Sigmoidal heat production function

The diagram representing the sigmoidal heat production function and the line of heat removal shows that the wire ignites at a gas preheating temperature of around 150°C, which leads to a wire temperature of around 900°C. 

Figure 4.5.12 shows the overall sigmoidal curve of the heat production function and selected hnes representing the heat removal for different gas phase temperatures. 

Figure4.10.26 Heat production function (sigmoidal curve) and heat removal lines for an exothermic first-order reaction in an adiabatic CSTR.

A steady-state analysis can also predict the stability of a chemical reactor. Such an analysis is carried out by plotting the heat production and heat removal as a function of reactor temperature. Usually the heat production curve is sigmoid while that for heat removal is linear. Any intersection of the two curves results in a steady-state condition. Figure 4.11 shows that three intersections are possible (Van Heerden, 1953). If the slope of the heat production curve is greater than that of the heat removal curve, then the steady state is unstable. This is illustrated by point B in Figure 4.11. If the slope of the heat production curve is less than that of the heat removal curve, then the steady state is stable. This is illustrated by points A and C. 

Cp n T) is the heat capacity function of the native state, ACp T) = Cp j) T)-Cp n(T) is the difference between the extrapolated heat capacity functions of the denatured and native states at temperature T, and the term ACpOiD describes the sigmoidal baseline under the transition peak. The term [A°/f°(T)] aDQ N characterises the heat absorption peak. The product Q n d = ctN(l Q n) is responsible for the appearance of the characteristic shape of the heat capacity peak. Typical curves are given in Figures 1 and 4. 

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