The thermal conductivity appears in equations describing conduction within the bed (see Eq. (18.9) in Sect. 18.3.2). Little attention has been given to direct experimental determination of thermal conductivities of solid beds, with many workers simply using values tabulated for foodstuffs. Lai et al. (1989) describe a simple system that can be used to determine the thermal diffusivity of the bed (ab, m2 h-1 ) (Fig. 20.1), from which the thermal conductivity of the bed (kb, J h- m-°C-1) can be calculated by the following equation:
where CPb is the heat capacity of the bed (J kg-bed-1 °C-1) and pb is the bed density (kg m-3-bed). Over a 10-day fermentation of sorghum mash, the thermal diffusiv-
ity of the bed varied between 3.8x10- m h- and 4.0x10- m h-, indicating that the thermal diffusivity itself does not change significantly as a result of microbial
Ts from surface thermocouple (on inside surface)
4 cylindrical copper tube waterbath controlled at Tw
analysis of heating curve to determine thermal diffusivity
Fig. 20.1 Apparatus that can be used for the determination of the thermal diffusivity of a solid substrate (adapted from Lai et al. 1989). For the determination of thermal diffusivity, the "diffusivity cell" was initially equilibrated at 20°C and then quickly transferred to a 46°C waterbath growth. However, it will be sensitive to any changes in the bed packing density and bed moisture content, as shown by the work of Costa et al. (1998) who determined the thermal conductivity of defatted rice bran over a range of packing densities and moisture contents, and derived the following equation:
kb = 47.508 +0.0115^ + 0.1295M -6.0737lnpb - 5.5555lnM, (20.2)
where kb is in J s-1 m-1 °C-1, pb is the bed packing density (kg m-3), and M is the percentage moisture content (wet basis). Under the various conditions tested, the value of kb varied between 0.1166 and 2.6551 J s-1 m-1 °C-1. Oostra et al. (2000) determined the thermal conductivity of moisturized oats, with a water content of 1.1 kg-water kg-dry-matter-1, as 0.1 J s-1 m-1 °C-1.
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