Unsteady state energy balances

Several other dehnitions need to be discussed here. Steady-state behavior pertains to the case where there is no variation in the process variables with respect to time. If the system is in equilibrium (at steady state), it can be described by algebraic equations, such as material and energy balances. Unsteady-state (dynamic) behavior occurs when the process variables change as a function of time. The required mathematical model for this case includes ordinary differential equations as well as algebraic relationships. 

To describe the dynamic behaviour of this semi-batch process, unsteady-state mass and energy balances are needed. Their interrelationships are depicted in Fig. 3.65. 

The input and output terms of equation 1.5-1 may each have more than one contribution. The input of a species may be by convective (bulk) flow, by diffusion of some kind across the entry point(s), and by formation by chemical reaction(s) within the control volume. The output of a species may include consumption by reaction(s) within the control volume. There are also corresponding terms in the energy balance (e.g., generation or consumption of enthalpy by reaction), and in addition there is heat transfer (2), which does not involve material flow. The accumulation term on the right side of equation 1.5-1 is the net result of the inputs and outputs for steady-state operation, it is zero, and for unsteady-state operation, it is nonzero. 

Similarly, energy balances in the reactor and the jacket can be drawn. However, the energy balance in the reactor can be rather complicated depending on the rate law and the stoichiometry of the reaction [3], [9], [14]. The general equation of the unsteady state of the energy balance is the following ... 

The energy balance (3.301) is applicable for catalysis, adsorption, and ion exchange. More specifically, in catalysis, where the steady-state condition exists, frequently the accumulation term is zero. In contrast, adsorption and ion exchange operate under unsteady-state condition. The analysis of the energy balance equation for catalytic fixed beds is presented in detail in Section 5.3.4. 

The temperature of the thermocouple 0, will also vary with time. It is required to determine the relationship between 0O and 0,. Writing an unsteady-state energy balance for the junction ... 

Using the usual assumptions, we obtain the following dimensionless unsteady-state material and energy balance equations for the dense (emulsion) phase of the bubbling fluidized bed ... 

UN-SS Energy Balance. To predict the outlet temperature, an unsteady-state (UN-SS), energy balance (1) must be written around the reactor jacket. That balance is ... 

Comparison of Redler and Zippered Belt Conveyors 88 Density of a Nonideal Gas from Its Equation of State 91 Unsteady Flow of an Ideal Gas through a Vessel 93 Units of the Energy Balance 94... 

The unsteady-state energy balance for an open system that has n species, each entering and leaving the system at its respective molar flow rates Fi (moles of i per time) and with its respective energy (joules per mole of i), is... 

Up to now we have focused on the steady-state operation of nonisothermal reactors. In this section the unsteady-state energy balance wtU be developed and then applied to CSTRs, plug-flow reactors, and well-mixed batch and semibateh reactors. 

We begin by recalling the unsteady-state form of the energy balance developed in Chapter 8. 

The mathematical model consists of the unsteady state energy balance in the dried and frozen regions ... 

Write down the macroscopic unsteady-state material and energy balances in words and in symbols. 

Unsteady-State Material and Energy Balances Chap. 6... 

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