Balances and conservation principles

Formulating mathematical models by applying balance and conservation principles and constitutive relations for fluxes is the topic of this chapter. The aim is to give the reader tools and skills for  

This relation is very general. The objective of model building is to transform the verbal concept into mathematical statements that are specific to the quantify of interest. We may balance mass, energy, and momentum as well as, for example, entropy and countable entities such as size and age distributions (population balances). Some of these entities are conserved, for example total mass, whilst some are not, for example the mass of a species in a mixture (due to chemical reactions). 

By using the balance principle, we can derive model equations balancing the quantities within the defined system boundary. A few examples of important balance equations are given in the following. 

The overall total mass balance describes the total mass in a system. Obviously there can be only one total mass balance equation, and the net generation term is zero, which means that mass is a conserved quantity. 

Most chemical engmeermg systems contain more than one component. In contrast to the total mass, the components or species are not always conserved they may be generated or consumed due to chemical reactions. In this case, the net generation rate within the system must be quantified by reaction rate equations. 

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