Energy balance expressions dimensionless

The quantities h, f,. e, and do not change v/ith time, and thus we do not need to use the superscript / for them. Also, the energy balance expressions are simplified using the definitions of thermal diffusivity a = A/pCp and the dimensionless mesh Fourier number t = aUtiP, where Ax = Ay - I. 

Equation 5.2.18 is the dimensionless, differential energy balance equation of ideal batch reactors, relating the reactor dimensionless temperature, 0(t), to the dimensionless extents of the independent reactions, Z (t), at dimensionless operating time T. Note that individual dZ /dfr s are expressed by the reaction-based design equations derived in Chapter 4. 

The design equations and the species concentration relations contain another dependent variable, 6, the dimensionless temperature, whose variation during the reactor operation is expressed by the energy balance equation. For ideal batch reactors with negligible mechanical shaft work, the energy balance equation, derived in Section 5.2, is... 

In this chapter, the analysis of chemical reactors is expanded to additional reactor configurations that are commonly used to improve the yield and selectivity of the desirable products. In Section 9.1, we analyze semibatch reactors. Section 9.2 covers the operation of plug-flow reactors with continuous injection along their length. In Section 9.3, we examine the operation of one-stage distillation reactors, and Section 9.4 covers the operation of recycle reactors. In each section, we first derive the design equations, convert them to dimensionless forms, and then derive the auxiliary relations to express the species concentrations and the energy balance equation. 

The three-halves power of dimensionless temperature in the expression for eA( ) is based on the temperature dependence of gas-phase ordinary molecular diffusion coefficients when the catalytic pores are larger than 1 p.m. In this pore-size regime, Knudsen diffusional resistance is negligible. The temperature dependence of the collision integral for ordinary molecular diffusion, illustrated in Bird et al. (2002, pp. 526, 866), has not been included in ea) ). The thermal energy balance given by equation (27-28), which includes conduction and interdiffu-sional fluxes, is written in dimensionless form with the aid of one additional parameter,... 

Saatdjian and Large [7] observed that the heat transfer rate of the gas-flowing solids-fixed bed exchanger is determined by the fraction of active flowing solids. They developed an expression for thermal efficiency (dimensionless temperature), which was derived from energy balances for both the solids and gas phases ... 

The energy balance Equation 5.209 bears a mathematical resemblance to the mass balance Equation 5.178. Let us now introduce the dimensionless coordinates, z and according to expressions 5.179 and 5.180. Consequently, the energy balance Equation 5.209 is transformed to... 

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