Drying Constant

A mathematical model was developed for optimization of heat and mass transfer in capillary porous media during drying process to predict the drying constants. The modeling equations verified the experimental results and proved to be an important tool in predicting the drying rate under different drying conditions. 

The above transport properties in conjunction with a transport phenomena mechanistic model can adequately describe the drying kinetics, but sometimes an additional property, the drying constant, is also used. The drying constant is essentially a combination of the above transport properties and it must be used in conjunction with the so-called thin-layer model. 

Effective moisture diffusivity and effective thermal conductivity are in general functions of material moisture content and tanperature, as well as of the material structure. Air boundary coeffiamts are functions of the conditions of the drying air, that is humidity, tonperature, and velocity, as well as system geometry. Equilibrium moisture content of a given material is a function of air humidity and temperature. The drying constant is a function of material moisture content, temperature, and thickness, as weU as air humidity, tonperature, and velocity. 

The transport properties discussed above (moisture diffu-sivity, thermal conductivity, interface heat, and mass transfer coefficients) describe completely the drying kinetics. However, in the literature sometimes (mainly in foods, especially in cereals) instead of the above transport properties, the drying constant K is used. The drying constant is a combination of these transport properties. 

The drying constant K is the most suitable quantity for purposes of design, optimization, and any situation in which a large number of iterative model calculations are needed. This stems from the fact that the drying constant embodies all the transport properties into a simple exponential function, which is the solution of Equation 4.14 under constant air conditions. On the other hand, the classical partial differential equations, which analytically describe the four prevailing transport phenomena during drying (internal-external, heat-mass transfer), require a lot of time for their numerical solution and thus are not attractive for iterative calculations. 

The measurement of the drying constant is obtained from drying experiments. In a drying apparatus, the air temperature, humidity, and velocity are controlled and kept constant,... 

The drying constant depends on both material and air properties as it is a phenomenological property representative of several transport phenomena. So, it is a function of material moisture content, temperature, and thickness, as well as air humidity, temperature, and velocity. 

Some relationships describing the effect of the above factors on the drying constant are presented in Table 4.11. Equations Tll.l and T11.2 are Arrhenius-type equations, which take into account the temperature effect only. The effect of water activity can be considered by modifying the activation energy (Equation Tll.l) on the preexponential factor (Equation T11.2). Equations Tll.l and T11.2 consider the same factors in a different form. Equation T11.4 takes into account only the air velocity effect, whereas Equation T11.5 considers all the factors affecting the drying constant. Table 4.12 lists parameter values for typical equations of Table 4.11. 

K, drying constant temperature air velocity water activity d, particle diameter i>, parameters. 

FIGURE 4.10 Effect of various factors on the drying constant. (Data for green pepper are from Kiranoudis, C.T. et al.. Drying Technol., 10(4), 995, 1992 and data for shelled com are from Westerman, P.W. et al., Trans. ASAE, 16,1136, 1973.)... 

Alternatively, if the drying eonstant is assumed to describe the drying kinetics by the thin-layer equation, then the drying constant can be estimated using this method. 

Eigure 7.8 presents typical curves, which express the drying constant versus temperature for various air humidities and velocities. 

The drying constant is a function of gas conditions and the following empirical equation can be used ... 

It should be noted that drying constants in the models mentioned earlier are anpirical and depoid on the type of material operating conditions as well as dryer dimensions. If one of these models is used for FBD design, experimental investigation on drying kinetics has to be conducted to obtain the drying constant for the particular material prior to the dryer design. 

In writing Equation 24.17, two assumptions have been made (1) the distribution of moisture within the product is uniform and (2) the drying rate is much dependent on the drying constant k and the equilibrium moisture M. The value of k must be found experimentally. Usually a thin layer of product is fully exposed to a highly controlled hot air. Equation 24.17 is fitted to the experimental drying data. 

A solution to Equation 24.17 takes the form of M, = exp(-fct) or its variation = exp(-M"). ASAE [28] publishes values of k and n for a number of foods (ASAE Standard S448— Thinlayer Drying of Agricultural Crops). ASAE [28] also describes a standardized experimental technique for estimating the drying constants k and n. 

These ideas can now be applied to the drying of lumber boards, which is assumed to be stress-free at the beginning. At the beginning of drying (constant drying-rate period),... 

The best sclerotia growth is assured by dry, constantly moderate weather conditions. In hot weather, the growing period of sclerotia is shortened causing less developed scerotia of lower alkaloid content. According to the experiments of Kiniczky (1992) under controlled conditions, the alkaloid level of the sclerotia at 22°C was 5.1%, while the rising the temperature to 25"C decreased the alkaloid content to 2.7%. Higher temperature (up to 30"C) had a significant effect also on the individual sclerotium mass, but their number in the ear was not influenced. 

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