Boiling number

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

Figure 6.34 shows the dependence of the dimensionless period of phase transformations (i.e., the time between bubble venting), t, on boiling number Bo f =t/Ud, ... 

Fig. 6.34 Dependence of dimensionless time interval between cycles on boiling number circles (o) represent Jh = 100 pm, water, triangles (A) represent = pm, water, diamonds (0) represent Jh = 220 pm, water, star ( ) represents d = 220 pm, ethanol. Reprinted from Hetsroni et al. (2006b) with permission...

Figure 6.35 shows dependence of the dimensionless initial liquid thickness of water and ethanol 5, on the boiling number Bo, where 5 = 5U/v, f/ is the mean velocity of single-phase flow in the micro-channel, and v is the kinematic viscosity of the... 

It was observed that at the same boiling number and inlet temperature, an increase in diameter shifts the ONB further from the inlet. The region of the local dryout decreases and the average heated surface temperature decreases as well. Under this condition the heat transfer coefficient increases with increased hydraulic diameter. 

In order to take into account the effect of surface tension and micro-channel hydraulic diameter, we have applied the Eotvos number Eo = g(pL — pG)d /(y. Eig-ure 6.40 shows the dependence of the Nu/Eo on the boiling number Bo, where Nu = hd /k] is the Nusselt number, h is the heat transfer coefficient, and k] is the thermal conductivity of fluid. All fluid properties are taken at the saturation temperature. This dependence can be approximated, with a standard deviation of 18%, by the relation ... 

The large heated wall temperature fluctuations are associated with the critical heat flux (CHE). The CHE phenomenon is different from that observed in a single channel of conventional size. A key difference between micro-channel heat sink and a single conventional channel is the amplification of the parallel channel instability prior to CHE. As the heat flux approached CHE, the parallel channel instability, which was moderate over a wide range of heat fluxes, became quite intense and should be associated with a maximum temperature fluctuation of the heated surface. The dimensionless experimental values of the heat transfer coefficient may be correlated using the Eotvos number and boiling number. 

The boiling number (Bo) is the ratio of vapor velocity away from the heating surface to flow velocity parallel to the surface, V The vapor velocity is evaluated on the basis of heat transfer by latent heat transport. 

The boiling number, Bo, Eq. (2-79) was used to represent the nucleate boiling term. Thus Kandlikar s correlation for vertical flow is expressed as... 

For sufficiently large heat flux to mass flow ratios, the nucleation mechanism predominates and the heat transfer becomes independent of the two-phase flow characteristics of the system. Thus at large values of the boiling number, the heat transfer coefficients are virtually independent of the Lockhart-Martinelli parameter, Xn. 

Figure 5 Heat transfer coefficient versus Boiling number (Dh = 2 mm).

From an analysis conducted on figures 4 and 5 with the dimensionless boiling number, the following tendencies can be outlined. For = 2 mm ... 

These results are in agreement with the Huo et al. (2004) study which highlighted the prevalence of heat flux dependent boiling and early dry-out in a 2 mm diameter tube with refrigerant R134a In their work the boiling number was always greater than 8 x 10 which is coherent with the present results. 

To explain why the boiling number seems to govern the transition between heat flux increasing a and vapour quality increasing a, the following interpretation is proposed, based on macroscale boiling mechanisms. From the Rohsenow (1952) and Kew and Cornwell (1997) analysis, an inertial characteristic time "Ccv for the liquid layer and a characteristic time Xb for bubbles leaving the wall can be defined. Then, from the Kutaleladze (1981) and Rohsenow (1952) analysis it can be shown that the ratio of these two characteristic times can be written ... 

This ratio is a comparison of convective effects in the liquid layer (causing a to increase with x) and bubble dynamics at the wall (causing a to increase with q). Thus Xcv/Xb is proportional to Bo and a function of vapour quality so that the boiling number is the appropriate dimensionless number to study the transition between these two boiling regimes. 

Biot number for mass transfer boiling number... 

Bocrit boiling number corresponding to critical heat flux (Eq. 15.297)... 

Bo Boiling number, defined in Thermal conductivity of Phase... 

The parameters selected included Re)molds number, Prandtl number, fluid quality, nucleate-boiling-length-to-tubediameter ratio, inlet temperature ratio, and boiling number. The boiling number, which is a parameter described by McAdams [5] for consideration in a boiling process, consists of several fluid-property terms, including liquid viscosity, vapor density, surface tension, and the tube diameter. 

The water data were sufficient to evaluate the relations between the parameters used, with the exception of the boiling number. A simple power function of the boiling number was sufficient to bring all the data together on a single curve. The resulting correlation curve is shown in Fig. 6, in which a rate-of-vaporization parameter / ) is plotted as a function of a boiling-flow parameter /(G). The fix) parameter consists of, while the/(G)... 

L = tube length from entrance to burnout point (nucleate boiling length), ft L = distance along tube measured from burnout point, ft Ng = Boiling number gP[Pg.268]

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