Modelling Based on Transport Phenomena

The transport phenomena of mass, heat or momentum, are characterized by an assembly of general equations which can be easily particularized. Each particularization of these equations to an actual example defines the mathematical model of the example. 

We consider that the notion introduced with the term transfer of property makes reference to the exchange between two fluids, which are separated by a thin wall (interface or membrane). We observe that the transfer includes the motion of the property in each fluid - a process frequently called transport (transport of property) as well as the transfer of the property through the wall. 

In the case of momentum transfer, we have a particular situation where the property transport occurs towards the walls and its transformation is controlled by the geometry of the wall. 

The problems of mathematical modelling based on transport phenomena always begin with the establishment of equations which are all based on the general equation for the conservation of properties [3.1-3.5]. 

Inside this microvolume and through its microsurface, the property is generated and transported as in the surface A and control volume V. 

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For the mathematical models based on transport phenomena as well as for the stochastic mathematical models, we can introduce new grouping criteria. When the basic process variables (species conversion, species concentration, temperature, pressure and some non-process parameters) modify their values, with the time and spatial position inside their evolution space, the models that describe the process are recognized as models with distributed parameters. From a mathematical viewpoint, these models are represented by an assembly of relations which contain partial differential equations The models, in which the basic process variables evolve either with time or in one particular spatial direction, are called models with concentrated parameters. 

At this time, only a small number of nanoscale processes are characterized with transport phenomena equations. Therefore, if, for example, a chemical reaction takes place in a nanoscale process, we cannot couple the elementary chemical reaction act with the classical transport phenomena equations. However, researchers have found the keys to attaching the molecular process modelling to the chemical engineering requirements. For example in the liquid-vapor equilibrium, the solid surface adsorption and the properties of very fine porous ceramics computed earlier using molecular modelling have been successfully integrated in modelling based on transport phenomena [4.14]. In the same class of limits we can include the validity limits of the transfer phenomena equations which are based on parameters of the thermodynamic state. It is known [3.15] that the flow equations and, consequently, the heat and mass transport equations, are valid only for the... 

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