metabolic heat production heat removal through the wall heat removal by the dry air

- FAHvap(H - Hin) latent heat removal by evaporation

- FCPvapor(HT-HjnTjn) sensible heat removal by water vapor many of the terms within the balance equations describe transport phenomena and these equations include the various operating variables

Variables, related with the aeration, agitation, and cooling systems, that can be manipulated by the operator. In this case the conditions of the inlet air (F, Hn, and Tin) and the temperature of the surroundings TSurr (which could be water in a cooling jacket)

Fig. 12.4. A simple mathematical model for predicting the temperature within a well-mixed SSF bioreactor: The model equations, showing the kinetic and balance/transport submodels and their interrelations

Operating variables. These are variables that we can control the value of and which affect the performance of the bioreactor. We can use these in an attempt to control the state variables at their optimum values for the fermentation. In the current example, the operating variables are the conditions of the inlet air (F, Hin, and Tin) and the temperature of the surroundings Tsutr.

Parameters. These represent various physical and biological properties of the system. They may be constants or their value at a certain time and position might depend on the state of the system (e.g., its temperature). In SSF systems there are various different types of parameters:

• design parameters, related to how the bioreactor was built. For example, in the current example, the area for heat transfer (A) is a design parameter.

• transport parameters, related to the transport of material and energy within and between phases. For example, in the current example, the coefficient for heat transfer between the bioreactor wall and the cooling water (h, J m-2 s-1 °C-1) is a transport parameter.

• thermodynamic parameters, related to quantities of energy and the equilibrium state of materials. The enthalpy of vaporization of water (AHvap) is one of the thermodynamic parameters in the current example.

• biological parameters, related to the behavior of the microorganism. In the current example, the maximum possible biomass content (Xmax) and the yield of waste metabolic heat from growth (Yq) are biological parameters.

Figure 12.5 shows various variables and parameters that might be included within bioreactor models that are more complex than the simple model shown in Fig. 12.4. The biological parameters are addressed in detail in Chaps. 14 to 17 while the transport and thermodynamic parameters are addressed in Chaps. 19 and 20.

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