Thermal mass transfer

Thermal mass transfer (see also Section 2.9) When a temperature gradient... 

Wood, J.R. (1986) Thermal mass transfer in systems containing quartz and calcite. In Roles of Organic Matter in Sediment Diagenesis (Ed. Gautier, D.L.), Spec. Publ. Soc. econ. Paleont. Miner., Tulsa, 38, 169-180. 

FIGURE 12 Thermal mass transfer printing process. [From Ohno, T. (1981). J. Appl. Photogr. Eng. 7, 171 by permission of the copyright holder, the Society for Imaging Science and Technology]. 

Caffeine is extracted from beverages by a solid-phase microextraction using an uncoated fused silica fiber. The fiber is suspended in the sample for 5 min and the sample stirred to assist the mass transfer of analyte to the fiber. Immediately after removing the fiber from the sample it is transferred to the gas chromatograph s injection port where the analyte is thermally desorbed. Quantitation is accomplished by using a C3 caffeine solution as an internal standard. 

The time constant R /D, and hence the diffusivity, may thus be found dkecdy from the uptake curve. However, it is important to confirm by experiment that the basic assumptions of the model are fulfilled, since intmsions of thermal effects or extraparticle resistance to mass transfer may easily occur, leading to erroneously low apparent diffusivity values. 

In general, the desorptive behavior of contaminated soils and soHds is so variable that the requited thermal treatment conditions are difficult to specify without experimental measurements. Experiments are most easily performed in bench- and pilot-scale faciUties. Full-scale behavior can then be predicted using mathematical models of heat transfer, mass transfer, and chemical kinetics. 

Mass Transfer and Kinetics in Rotary Kilns. The rates of mass transfer of gases and vapors to and from the sohds iu any thermal treatment process are critical to determining how long the waste must be treated. Oxygen must be transferred to the sohds. However, mass transfer occurs iu the context of a number of other processes as well. The complexity of the processes and the parallel nature of steps 2, 3, 4, and 5 of Figure 2, require that the parameters necessary for modeling the system be determined empirically. In this discussion the focus is on rotary kilns. 

A closer look at the Lewis relation requires an examination of the heat- and mass-transfer mechanisms active in the entire path from the hquid—vapor interface into the bulk of the vapor phase. Such an examination yields the conclusion that, in order for the Lewis relation to hold, eddy diffusivities for heat- and mass-transfer must be equal, as must the thermal and mass diffusivities themselves. This equahty may be expected for simple monatomic and diatomic gases and vapors. Air having small concentrations of water vapor fits these criteria closely. 

The thermal design of cooling towers follows the same general procedures already presented. Integration of equation 35 is usually done numerically using the appropriate software, mass-transfer coefficients, saturation enthalpies, etc. In mechanical-draft towers the air and water dows are both suppHed by machines, and hence dow rates are fixed. Under these conditions the design procedure is straightforward. 

In the mass-transfer limited region, conversion is most commonly increased by using more catalyst volume or by increasing cell density, which increases the catalytic wall area per volume of catalyst. When the temperature reaches a point where thermal oxidation begins to play a role, catalyst deactivation may become a concern. 

Consider a closed PVT system, either homogeneous or heterogeneous, of uniform T and P, which is in thermal and mechanical equilibrium with its surroundings, but which is not initially at internal equilibrium with respect to mass transfer or with respect to chemical reaction. Changes occurring in the system are then irreversible, and must necessarily bring the system closer to an equihbrium state. The first and second laws written for the entire system are... 

Thermal Design If the controUing resistance for heat and mass transfer in the vapor is sensible-heat removal from the cooling vapor, the following design equation is obtained ... 

Many reactions of solids are industrially feasible only at elevated temperatures which are often obtained by contact with combustion gases, particularly when the reaction is done on a large scale. A product of reaction also is often a gas that must diffuse away from a remaining solid, sometimes through a solid product. Thus, thermal and mass-transfer resistances are major factors in the performance of solid reactions. 

K = Equilibrium constant equals y/x Kp = Diffusivity. ft"/hr Km = Mass transfer coefficient, Ib/hrft Ay Kf = Thermal conductivity, Btu/hrft"(°F/ft)... 

Conduction takes place at a solid, liquid, or vapor boundary through the collisions of molecules, without mass transfer taking place. The process of heat conduction is analogous to that of electrical conduction, and similar concepts and calculation methods apply. The thermal conductivity of matter is a physical property and is its ability to conduct heat. Thermal conduction is a function of both the temperature and the properties of the material. The system is often considered as being homogeneous, and the thermal conductivity is considered constant. Thermal conductivity, A, W m, is defined using Fourier s law. 

The Fourier law gives the rate at which heat is transferred by conduction through a substance without mass transfer. This states that the heat flow rate per unit area, or heat flux, is proportional to the temperature gradient in the direction of heat flow. The relationship between heat flux and temperature gradient is characterized by the thermal conductivity which is a property of the substance. It is temperature dependent and is determined experimentally. 

Convective heat transmission occurs within a fluid, and between a fluid and a surface, by virtue of relative movement of the fluid particles (that is, by mass transfer). Heat exchange between fluid particles in mixing and between fluid particles and a surface is by conduction. The overall rate of heat transfer in convection is, however, also dependent on the capacity of the fluid for energy storage and on its resistance to flow in mixing. The fluid properties which characterize convective heat transfer are thus thermal conductivity, specific heat capacity and dynamic viscosity. 

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