Measurements of Thermal Conductivity and Permeability of the Dried Layer during Freeze-Drying of Beef

Abstract

Thermal conductivities and permeabilities for the dried layer of beef samples were determined by applying data obtained during freeze-drying to a model based on the rates of heat and mass transfer in the sample. The drying data and physical properties needed for the proposed model were obtained either from the literature or from the experiments using a radiant heating upon the sample surfaces.The relationships between these transport properties and temperatures as well as water-vapor pressures of the dried layer were determined and the temperature and pressure dependances of transport properties were discussed with reference to practical freeze-drying operations.
The results obtained were as follows;
(1) Thermal conductivity had a tendency to decrease as the dried layer temperature increased as shown in Fig. 7 and there was no definite effect of water-vapor pressure in the dried layer on thermal conductivity in its pressure range from 0.29 to 0.66 torr under conditions of the total pressure in the chamber ranging from 0.3-1.5 torr as shown in Fig. 9.
(2) The regression equation determined for predicting thermal conductivity as a function of the dried layer temperature in the range of 3 to 41°C, was presented by;
k_e=-4.189×10^-7θ+1.511×10^-4
(3) In the model thermal conductivities were calculated by assuming the latent heat of sublimation to be equal to the value for frozen beef juice. The results obtained were about 7% higher than the values using the heat of sublimation of pure ice and about 12% lower than those using bovine muscle.
(4) Effect of error involved in neglecting the heat absorbed by water vapor flowing through the dried layer on thermal conductivity increased in proportion to the dried layer temperature; namely, increasing the temperature from 3 to 45°C leaded to a increase in error ranging from 3 to 7% as shown in Fig. 8.
(5) Permeability K and K* were calculated from both equilibrium water-vapor pressure of pure ice and frozen beef, respectively. The difference between the two values, ΔK was 15-43% as presented in Table 3.
(6) Permeabilities vs. the dried layer pressures of water-vapor relationships were shown in Fig. 10. The values for K were in good agreement with Mellor and Lovett's theoretical curve based on the collision theory developed by Pollard and Present and also with their experimental results using completely freeze-dried samples under steady-state conditions. On the other hand, the discrepancy between K* and their theoretical curve was apparent, as could be seen from Fig. 10.
(7) The relation between permeability and the dried layer temperature was obtained as shown in Fig. 11. As the dried layer temperature was increased, permeability had a tendency to increase at the surface temperature ranging from 30 to 80°C and to decrease from 80 to 100°C. This decrease was attributed to temperature rise at the sublimation front as shown in Table 2. It was considered that in this surface temperature range the heat supplied across the dried layer was dissipated as both sensible heat to raise the temperature of the frozen layer and latent heat of sublimation. Thus the model applied over this temperature range was found to provide invalid values because the drying conditions did not satisfy the assumption used in the model, as expressed by equation (2).
(8) Agreement between calculated values by the regression equation (21) and from Mellor and Lovett's theoretical equation (17) for permeability was generally good at the dried layer temperature up to 20°C as indicated in Table 5, and it was suggested that the effect of the dried layer temperature on permeability was greater than that assessed by equation (17).