Moisture fluxes

All heat flux and moisture flux elements m Eqs. (11,13) to (11.16) are also time-dependent,... 

The next step in developing an equation to describe moisture uptake in one dimension is to determine W p by applying Eq. (39). Note that the partial pressure gradient (dPJdx) must be calculated to solve for the moisture flux. We could take the derivative of either Eq. (42) or (43) for this purpose. If we take the derivative of Eq. (42), the resulting solution is given by... 

The actual variability in the heat and moisture fluxes almost does not influence the BSGC [48]. In addition, the former flux suppresses the effect of wind forcing. The weakness of the abyssal currents in the Black Sea results in a decrease in the efficiency of the their interaction with the bottom relief (JEBAR) that generates additional relative vorticity and BSGC energy. One more result of the particular baroclinicity of the Black Sea is the weakness of the vertical water circulation, which, with respect to the integral mass transport, is 25 times lower than that of the horizontal BSGC. 

In addition to the results presented above, we should also note the studies of the climatic BSGC [56] based on the basic Russian prognostic model [57]. The distinctive features of [56] were related to the dependence of the coefficients of horizontal turbulence on lateral velocity shears and to the specifying of the monthly climatic temperature and salinity field at the surface [29] instead of the heat and moisture fluxes. Despite the relatively coarse horizontal calculation grid (about 22 km), this allowed the authors to reproduce [56] a relatively distinct MRC jet and the known NSAEs off the Turkish and Caucasian coasts and off the Danube River mouth. The results of the tuning in [56] of the Munk-Anderson s formula for the coefficient of the vertical turbulent exchange from the point of view of reproduction of the actual CIL were used in [53,54]. 

Consideration of the thermohaline structure of the Black Sea provides new results on the statistical and physical analysis of the historical data of ship-borne observations of the vertical profiles of the temperature and salinity of the waters. The general features of the vertical thermohaline structure of the Black Sea waters, the seasonal and interannual variabilities of the horizontal structure of the temperature and salinity in all the main water layers are described. The relations of the large-scale features of the hydrology of the Black Sea waters to external forcing (heat and moisture fluxes across the water surface, river mouths and straits, fluxes of the momentum and relative vorticity of wind) are shown. The generalization of the results of the studies of the T,S-structure of the Black Sea waters and of its seasonal and interannual variability allows the following conclusions to be made. 

Molion, L. 1975. A climatonomic study of the energy and moisture fluxes of the Amazon basin with consideration on deforestation. Ph.D. Dissertation, Department of Meteorology, University of Wisconsin, Madison, p. 190. 

The Moisture Diffusion Coefficient. The one-dimensional moisture flux (/) (g/cm s) of water through wood customarily is given as the product of the moisture diffusion coefficient D (cm /s) and the gradient dcjdx of moisture concentration (g/cm ) in the direction of flow, or... 

Consider the external atmospheric flow now, z > h. The external profiles U z) and E(z) are formed by the impulse flux rh and by the moisture flux jEh from the rough surface z = h that are taken constant over it, t(z) = rh and jE(z) = jEh. The algebraic turbulence model (3.131) links the turbulence exchange coefficients with the air velocity gradient... 

The moisture flux due to capillarity can be expressed in terms of the product of a liquid conductivity parameter and moisture gradient. In this case, the governing equation has, in fact, the same form as the diffusion equation. 

Farnworth [14] reported a numerical model describing the combined heat and water-vapor transport through clothing. The assumptions in the model did not allow for the complexity of the moisture-sorption isotherm and the sorption kinetics of fibers. Wehner et al [30] presented two mechanical models to simulate the interaction between moisture sorption by fibers and moisture flux through the void spaces of a fabric. In the first model, diffusion within the fiber was considered to be so rapid that the fiber moisture content was always in equilibrium with the adjacent air. In the second model, the sorption kinetics of the fiber were assumed to follow Fickian diffusion. In these models, the effect of heat of sorption and the complicated sorption behavior of the fibers were neglected. 

