Moisture balance equation

The problems experienced in drying process calculations can be divided into two categories the boundary layer factors outside the material and humidity conditions, and the heat transfer problem inside the material. The latter are more difficult to solve mathematically, due mostly to the moving liquid by capillary flow. Capillary flow tends to balance the moisture differences inside the material during the drying process. The mathematical discussion of capillary flow requires consideration of the linear momentum equation for water and requires knowledge of the water pressure, its dependency on moisture content and temperature, and the flow resistance force between water and the material. Due to the complex nature of this, it is not considered here. 

The hunnidity ratio oJ a rotjm at any given time is given by a Jatent heat balance equation including the water vapor flows due to infiltration to ventilation to moisture transport through envelope elements... 

The TDE moisture module (of the model) is formulated from three equations (1) the water mass balance equation, (2) the water momentum, (3) the Darcy equation, and (4) other equations such as the surface tension of potential energy equation. The resulting differential equation system describes moisture movement in the soil and is written in a one dimensional, vertical, unsteady, isotropic formulation as ... 

The rice taste analyzer, developed first by Satake Engineering Co., Ltd., consists of NIR instrument provided by Bran Luebbe Company. This analyzer is based on the experimental result that rice taste is fixed by the balance of moisture, protein, amylose, and fatty acid. From a practical stand point, milled rice is ground, and the ground sample is kept at a constant temperature oven for more than one hour, after which the NIR measurement is performed to determine the amount of different constituents. From these constituents, taste scores can be calculated using taste-related equation which relates the constituents to taste score. A taste score can be generated in only a few minutes by the NIR instrument. The rice taste analyzer includes the software that calculates the blending ratio to perform lowest price at the same taste, or to perform best taste at the same price. 

TABLE 12-8 Mass-Balance Equations for Drying Modeling When Diffusion Is Mass-Transfer Mechanism of Moisture Transport... 

The moisture balance equation for water saturation S(r,t) in the radial case for the annular region between canister wall (r = ) and rock (r,) reads... 

Combining (3) and (6) we may eliminate the temperature derivative. We may now write the moisture balance equation (5) in the following way... 

Corrosion of metals costs us billions of dollars annually, slowly destroying cars, bridges, and buildings. Corrosion of a metal involves the oxidation of the metal by the oxygen in the air, typically in the presence of moisture. Write a balanced equation for the reaction of each of the following metals with O2 Zn, Al, Fe, Cr, and Ni. 

In order to estimate the moisture content of the particle at the dryer outlet, two additional common assumptions are needed, namely, isothermal flow and particle s exit temperature similar to the gas temperature. Based on these assumptions, various macroscopic mass and energy balance equations can be solved [16,17]. 

Many researches adopted one of the aforanentioned approaches and modified it to include various aspects of the pneumatic drying process. Andrieu and Bressat [16] presented a simple model for pneumatic drying of polyvinyl chloride (PVC), particles. Their model was based on elementary momentum, heat and mass transfer between the fluid and the particles. In order to simplify their model, they assumed that the flow is unidirectional, the relative velocity is a function of the buoyancy and drag forces, solid temperature is uniform and equal to the evaporation temperature, and that evaporation of free water occurs in a constant rate period. Based on their simplifying assumptions, six balance equations were written for six unknowns, namely, relative velocity, air humidity, solid moisture content, equilibrium humidity, and both solid and fluid temperatures. The model was then solved numerically, and satisfactory agreanent with their experimental results was obtained. A similar model was presented by Tanthapanichakoon and Srivotanai [24]. Their model was solved numerically and compared with their experimental data. Their comparison between the experimental data and their model predictions showed large scattering for the gas temperature and absolute humidity. However, their comparisons for the solid temperature and the water content were failed. 

The first step toward any dryer design is the consideration of heat and mass balance within the dryer. Consider the heat and mass balance when wet materials with the moisture content Wq (kg-water/kg-dry solid) and temperature Tq (K) are dried in a dryer and the dry products with the moisture content Wj (kg-water/kg-dry solid) and temperature (K) are obtained. Suppose that the heat loss is negligibly small, the total heat balance equation is expressed by... 

The moisture mass balance and the energy balance equations can be developed as follows (Pang and Xu, 2010) ... 

As seen from Equations 62.11 and 62.12, the strains and thus the stresses are strongly dependent on moisture content and temperature. So, in order to calculate these mechanical quantities, the kinetics of drying needs to be determined. The drying kinetics is described by the conpled system of differential equations developed on the basis of mass and energy balances and the rate equations for the heat and mass transfer. Assuming that the moisture in pore volnme of dried body consists of liquid (Z) and vapor (v), the local forms of mass balance equations for these constitnents read ... 

In zone II, unsaturated surface and bound moisture are evaporated and the solid is dried to its final value Xj. The humidity of the entering gas entering zone II isH and it rises to The material-balance equation (9.10-23) may be used to calculate f/c as... 

The key unit of the desiccant cooling system is the dehumidifier. The potential for further increase in the system performance lies in the design of this dehumidifier. Therefore, much of the attention was in modeling and optimizing the performance of the dehumidifier. The simultaneous heat and mass transfer in air-water-desiccant systems has been modeled by a number of investigators [34-41]. These models have been used to optimize the performance in terms of flow rates, rotation speed, desiccant properties, and desiccant-matrix composition. The moisture balance equation can be written as [42] ... 

General 3D microscopic population balance equations, including several distributed properties, e.g. size and moisture content, can be derived using the same balance method. 

The basic assumption for a mass transport limited model is that diffusion of water vapor thorugh air provides the major resistance to moisture sorption on hygroscopic materials. The boundary conditions for the mass transport limited sorption model are that at the surface of the condensed film the partial pressure of water is given by the vapor pressure above a saturated solution of the salt (Ps) and at the edge of the diffusion boundary layer the vapor pressure is experimentally fixed to be Pc. The problem involves setting up a mass balance and solving the differential equation according to the boundary conditions (see Fig. 10). 

Equation 4.16 indicates that the feed rate of wet solids must be below that which would result in saturation of the exhaust air stream. Failure to satisfy the moisture balance leads to wet quenching of the bed (see Chapter 5). 

Enthalpy balances for the dry layers and the wet layer can be formulated along with a pertinent drying rate equation. Formulation by Beckwith and Beard results in three ordinary differential equations that describe the dry fabric temperature, the wet layer temperature and most importantly, the moisture content of the total fabric as a function of timeQJ. By predetermining the fabric speed through the dryer, residence time can be converted to dryer length. 

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