Homogeneous continuum heat

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). 

In situations where the surrounding fluid behaves as a non-continuum fluid, for example at very high temperatures and/or at low pressures, it is possible for Nu to be less than 2. A gas begins to exhibit non-continuum behaviour when the mean free path between collisions of gas molecules or atoms with each other is greater than about 1/100 of the characteristic size of the surface considered. The molecules or atoms are then sufficiently far apart on average for the gas to begin to lose the character of a homogeneous or continuum fluid which is normally assumed in the majority of heat transfer or fluid... 

However, thermodynamics does not state how the heat transferred depends on this temperature driving force, or how fast or intensive this irreversible process is. It is the task of the science of heat transfer to clarify the laws of this process. Three modes of heat transfer can be distinguished conduction, convection, and radiation. The following sections deal with their basic laws, more in depth information is given in chapter 2 for conduction, 3 and 4 for convection and 5 for radiation. We limit ourselves to a phenomenological description of heat transfer processes, using the thermodynamic concepts of temperature, heat, heat flow and heat flux, fn contrast to thermodynamics, which mainly deals with homogeneous systems, the so-called phases, heat transfer is a continuum theory which deals with fields extended in space and also dependent on time. 

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. 

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. 

When a themally expansible homogeneous isotropic elastic continuum is deformed iso thermally the mechanical work done on the body is partly stored as internal energy partly converted to heat. In the range of strain up to about 10 percent (which is typical of natural rubber) the internal energy storage exceeds the work done so that heat must be added to the sample. Beyond the strain of 10 percent heat is increasingly liberated. An equivalent statement conveys the information that if the sample be stretched adiabatically there is an initial temperature drop then subsequent rise. 

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],... 

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