Nonisothermal Heterogeneous Systems

In this section we develop the heat-balance design equations for heterogeneous systems. Based on the previous sections it is clear how to use the heat-balance and heat-balance design equations that were developed earlier for homogeneous systems, as well as the principles that were used to develop the mass-balance and mass-balance design equations for heterogeneous systems for our purpose. We will start with lumped systems. 

We have developed the following heat-balance equation earlier in Chapter 3  

Recall how to transform this enthalpy equation into an enthalpy difference equation using enthalpy of each component at the reference condition Hir. Thus 

This term can be replaced by using the mass-balance relation 

In order to convert equation (6.66) into a nonisothermal heat-balance design equation, we replace r with r V, where r is the rate of reaction per unit volume V and V is the volume of the reactor. Then equation (6.66) becomes 

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The same very simple principles apply to the heat-balance equations for nonisothermal system and also to distributed systems as will be shown in the following subsections. The same principles also apply to heterogeneous systems. 

Example 9.16 Nonisothermal heterogeneous autocatalytic reactions-diffusion system Consider an autocatalytic... 

Example 9.11 Nonisothermal heterogeneous autocatalytic reaction-diffusion system... 

The purpose of the recent work just reviewed was to develop and verify a reasonably simplified theoretical approach to heterogeneous reactions in a nonisothermal low pressure plasma. With this purpose in mind, we first considered a simple statistical model of the plasma which has brought about a better understanding of the dependence of the chemical composition of the plasma on energy. Comparison of this model with several real systems which had been experimentally investigated illustrated the applicability of the theoretical ideas to such systems as well as their limitations. 

Multiplicity of steady states not only occurs in nonisothermal systems. In the 1950s and 1960s, this phenomenon was found in many isothermal heterogeneous catalytic oxidation systems such as the platinum-catalyzed oxidation of hydrogen and carbon monoxide. 

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