Mass flux, evaporating

The mass flow rate of vapor due to evaporation can be similarly represented. From Equation (6.35) it is seen that the dimensionless evaporation mass flux is... 

Cairncross et al. (1995). Parrouffe (1992) has demonstrated on the basis of extensive experimental data that one may, within engineering accuracy, use analogy between heat and mass nans-fer to estimate the convective heat or mass transfer coefficients even in the presence of intense radiative heat flux on the evaporating surface. Appropriate corrections must be employed, however, for the high evaporative mass flux at the surface. 

Application of the entropy generation minimization (EGM) method to (21.7) allows identifying the optimal parameters to be considered in the optimization [6]. Concerning the entropy generated by the evaporated mass flux, that parameter is the fraction x of evaporated mass and its optimal value is found by equating to zero the partial derivative of (21.7) with respect to % The optimal evaporated mass fraction is thus found to be... 

Fig. 3.5 Representative streamlines and velocity vectors for a pinned droplet in which the evaporative mass flux is given by Eq. (3.9). Fluid flows from the center of the droplet toward the contact line [52]. Adapted with permission from ref [52], Copyright 2001 American Chemical Society...

From the kinetic theory of gases, an expression for the net-mass flux at the interphase can be derived based on the works of Hertz [223] and Knudsen [224]. From a statistical consideration under the assumption of a Maxwell-Boltzmann distribution for the velocity of the gas molecules, the maximum condensation mass flux can be calculated. The evaporation mass flux has to equal the condensation mass flux at equilibrium. The resulting Hertz-Knudsen equation for calculating the area specific net-mass flux is given below ... 

Mass and heat flux during evaporation are strongly coupled by the heat of vaporization of water from phosphoric acid. Kablukov and Zagwosdkin [185] and Brown and Whitt [173] published data for the heat of vaporization for acid concentrations up to 100 wt%. Very little is known about the vapor-liquid interphase area within the catalytic layer, which is needed for the calculation of the evaporation mass flux. The interphase area within the porous medium depends on the acid holdup and the wetting behavior of the catalyst surface which both also... 

Variation of evaporative mass flux with bulk superheat AT. 

Deviation of vapour composition y(ll) from the free boiling value y(l) with increasing evaporative mass flux... 

The term mass flux is the quantitative wording used for mass flow per unit area and is usually measured in kg/m s. In this monograph, the term is used to describe the surface evaporative mass flux . 

The highest liquid temperature, or maximum liquid superheat, is undoubtedly in the boundary flow at the container wall/liquid-vapour interface. Surface evaporation instabilities are likely to be induced near this region where the evaporation mass flux is significantly larger than at the centre of the liquid pool. 

In the example, the LNG has bulk liquid superheats of 0.1,0.2 and 0.4 K, which together with corresponding evaporative mass fluxes of 0.12,0.26 and 0.57 g/m s (from (2.4)) are equivalent to boil-off figures of 0.05, 0.1 and 0.23 %/day. These boil-off rates will dissipate thermal overfill at the rates of about 10,500,22,750 and 49,800 MJ/day, daily figures which are similar in magnitude to the thermal overfills of the bulk superheated liquid. 

The evaporation mass flux, in terms of mass evaporated per unit area of liquid free surface, varies with bulk liquid superheat AT as AT for LNG and LCH4. Conversely, the liquid must be superheated for surface evaporation to take place. 

During normal equilibrium evaporation, these three mechanisms are in a state of fine balance while flie evaporation mass flux is determined by the overall temperature difference across these three layers, which is the same as the liquid superheat. 

The highest fluid temperature is undoubtedly at the wall-Uquid-vapour interface, where the evaporative mass flux will be larger than at the centre of flie liquid pool. The mechanism of surface evaporation during inward radial flow is extraordinarily complicated and sensitive, while the rate of evaporating mass flow through the surface is controlled by several local factors. Let us develop the picture of this mechanism as it was discovered at Southampton. 

Surface Evaporation Mass Flux and Bulk Superheat... 

To gain an understanding of the relationship between evaporation mass flux and bulk superheat, microthermometer studies were first made on LIN, LCH4 and LNG [8-11]. 

Fig. 4.2 Evaporation mass flux versus bulk superheat AT for LIN, LAR and LNG (North Sea)...

Another important observation from the video Schlieren recordings is that the number of convection lines, and hence the number of cells enclosed by flie convection lines, increases with evaporation rate. Indeed, there appears to be a linear variation between evaporation rate and total lengfli of convection lines or streamers in the surface. The evaporative mass flux per meter length of convection line was never specifically measured, but it is estimated fi om the Schlieren video pictures to be of flie order of 7 g/m for LIN over a wide range of surface mass fluxes from 1.0 to 20 g/nF s. 

If one could devise an experiment to scan flie surface and measure the local instantaneous evaporation mass flux, one should see a correlation between the... 

It is this thin high-impedance region which is separating the bulk superheated liquid from the surface molecular evaporation region, and is preventing a much larger evaporation mass flux from taking place. 

On a short time scale, surface evaporation is observed to vary continuously with time, with peaks and troughs in the evaporation mass flux, and hence the surface evaporation impedance, up to 10 % of the mean figure. This was the first discovery made on commencing the monitoring of boil-off rates using instantaneously recording vapour flow meters, with an integration time of less than 1 s. 

T-x) data for surface evaporation of LNG and LPG mixtures may not be the same as the (T-x) free-boiling data used for distillation. The deviation in vapour composition from the equilibrium data is proportional to the surface evaporation mass flux. 

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