The moisture flux g (kg/(m, s)) in the bentonite has a liquid and a vapor component. The liquid flux g, is proportional to the gradient of the pore water pressure P with a hydraulic conductivity k(S) that is a function of the degree of water saturation S. The flux is inversely proportional to the viscosity rj(T). The water vapor flux g, is proportional to the gradient of the water vapor density in the gas phases in the pores with a vapor conductivity factor D,(5) that is a decreasing function of S. The heat flux q (W/m ) has a conductive part with a thermal conductivity. /i(S). There is also a negligible convective part. We have... 

The moisture flux g and the total flux G r,t) (kgVs) over the height H may now be written in the following general form... 

Here, Vp is the porosity or pore volume per unit volume of bentonite. The total radial moisture flux G(r,l) is given by (3). 

All above functions for bentonite and water are represented by explicit formulas with an error below 1% in the interval 10<7 <100°C and 0.3 < 5 < 1. The mathematical program Mathcad is used. The coefficient functions K (S,T) and Kj (S,T) for moisture flux are readily obtained. 

The initial degree of saturation in the bentonite is 5 . Full saturation 5=1 is maintained at the rock boundary r = r. The moisture flux is zero at the canister boundary. The boundary conditions and the initial condition are ... 

In one study on wound-covering materials with controlled physicochemical properties, an artificial skin was designed with a crosslinfced collagen-polysaccharide (chondroitin 6-sulfate) composite membrane. This was specifically chosen to have controlled porosity (5 to 150 /rm in diameter), flexibihty (by varying crosslink density), and moisture flux rate. 

Compared with heat transfer, the process of moisture transport is slower by a factor of approximately 10. For example, moisture equilibration of a 12 mm thick composite, at 350 K, can take 13 years whereas thermal equilibration only takes 15 s. Fick adapted the heat conduction equation of Fourier, and his (Pick s) second law is generally considered to be applicable to the moisture diffusion problem. The one-dimensional Fickian diffusion law, which describes transport through the thickness, and assumes that the moisture flux is proportional to the concentration gradient, is ... 

In view of the aforementioned assumption, it is sufficient to consider the liquid content in drying material only. The gravitational force was already assumed as insignificant, so the moisture flux depends on the gradient of liquid chemical potential 0, e) expressed as follows... 

Sensible heat flux = pCpCr T - T ir)U o = Hs Latent heat flux = LTpCEiqsea - qakWw = Hi Moisture flux = /OCfC sea - qairWw = E... 

Transient moisture sorption under ramp changes in external humidity is analyzed. A general model describing the dynamics of moisture sorption is derived. The paper sheet is considered as a composite structure of fibers and voids through which moisture is transported by diffusion. The mathematical description of moisture transport embodies two suitably averaged concentration fields, c and q. Two unsteady state diffusion equations describe the time and spatial evolution of these fields. The average moisture content of the sheet and the moisture flux at the surface are evaluated. 

Finally, when sheet internal resistance becomes important, the role of intrafiber diffusion in the sheet transverse direction can be examined by steady state diffusion experiments under the same RH conditions. A strong dependence of the steady state moisture flux on the RH indicates intra-fiber diffusion providing yet another critical test of the hypothesis. 

B moisture flux coefficient P moisture vapor pressure... 

Furthermore, in this case, moisture flux has two components/i and/2, both of which are related to a single component of the gradient of chemical potential zi = d ijdx, according to... 

Since the fiber has a small proportion of volume in the fabric, the main contribution of moisture flux is fi om the diffusions process through the air in the fiber interstices. However, it was identified by Wenhner et al. [6] that absorption of moisture by the fiber also importantly affected the response of fabric to the moisture gradient. The water vapor concentration on the fiber surface, theoretically, depends on the amount of absorbed moisture onto the surface and the local temperature of the fiber. The fiber will keep absorbing as much moisture as it can until it reaches a saturated status with respect to the absorption rate. And when the fiber becomes saturated, additional vapor moisture may condense into liquid phase onto the fiber surface. With regard to the physic nature of fibrous materials, condensate water may be held on the surface of the fiber and be relative immobile, or may be transferred across the textile stmcture by capillary actions. 

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