Heat conduction mass transfer

Consider the heat conduction/mass transfer problem in a cylinder.[6] [9] [10] The governing equation in dimensionless form is... 

Heat and mass transfer are analogous processes. Molecular diffusion in homogeneous materials or phases is similar to heat transfer. Convective diffusion or convection in homogeneous materials or phases corresponds to heat transfer by convection. Mass transfer at the phase boundary corresponds to heat conduction. Mass transfer between phases occurs like heat transfer in several chronological steps. The slowest step controls the rate of the entire process. Thus the mathematical descriptions of heat and mass transfer operations are analogous. Calculation methods and approaches to calculate the heat transfer coefficients may similarly be used to calculate mass transfer coefficients. (See Table 1-18 in Chapter 1.7.2 for the analogy of heat and mass transfer.)... 

At high velocities where turbulence dominates, the main body of flowing fluid is well mixed in the direction normal to the flow, minor differences in temperature and concentration can be neglected, and the film concept can be applied. This describes the flow as if all gradients for temperature and concentration are in a narrow film along the interface with the solid (Nernst 1904), and inside the film conduction and diffusion are the transfer mechanisms. This film concept greatly simplifies the engineering calculation of heat and mass transfer. 

When a damp cloth is laid in an air flow, it settles after a certain time ic an equilibrium temperature, the so-called wet bulb temperature (0 ), which is determined through heat and mass transfer. Negotiating the heat flow obtained by radiation and conduction, the heat balance of the wet cloth in a stationary situation can be expressed as... 

Convection occurs in a moving fluid, generally from the fluid to a solid surface or vice versa. Although heat transfer between single particles is by conduction, it is the energy transfer with the matter that governs the heat transfer. The basic laws of heat and mass transfer have to be considered in order to describe convection mathematically. 

In the previous chapters, the stresses arising from relative motion within a fluid, the transfer of heat by conduction and convection, and the mechanism of mass transfer are all discussed. These three major processes of momentum, heat, and mass transfer have, however, been regarded as independent problems. 

Mala GM, Li D, Werner C (1997b) Flow characteristics of water through a micro-channel between two parallel plates with electro kinetic effects. Int J Heat Fluid Flow 18 491 96 Male van P, Croon de MHJM, Tiggelaar RM, Derg van den A, Schouten JC (2004) Heat and mass transfer in a square micro-channel with asymmetric heating. Int J Heat Mass Transfer 47 87-99 Maranzana G, Perry I, Maillet D (2004) Mini- and micro-channels influence of axial conduction in the walls. Int J Heat Mass Transfer 47 3993 004 Maynes D, Webb BW (2003) Full developed electro-osmotic heat transfer in microchannels. Int J Heat Mass Transfer 46 1359-1369... 

We studied the polyamidation of nylon 4,6, and varied the reaction time, reaction temperature, partical size, starting molecular weight, and type of reactor gas. At the same time we looked at the molecular weight broadening and the degradation with colour formation. In order to have good heat and mass transfer the reactions were mainly conducted on fine powder in a fluidized bed reactor and with dry nitrogen as carrier gas. 

The analogies between heat and mass transfer are reflected in the equations used to describe them. Thermal conduction is described by Fourier s law, which in one dimension is... 

In Volume 1, the behaviour of fluids, both liquids and gases is considered, with particular reference to their flow properties and their heat and mass transfer characteristics. Once the composition, temperature and pressure of a fluid have been specified, then its relevant physical properties, such as density, viscosity, thermal conductivity and molecular diffu-sivity, are defined. In the early chapters of this volume consideration is given to the properties and behaviour of systems containing solid particles. Such systems are generally more complicated, not only because of the complex geometrical arrangements which are possible, but also because of the basic problem of defining completely the physical state of the material. 

There is apparently an inherent anomaly in the heat and mass transfer results in that, at low Reynolds numbers, the Nusselt and Sherwood numbers (Figures. 6.30 and 6.27) are very low, and substantially below the theoretical minimum value of 2 for transfer by thermal conduction or molecular diffusion to a spherical particle when the driving force is spread over an infinite distance (Volume 1, Chapter 9). The most probable explanation is that at low Reynolds numbers there is appreciable back-mixing of gas associated with the circulation of the solids. If this is represented as a diffusional type of process with a longitudinal diffusivity of DL, the basic equation for the heat transfer process is ... 

Rapid evaporation introduces complications, for the heat and mass transfer processes are then coupled. The heat of vaporization must be supplied by conduction heat transfer from the gas and liquid phases, chiefly from the gas phase. Furthermore, convective flow associated with vapor transport from the surface, Stefan flow, occurs, and thermal diffusion and the thermal energy of the diffusing species must be taken into account. Wagner 1982) reviewed the theory and principles involved, and a higher-order quasisteady-state analysis leads to the following energy balance between the net heat transferred from the gas phase and the latent heat transferred by the diffusing species ... 

