Heat and energy transport

The scientific basis of extractive metallurgy is inorganic physical chemistry, mainly chemical thermodynamics and kinetics (see Thermodynamic properties). Metallurgical engineering reties on basic chemical engineering science, material and energy balances, and heat and mass transport. Metallurgical systems, however, are often complex. Scale-up from the bench to the commercial plant is more difficult than for other chemical processes. 

The main problem in the system design is the heat and vapor transport in and out of the adsorbent. Advanced heat exchanger technologies have to be implemented in order to keep up the high energy density in the storage, which would be reduced by the amount of inactive heat exchanger material. 

The energy equation follows from Equation (3.45) where the loss terms are grouped to include both heat and enthalpy transport rates as Q. ... 

In this paper a transfer model will be presented, which can predict mass and energy transport through a gas/vapour-liquid interface where a chemical reaction occurs simultaneously in the liquid phase. In this model the Maxwell-Stefan theory has been used to describe the transport of mass and heat. On the basis of this model a numerical study will be made to investigate the consequences of using the Maxwell-Stefan equation for describing mass transfer in case of physical absorption and in case of absorption with chemical reaction. Despite the fact that the Maxwell-Stefan theory has received significant attention, the incorporation of chemical reactions with associated... 

To model mass and energy transport in monolith systems, several approaches are discussed, leading from a representative channel spatially ID approach to 2D (1D+1D) modeling explicitly including washcoat diffusion. Correlations are given to describe heat and mass transfer between bulk gas phase and catalytic washcoat. For the detailed study of reaction-transport interactions in the porous catalytic layer, the spatially 3D model of the computer-reconstructed washcoat section can be employed. 

If we can expect that the eddy momentum and energy transport will both be increased in the same proportion compared with their molecular values, we might anticipate that heat-transfer coefficients can be calculated by Eq. (5-56) with the ordinary molecular Prandtl number used in the computation. It turns out that the assumption that Pr, = Pr is a good one because heat-transfer calculations based on the fluid-friction analogy match experimental data very well. For this calculation we need experimental values of C/ for turbulent flow. 

The close interrelations among mass, momentum, and energy transport can be explained in terms of a molecular theory of monatomic gases at low density. The continuity, motion, and energy equations can all be derived from the Boltzmann equation for the velocity distribution function, from which the molecular expressions for the flows and transport properties are produced. Similar derivations are also available for polyatomic gases, monatomic liquids, and polymeric liquids. For monatomic liquids, the expressions for the momentum and heat flows include contributions associated with forces between two molecules. For polymers, additional forces within the polymer chain should be taken into account. 

Penetration Depth Heat Production Mass and Energy Transport... 

The following discussion shows how the chemical composition, rate of formation, and heat of combustion of the pyrolysis products are affected by the variations in the composition of the substrate, the time and temperature profile, and the presence of inorganic additives or catalysts. The latter aspect, however, is discussed in more detail in Chapter 14. Combustion may be defined as complex interactions among fuel, energy, and the environment. Consequently, the combustion process is controlled not only by the above chemical factors, but also by the physical properties of the substrate and other prevailing conditions affecting the phenomena of heat and mass transport. Discussion of this phenomenon is beyond the scope of this chapter. 

The phenomenon of charge transport, which is unique to all electrochemical processes, must be considered along with mass, heat, and momentum transport. The charge transport determines the current distribution in an electrochemical cell, and has far-reaching implications on the current efficiency, space-time yield, specific energy consumption, and the scale-up of electrochemical reactors. 

In addition to the complex flow structure encountered in these reactor systems, typically one has to deal with component and energy transport within the individual phases and momentum, heat and mass transfer both between the various phases and to the external reactor walls. The interactions with chemical reaction kinetics are difficult both with respect to physical modeling and numerical solution approximations due to the very wide range of time and length scales involved. 

The discussion in the previous sections concentrated on transport by a single carrier, that is, heat conduction by electrons or phonons, charge transport by electrons, and energy transport... 

Based on the mechanism of nonequilibrium Joule heating, the governing equations for charge and energy transport are... 

An alternative interpretation may be ascribed to the Reynolds number, consistent with our earlier analogy of the similarity of momentum, heat, and mass transport. We may then interpret the dimensionless parameters appearing in the energy and diffusion equations in an analogous manner that is. 

With the presence of the liquid-phase and interphase mass, momentum, and energy transport, additional source terms are added into the continuity, momentum, and scalar transport equations. As the droplets evaporate the heat of vaporization is taken from the gas phase and there is evaporative cooling of the surrounding gas. This gives rise to a sink term in the energy equation. By assuming adiabatic walls and unity Lewis number, the energy and scalar equations have the same boundary conditions and are linearly dependent [5]. 

General mass and momentum balances for an interfadal region were derived in Chapter 5 and used in the analyses of interfadal stability presented there. In dealing with heat and mass transport near interfaces we require additional balances for energy and individual spedes. 

The stability analysis is very similar to that of Section 8 except that there are equations analogous to Equations 6.61 and 6.62 for both heat and mass transport in the liquid. Moreover, interfacial conservation equations both for energy and for the reactant A must be invoked. 

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