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

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.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:

Dividing by the surface tension forces throughout and simplifying results in the desired relationship among the nondimensional groups of interest in this discussion.where K_2,CHF represents the nondimensional group K₂ at the CHF condition, θ_R 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.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: