Heat transfer drying process calculation

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. 

Equation (5) is equivalent to stating that sublimation and subsequent transport of 1 g of water vapor into the chamber demands a heat input of 650 cal (2720 J) from the shelves. The vial heat transfer coefficient, Kv, depends upon the chamber pressure, Pc and the vapor pressure of ice, P0, depends in exponential fashion upon the product temperature, Tp. With a knowledge of the mass transfer coefficients, Rp and Rs, and the vial heat transfer coefficient, Kv, specification of the process control parameters, Pc and 7 , allows Eq. (5) to be solved for the product temperature, Tp. The product temperature, and therefore P0, are obviously determined by a number of factors, including the nature of the product and the extent of prior drying (i.e., the cake thickness) through Rp, the nature of the container through Kv, and the process control variables Pc and Ts. With the product temperature calculated, the sublimation rate is determined by Eq. (4). 

Example ps at the sublimation front is 0.937 mbar (-21 °C) (see example in Table 1.9), in the chamber a pU20 = 0.31 mbar has been measured, resulting in a pressure difference of approx. 0.6 mbar. With these data, the water vapor permeability blp = 1.1 10 2 kg/h m mbar is calculated. With this data known, it is possible to calculate dp for different conditions, if the mass of frozen water miCL, the time /MD, the thickness (d) and the surface (F) are known. This dp depends from the amount vapor transported and thereby from the heat transfer (Table 1.9). In the examples given it changes between 0.17 mbar in a slow drying process (6 h) to 0.6 mbar for a shorter drying time, 2.5 h. 

The calculation of drying processes requires a knowledge of a number of characteristics of drying techniques, such as the characteristics of the material, the coefficients of conductivity and transfer, and the characteristics of shrinkage. In most cases these characteristics cannot be calculated by analysis, and it is emphasized in the description of mathematical models of the physical process that the so-called global conductivity and transfer coefficients, which reflect the total effect on the partial processes, must frequently be interpreted as experimental characteristics. Consequently, these characteristics can be determined only by adequate experiments. With experimental data it is possible to apply analytical or numerical solutions of simultaneous heat and mass transfer to practical calculations. 

Other methods of moisture control employ temperature sensors coupled with models of the conveyor drying process. The temperature drop through the bed of product can be used to calculate the amount of heat transfer occurring as the air passes through the product. If, for example, the product moisture into the dryer suddenly drops, the heat transfer will be reduced. A temperature sensor on the return-air side of the bed will sense this drop in heat transfer as a rise in temperature and the control loop can take corrective action. 

A 3D simultaneous heat and moisture transfer drying model for a single wheat kernel was mathematically developed under the assumption of a non-uniform initial moisture distribution and two different values of water diffusion coefficients in the germ and endosperm of a wheat kernel. Model-predicted moisture data were compared with the results obtained from MR images under similar drying conditions. Activation energies of the water removal process in the endosperm and germ were calculated to be 26.5 and 13.8 kJ mol respectively. 

---