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Research Papers: Electronic Cooling

# Measurement of Entropy Generation in Microscale Thermal-Fluid Systems

[+] Author and Article Information

Department of Mechanical and Mechatronics Engineering, Microelectronics Heat Transfer Laboratory, University of Waterloo, Waterloo, ON, N2L 3G1, Canadamsaffari@engmail.uwaterloo.ca

Richard Culham

Department of Mechanical and Mechatronics Engineering, Microelectronics Heat Transfer Laboratory, University of Waterloo, Waterloo, ON, N2L 3G1, Canadarix@mhtlab.uwaterloo.ca

J. Heat Transfer 132(12), 121401 (Sep 17, 2010) (9 pages) doi:10.1115/1.4002026 History: Received January 01, 2009; Revised May 22, 2010; Published September 17, 2010; Online September 17, 2010

## Abstract

A new nonintrusive and whole field method for the measurement of entropy generation in microscale thermal-fluid devices is presented. The rate of entropy generation is a measure of the thermodynamic losses or irreversibilities associated with viscous effects and heat transfer in thermal-fluid systems. This method provides the entropy generation distribution in the device, thus enabling the designers to find and modify the areas producing high energy losses characterized by large entropy production rates. The entropy generation map is obtained by postprocessing the velocity and temperature distribution data, measured by micro particle image velocimetry and laser induced fluorescence methods, respectively. The velocity and temperature measurements lead to the frictional and thermal terms of entropy generation. One main application of this method is optimizing the efficiency of microchannel heatsinks, used in cooling of electronic devices. The minimum amount of entropy generation determines the optimum design parameters of heatsinks, leading to highest heat removal rates and at the same time, the lowest pressure drop across the heatsink. To show the capability of this technique, the entropy generation field in the transition region between a $100 μm$ wide and a $200 μm$ wide rectangular microchannel is measured. This method is used to measure thermal and frictional entropy generation rates in three different flow area transition geometries. The results can be used to determine which geometry has the highest thermal and hydraulic efficiencies.

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## Figures

Figure 1

Schematic of a micro-PIV system

Figure 2

LIF calibration curve

Figure 3

(a) Schematic of the microchannels under study. (b) Three-dimensional schematic of the expansion/contraction geometries.

Figure 4

Microfluidic assembly for PIV and LIF measurements

Figure 5

Schematic of the measurement plane relative to the geometry under study

Figure 6

Streamwise and normal velocity profiles in a fully developed region of the channel compared with analytical fully developed velocity profile (18)

Figure 7

Velocity field at the sudden expansion with rectangular shoulders, at flow rates of (a) 100 μl/min, (b) 300 μl/min, and (c) 500 μl/min. (d) Velocity field at the rounded expansion at a flow rate of 500 μl/min.

Figure 8

Contours of constant frictional entropy generation at the expansion with rounded shoulders, at flow rates of (a) 100 μl/min, (b) 300 μl/min, and (c) 500 μl/min

Figure 9

Frictional entropy generation at a plane in the middle of the expansion (a) and contraction (b) section as a function of flow rate

Figure 10

Temperature distribution in the flow at the expansion with rounded shoulders, at a constant surface wall temperature of 90°C, at flow rates of (a) 100 μl/min, (b) 300 μl/min, and (c) 500 μl/min

Figure 11

Thermal entropy generation distribution in the flow at the expansion with rounded shoulders, at a constant surface wall temperature of 90°C, and at flow rates of (a) 100 μl/min, (b) 300 μl/min, and (c) 500 μl/min

Figure 12

Variations of thermal entropy generation with flow rate in the contraction (a) and expansion (b) of the microchannels

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