Joined heat and mass exchange

In practice, under most weather conditions, the mass exchange and the heat exchange act simultaneously. The difficulty in solving the complete problem (3.99M3.101) under such conditions lies in the fact that two first left equations become linked due to the third one. 

First of all, the method of numerical treatment needs a modification. In the case where each of the physical processes acts independently, the corresponding conjugation boundary-value problems led to one transcendental equation with one unknown. It was natural to expect that, from the physical meaning of the problem, the last equation admits a unique solution. 

The left and right boundary-value problems require one boundary condition each on the interface z = 1. Like before, let us supply them by two auxiliary values 

each droplet temperature curve is attracted by two corresponding air temperature curves, T(z) and TE(z). At top levels of the EPR, the droplet temperature exceeds both air temperatures, t(z) T(z) and t(z) TE(z). Therefore, both the heat and mass flows are directed from droplets to air, and both flows jE and jH are positive on these levels z as seen from Figs. 3.14, C and D. However, starting from a certain level labelled by small arrows, the droplet temperature finds itself lower that the air temperature but still tends to the formal temperature, t(z) T(z) but t(z) Te(z). This means that the evaporation still exists and cools droplets, but air began to warm them. Therefore, the possible minimum droplet temperature lies always between T(z) and Te(z). The last phenomenon is well known in meteorology. 

The content of moisture in air is always less that the saturating content for a given air temperature found via (3.94) as E = e T). If it occasionally turned out that E Zs , it would be dewed that is not accounted for in this model yet. The ratio p = Zs/Zs is called relative humidity. The distributions of the last over different cross sections of the droplet boundary layer are presented in Fig. 3.21,B. This practically important flow aerothermal characteristic, the relative humidity, reaches the largest values (up to 100%) within the droplet layer but decreases to a certain value far away over it, which has been prescribed by weather conditions Too and (or Too and Ifoo — Eoo/E oo). There is no further droplet cooling in the zones where p = l. 

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Figure 3.21 Computed aerothermal profiles for the joined heat and mass exchange (A) temperatures of air and droplets (B) air humidity (C) and (D) mass and heat flows (fluid mechanics criteria A = 0, B = 450, and p = 40 thermal parameters Ae = 2, Be = 300, and AH = 10, B = 100, Pr = Sc = 1).

Similarly, the problem of the joined heat and mass exchange can be formulated (with integral terms like (3.115) or integral sums like (3.116)) and solved. The results presented in Fig. 3.23 highlight the extending aerothermal boundary layer over the EPR along with K = 3 droplet temperatures for each fraction under study. The droplet fractions are turned out to be differently cooled fraction 3 reaches the wet bulb temperature T, and has not been cooled during the rest of the droplet fall fraction 2 is cooled so slowly that cannot even reach the air temperature T, and fraction 1 tends to a certain temperature between T and T. 

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