Since the results of zone refining depend on the interaction of momentum, heat and mass transfer in the system, all the basic factors affecting these three processes, both molecular and convective, have to be taken into consideration. These basic factors are concentration W, Density f, viscosity /i, heat capacity Cp, temperature den-sification coefficient, thermal conductivity k, molecular dif-fusivity D, zone diameter d, zone length L, zone travel speed u, temperature difference in zone A T and acceleration g. The concentration W may affect, JJi, Cp,, k, and D as well as the properties of the P.S.Z. (mushy region). Aside from the concentration W, all... 

The most important processes in monolith channel convection of exhaust gas, heat and mass transfer between the flowing gas and the washcoat, internal diffusion, catalytic reactions in the washcoat, heat and mass accumulation and heat conduction—are schematically depicted in Fig. 7. 

The following, well-acceptable assumptions are applied in the presented models of automobile exhaust gas converters Ideal gas behavior and constant pressure are considered (system open to ambient atmosphere, very low pressure drop). Relatively low concentration of key reactants enables to approximate diffusion processes by the Fick s law and to assume negligible change in the number of moles caused by the reactions. Axial dispersion and heat conduction effects in the flowing gas can be neglected due to short residence times ( 0.1 s). The description of heat and mass transfer between bulk of flowing gas and catalytic washcoat is approximated by distributed transfer coefficients, calculated from suitable correlations (cf. Section III.C). All physical properties of gas (cp, p, p, X, Z>k) and solid phase heat capacity are evaluated in dependence on temperature. Effective heat conductivity, density and heat capacity are used for the entire solid phase, which consists of catalytic washcoat layer and monolith substrate (wall). 

Because of the very small fluid channels (Re is very small), the flows in microreactor systems are always laminar. Thus, mass and heat transfers occur solely by molecular diffusion and conduction, respectively. However, due to the very small transfer distances, the coefficients of mass and heat transfer are large. Usually, film coefficients of heat and mass transfer can be estimated using Equations 5.9b and 6.26b, respectively. 

The second part of the chapter is devoted to the effect of pressure on heat and mass transfer. After a brief survey on fundamentals the estimation of viscosity, diffusivity in dense gases, thermal conductivity and surface tension is explained. The application of these data to calculate heat transfer in different arrangements and external as well as internal mass transfer coefficients is shown. Problems at the end of the two main parts of this chapter illustrate the numerical application of the formulas and the diagrams. 

The starting point of a number of theoretical studies of packed catalytic reactors, where an exothermic reaction is carried out, is an analysis of heat and mass transfer in a single porous catalyst since such system is obviously more conductive to reasonable, analytical or numerical treatment. As can be expected the mutual interaction of transport effects and chemical kinetics may give rise to multiple steady states and oscillatory behavior as well. Research on multiplicity in catalysis has been strongly influenced by the classic paper by Weisz and Hicks (5) predicting occurrence of multiple steady states caused by intrapellet heat and mass intrusions alone. The literature abounds with theoretical analysis of various aspects of this phenomenon however, there is a dearth of reported experiments in this area. Later the possiblity of oscillatory activity has been reported (6). 

The gas velocity affects heat and mass transfer between the particles and flowing gas as well as the axial dispersion and heat conduction phenomena. For a reactor operating near at the extinction boundary, an increase of inlet velocity results in a sudden decrease of exit conversion. Sometimes this effect is called the blow-out phenomenon (Fig. 17). On the other hand, for a very active catalyst a decrease of inlet velocity leads to an ignited upper steady state. 

Here we consider a spherical catalyst pellet with negligible intraparticle mass- and negligible heat-transfer resistances. Such a pellet is nonporous with a high thermal conductivity and with external mass and heat transfer resistances only between the surface of the pellet and the bulk fluid. Thus only the external heat- and mass-transfer resistances are considered in developing the pellet equations that calculate the effectiveness factor rj at every point along the length of the reactor. 

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

The governing heat transfer modes in gas-solid flow systems include gas-particle heat transfer, particle-particle heat transfer, and suspension-surface heat transfer by conduction, convection, and/or radiation. The basic heat and mass transfer modes of a single particle in a gas medium are introduced in Chapter 4. This chapter deals with the modeling approaches in describing the heat and mass transfer processes in gas-solid flows. In multiparticle systems, as in the fluidization systems with spherical or nearly spherical particles, the conductive heat transfer due to particle collisions is usually negligible. Hence, this chapter is mainly concerned with the heat and mass transfer from suspension to the wall, from suspension to an immersed surface, and from gas to solids for multiparticle systems. The heat and mass transfer mechanisms due to particle convection and gas convection are illustrated. In addition, heat transfer due to radiation is discussed. 

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