Heat and mass 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 majority of the cyanuric acid produced commercially is made via pyrolysis of urea [57-13-6] (mp 135°C) primarily employing either directiy or indirectly fired stainless steel rotary kilns. Small amounts of CA are produced by pyrolysis of urea in stirred batch or continuous reactors, over molten tin, or in sulfolane. The feed to the kilns can be either urea soHd, melt, or aqueous solution. Since conversion of urea to CA is endothermic and goes through a plastic stage, heat and mass transport are important process considerations. The kiln operates under slight vacuum. Air is drawn into the kiln to avoid explosive concentrations of ammonia (15—27 mol %). 

C. Heat and Mass Transport from the Gases to the Solid Surfaces.. 101... 

Estimation of parameters. Model parameters in the selected model are then estimated. If available, some model parameters (e.g. thermodynamic properties, heat- and mass-transfer coefficient, etc.) are taken from literature. This is usually not possible for kinetic parameters. These should be estimated based on data obtained from laboratory expieriments, if possible carried out isothermal ly and not falsified by heat- and mass-transport phenomena. The methods for parameter estimation, also the kinetic parameters in complex organic systems, and for discrimination between models are discussed in more detail in Section 5.4.4. More information on parameter estimation the reader will find in review papers by Kittrell (1970), or Froment and Hosten (1981) or in the book by Froment and Bischoff (1990). 

Heat and Mass Transport Hygroscopicity James Wright... 

A deliquescent material takes up moisture freely in an atmosphere with a relative humidity above a specific, well-defined critical point. That point for a given substance is defined as the critical relative humidity (RH0). Relative humidity (RH) is defined as the ratio of water vapor pressure in the atmosphere divided by water vapor pressure over pure water times 100% [RH = (PJP0) X 100%]. Once moisture is taken up by the material, a concentrated aqueous solution of the deliquescent solute is formed. The mathematical models used to describe the rate of moisture uptake involve both heat and mass transport. 

Since heat transport is unfamiliar to many pharmaceutical scientists, this chapter begins with a discussion of vapor-liquid equilibria, heat transport in rectangular coordinates, and heat transport in spherical coordinates. Once these basic principles are established, we can build models based on heat transport. Heat transport is the dominant mechanism for moisture uptake in an atmosphere of pure water vapor. In air, however, both heat and mass transport are involved. 

The solutions for moisture uptake presented in this section are based on the experimental condition of a pure water vapor atmosphere. In the next section a derivation of moisture uptake equations is based on both heat and mass transport that are characteristic of moisture uptake in air. The final section of this chapter presents the results of studies where heat transport is unimportant and mass transport dominates the process. Thus, we will have a collection of solutions covering models that are (1) heat transport limited, (2) mass transport limited, (3) heat and mass transport limited, and (4) mass transport limited with a moving boundary for the uptake of water by water-soluble substances. 

This review contains a great deal of information about the thermochemical conversion chemistry. The reader is referred to the original paper (Appendix B) for details. Here follows some of the most important findings on the heat and mass transport phenomena in a packed bed during thermochemical conversion. 

Appendix B includes a review and a classification of conversion concepts. It also investigates the potentials to develop an all-round bed model or CFSD code simulating the conversion system. This review also contains a great deal of information on the heat and mass transport phenomena taking place inside a packed bed in the context of PBC of biomass. The phenomena include conversion regimes, pyrolysis chemistry, char combustion chemistry, and wood fuel chemistry. The main conclusions from this review are ... 

This appendix consists of two parts, (a) a conceptual classification and review of the conversion system and (b) a review of conceptual models applied to the heat and mass transport of the thermochemical conversion of biomass. Both these parts are analysed in the context of PBC and the three-step model. Mathematical modelling is outside the scope of this survey. 

Below is a review of some of the most important conceptual models applied to describe the heat and mass transport phenomena and chemistry with respect to the thermochemical conversion of solid fuels in general and biofuels in particular, in the context of the three-step model. 

The thermochemical conversion of biofuels takes place in the conversion system and belongs to the science of two-phase phenomena (fluid-solid dynamics), that is, heat and mass transport processes take place inside and between a solid phase and a gas phase. This phenomenology is well illustrated by Balakrishnen and Pei [49], see Figure 40. 

Figure 40 The heat and mass transport mechanisms in a fuel bed. [49]...

Here follows a section outlining the heat and mass transport phenomena of the thermochemical conversion on both the micro- and the macro-scale of the fuel bed. Knowledge about the heat and mass transport phenomena on micro-scale is very important to be able to understand and model, for example, the mass flow of conversion gas. 

Figure 42 shows an overview of the heat and mass transport phenomena in the extraparticle and intraparticle phase during the thermochemical conversion of a single particle in one dimension. Several excellent reviews have been presented on this subject [22,23,39,54,55],... 

The heat and mass transport phenomena of the char gasification is not described in the literature as much as for the char combustion [11,28,78]. There are good reasons to believe that it is quite analogous to the char combustion phenomenology [79]. However, the heterogeneous gasification reactions are overall endothermic which results in some differences with respect to the intraparticle heat transport [79]. 

The heat and mass transport on the small scale during char combustion is similar to the single particle behaviour. The char combustion products generated in the intraparticle phase (see Figure 56) enter the interstitial gas flow, which transport it out of the bed by convection. 

One of the most important features of the heat and mass transport of the thermochemical conversion processes is the char combustion process, which can be divided into three oxidation regimes. The prevalent regime in PBC systems, labeled Regime III, is equivalent to conversion regime I and is controlled by interstitial gas diffusion of oxygen to the surface of the particle phase. 

As indicated by Fig. 23 and Fig. 24, the source function can be highly asymmetrical. For the liquid droplet corresponding to Fig. 23, one would expect the internal temperature to be higher near the back and front of the sphere because of the spikes in the source function in those regions. As a result, the evaporation rate should be enhanced at the rear stagnation point and the front of the sphere. To calculate the evaporation rate when internal heating occurs, one must solve the full problem of conduction within the sphere coupled with convective heat and mass transport in the surrounding gas. 

From an engineering perspective, deep-fat frying can be defined as a unit operation where heat and mass transport phenomena occur simultaneously. Convective heat is transferred from the frying media to the surface of the product, which is thereafter conducted within the food. Mass transfer is characterized by the loss of water from the food as water vapor and the movement of oil into the food (Singh, 1995). 

The radial dispersion coefficient for this case is, of course, the average eddy diffusivity as discussed in works on turbulence (H9). If the various analogies between momentum, heat, and mass transport are used. 

The gas film coefficient is dependent on turbulence in the boundary layer over the water body. Table 4.1 provides Schmidt and Prandtl numbers for air and water. In water, Schmidt and Prandtl numbers on the order of 1,000 and 10, respectively, results in the entire concentration boundary layer being inside of the laminar sublayer of the momentum boundary layer. In air, both the Schmidt and Prandtl numbers are on the order of 1. This means that the analogy between momentum, heat, and mass transport is more precise for air than for water, and the techniques apphed to determine momentum transport away from an interface may be more applicable to heat and mass transport in air than they are to the liquid side of the interface. 

---