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Research Papers: Evaporation, Boiling, and Condensation

# A Scale Analysis Based Theoretical Force Balance Model for Critical Heat Flux (CHF) During Saturated Flow Boiling in Microchannels and Minichannels

[+] Author and Article Information
Satish G. Kandlikar

Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY 14623sgkeme@rit.edu

J. Heat Transfer 132(8), 081501 (Jun 09, 2010) (13 pages) doi:10.1115/1.4001124 History: Received September 19, 2009; Revised December 26, 2009; Published June 09, 2010; Online June 09, 2010

## Abstract

Accurate prediction of critical heat flux (CHF) in microchannels and minichannels is of great interest in estimating the safe operational limits of cooling systems employing flow boiling. Scale analysis is applied to identify the relevant forces leading to the CHF condition. Using these forces, a local parameter model is developed to predict the flow boiling CHF. The theoretical model is an extension of an earlier pool boiling CHF model and incorporates force balance among the evaporation momentum, surface tension, inertia, and viscous forces. Weber number, capillary number, and a new nondimensional group introduced earlier by Kandlikar (2004, “Heat Transfer Mechanisms During Flow Boiling in Microchannels,” ASME J. Heat Transfer, 126, pp. 8–16), $K2$, representing the ratio of evaporation momentum to surface tension forces, emerged as main groups in quantifying the narrow channel effects on CHF. The constants in the model were calculated from the available experimental data. The mean error with ten data sets is 19.7% with 76% data falling within $±30%$ error band and 93% within $±50%$ error band. The length to diameter ratio emerged as a parameter indicating a stepwise regime change. The success of the model indicates that flow boiling CHF can be modeled as a local phenomenon and the scale analysis is able to reveal important information regarding fundamental mechanisms leading to the CHF condition.

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Copyright © 2010 by American Society of Mechanical Engineers
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## Figures

Figure 1

Results of a scaling analysis showing effect of channel diameter on forces experienced at the evaporating interface during flow boiling: (a) water and (b) FC-72

Figure 2

Forces acting on the liquid-vapor interface near the heater surface at the initiation of CHF condition

Figure 3

Comparison of the experimental and CHF from model predictions for ten data sets with eight fluids in Dh range from 127 μm to 3.36 mm

Figure 4

Variation in K2,CHF with We in high CHF (HC) and low CHF (LC) regions at x=0.1 plotted using Eqs. 17,18,19,20 without employing the LIR-HIR and L/D criteria

Figure 5

Variation in K2,CHF with We in the HIR-LC (We>900) using Eqs. 20,21 for x=0.1 and Ca=1×10−3

Figure 6

Variation in K2,CHF with We in the HIR-LC (We>900) using Eqs. 20,21 for x=0.1 and Ca=100×10−3

Figure 7

Contributions from surface tension, inertia, and viscous forces to the CHF at x=0.1 and Ca=1×10−3

Figure 8

Contributions from surface tension, inertia, and viscous forces to the CHF at x=0.1 and Ca=100×10−3

Figure 9

Variation in K2,CHF and different terms in Eq. 13 with hydraulic diameter for water at 1 atm saturation pressure in the HC Region for x=0.1 and G=20 kg/m2 s

Figure 10

Variation in K2,CHF and different terms in Eq. 13 with hydraulic diameter for R123 at 1 atm saturation pressure in the HC region for x=0.1 and G=20 kg/m2 s

Figure 11

Variation in K2,CHF with hydraulic diameter for water at 1 atm saturation pressure in the HC region for x=0.1 and G=20 kg/m2 s

Figure 12

Variation in K2,CHF and different terms in Eq. 13 with hydraulic diameter for R123 at 1 atm saturation pressure in the HC region for x=0.1 and G=20 kg/m2 s

Figure 13

Effect of L/D ratio on CHF for a fixed exit quality of 0.04 and a mass flux of 70,000 kg/m2 s for D=1 mm, 2 mm, and 3 mm. Replotted from Inasaka and Nariai (59).

Figure 14

Effect of L/D ratio on CHF in LIR-HC and LIR-LC regions indicating a transition region 140<L/D<230

Figure 15

Effect of L/D ratio on CHF in HIR-HC and HIR regions indicating a transition around L/D=60–80

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