Thermal energy equation single component

For the purpose of understanding pressure filtering, attention may be restricted to the single-component, constant-property, nonreacting equations for a perfect gas. Introducing the nondimensional variables into the vector forms of the mass-continuity, constant-viscosity Navier-Stokes, and perfect-gas thermal-energy equations yields the following nondimensional system ... 

Introducing specific length and velocity scales provides a more intuitive approach to nondi-mensionalization. In this section the thermal-energy equation is also included in the analysis. Assuming constant transport properties and a single-component fluid, a subset of the governing equations is derived from Section 6.2 as... 

It is good practice to enumerate the unknowns and applicable equations when setting up a model for the noni so thermal semi-batch reactor. As discussed in Chapter 4, for a single-phase system, the molar concentrations of the components, and the temperature and the pressure specify all Intensive variables of the reactor. If we use the reactor volume as the single extensive variable, then we have + 3 unknowns. As in Chapter 4, we have n.s equations from the material balances and one equation of state. The energy balance of this chapter provides an additional equation. Finally, we must specify the reactor pressure or some other/System. coBStraint. that. determines the reactor pressure. 

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