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# Closure to “Discussion of ‘Heat Transfer Mechanisms During Flow Boiling in Microchannels’ ” (2012, ASME J. Heat Transfer, 134 , p. 015501)OPEN ACCESS

[+] Author and Article Information
Satish G. Kandlikar

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

J. Heat Transfer 134(1), 015502 (Nov 29, 2011) (1 page) doi:10.1115/1.4004771 History: Received July 19, 2011; Revised July 27, 2011; Published November 29, 2011; Online November 29, 2011

The interrelations among different nondimensional groups shown by M. M. Awad are quite correct. The insight provided by the author is very much appreciated.

The use of the correct nondimensional group is derived mainly from the physical interpretation of the underlying processes. Whenever possible, an underlying model based on force balance or some such similar approach is recommended. This will help in arriving at equations and correlations that are able to accurately represent the form of the interrelationships among variables. Such an approach was adopted by Kandlikar [1] in modeling the flow boiling CHF, resulting in the following equations from a force balance analysis at the liquid–vapor–solid contact line at the CHF condition. Display Formula

$FM'=a1(FS,1'+FS,2')+a2FI'+a3Fτ'$
(1)
In this equation, a1 , a2 , and a3 are constants, and F′ represents the forces per unit length of the contact line, and subscripts stand for the respective forces as follows:

M—evaporation momentum

S,1 and S,2—surface tension at the advancing contact line and the top of the bubble interface, respectively

I—inertia

τ—viscous

Dividing by the surface tension forces throughout and simplifying results in the desired relationship among the nondimensional groups of interest in this discussion. Display Formula

$K2,CHF=a1(1+cosθR)+a2We(1-x)+a3Ca(1-x)$
(2)
where K2,CHF represents the nondimensional group K2 at the CHF condition, θR is the receding contact angle, and x is the vapor quality of the flow in the channel. As suggested by Awad, the Weber number may be replaced by the ratio K2 /K1 , but it may be better to retain the Weber number to clearly identify the contribution from the inertia term.

In analyzing the liquid–vapor interface during pool and flow boiling, there are four forces that have been identified to be of interest. These are evaporation momentum, surface tension, inertia, and viscous forces. The following six combinations emerge as nondimensional groups. Display Formula

$Evaporation Momentum ForceInertia force=K1$
(3)
Display Formula
$Evaporation Momentum ForceSurface tension force=K2$
(4)
Display Formula
$Evaporation Momentum ForceViscous force=K3$
(5)
Display Formula
$Inertia ForceSurface tension force=We,Weber number$
(6)
Display Formula
$Inertia ForceViscous Force=Re,Reynolds number$
(7)
Display Formula
$Viscous ForceSurface Tension Force=Ca,Capillary number$
(8)
The nondimensional group K3 has not been independently used yet, but it is relevant if the evaporation momentum and viscous forces are considered in a process. K3 can also be represented as: Display Formula
$K3=K1Re=K2/Ca$
(9)

In summary, recognizing the evaporation momentum force as an important force during the boiling process opens up the possibilities of three new relevant nondimensional groups, K1 , K2 , and K3 . Any two of these groups can be represented by combining the third one with one of the other relevant nondimensional groups Re, We, and Ca.

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