Homogeneous continuum heat transfer models

Homogeneous Continuum Heat Transfer Models We shall confine our study to homogeneous continuum models... 

In this paper the coupled elliptic partial differential equations arising from a two-phase homogeneous continuum model of heat transfer in a packed bed are solved, and some attempt is made to discriminate between rival correlations for those parameters not yet well-established, by means of a comparison with experimental results from a previous study (, 4). 

Quasi-continuum models Of these, the quasi-continuum model is the most common. Here, the solid-fluid system is considered as a single pseudo-homogeneous phase with properties of its own. These properties, for example, diffusivity, thermal conductivity, and heat transfer coefficient, are not true thermodynamic properties but are termed as effective properties that depend on the properties of the gas and solid components of the pseudo-phase. Unlike in simple homogeneous systems, these properties are anisotropic, that is, they have different values in the radial and axial directions. KuUcami and Doraiswamy (1980) have compiled all the equations for predicting these effective properties. Both radial and axial gradients can be accounted for in this model, as well as the fact that the system is really heterogeneous and hence involves transport effects both within the particles and between the particles and the flowing fluid. 

Simplified models that do not make a priori assumptions about one or more dominant resistances are often of the 1-D macrohomogeneous type. The 1-D assumption is similar to that in mass transfer-based models. The assumption of macrohomogeneity, based on work by Newman and Tobias [50], has proven useful in battery and fuel cell electrode modelling. It implies that the microstructure of the electrode is homogeneous at the level of the continuum equations governing mass transfer, heat transfer, and current conduction in the electrode (Eqs. (l)-(7) and (33)-(37)). This type of model can exploit solutions available in chemical reaction engineering practice and has been elaborated by several researchers in that field [51-55],... 

Classical chemical engineering has been intensively developed during the last century. Theoretical backgrounds of momentum, mass, energy balances, and equilibrium states are commonly used as well as chemical thermodynamics and kinetics. Physical and mathematical formalisms are related to heat, mass, and momentum transfer phenomena as well as to homogeneous and heterogeneous catalyses. Entire object models, continuum models, and constrained continuum models are frequently used for the description of the events, and for equipment designing. Usual, principal. 

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