspect ratio (0.25).

Figure 12

Plan view of laminar flow streamlines generated from single spherical dimple for a Reynolds number based on dimple footprint diameter of 6710 from Khalatov (12). Flow is moving from left to right with dye markers originating upstream of the dimple.

Figure 11

Normalized streamwise vorticity ωx* contour at the cross section of X∕L=0.7 (in plane components) for ReDh=274 and laminar microscale dimples. Vorticity ωx is normalized to ratio of mean velocity Um to hydraulic diameter Dh.

Figure 10

Normalized streamwise vorticity ωx* contour at the cross section of X∕L=0.63 (in plane components) for ReDh=274 and laminar microscale dimples. Vorticity ωx is normalized to ratio of mean velocity Um to hydraulic diameter Dh.

Figure 9

Normalized streamwise vorticity ωx* contour at the cross section of X∕L=0.57 (in plane components) for ReDh=274 and laminar microscale dimples. Vorticity ωx is normalized to ratio of mean velocity Um to hydraulic diameter Dh.

Figure 8

Normalized streamwise vorticity ωx* contour at the cross section of X∕L=0.3 (in plane components) for ReDh=274 and laminar microscale dimples. Vorticity ωx is normalized to ratio of mean velocity Um to hydraulic diameter Dh.

Figure 7

Velocity vectors at the cross section of X∕L=0.7 (in plane components) for ReDh=274 and laminar microscale dimples. The reference vector length represents 1m∕s.

Figure 6

Velocity vectors at the cross section of X∕L=0.63 (in plane components) for ReDh=274 and laminar microscale dimples. The reference vector length represents 1m∕s.

Figure 5

Velocity vectors at the cross section of X∕L=0.57 (in plane components) for ReDh=274 and laminar microscale dimples. The reference vector length represents 1m∕s.

Figure 4

Velocity vector at the cross section of X∕L=0.3 (in plane components) for ReDh=274 and laminar microscale dimples. The reference vector length represents 1m∕s.

Figure 3

Velocity vectors at the center plane Z=100μm for ReDh=274 and laminar microscale dimples. The reference vector length represents 10m∕s.

Figure 2

(a) Overall channel and dimple arrangement, and (b) schematic of the computation domain showing that only half of the dimpled micro-channel is simulated. All dimensions in μm.

Figure 1

Thermal performance parameter as dependent upon friction factor ratio for passive heat transfer enhancement techniques from Ligrani (1)

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