Nonisothermicity

Mittemeijer E J, Cheng L, der Schaaf P J V, Brakman C M and Korevaar B M 1988 Analysis of nonisothermal transformation kinetics tempering of iron-carbon and iron-nitrogen martensites Metall. Trans. A 19 925... 

Mittemeijer E J, Gent A V and der Schaaf P J V 1986 Analysis of transformation kinetics by nonisothermal dilatometry Metall. Trans. A 17 1441... 

Nonvolatile Solvents. In practice, some gases tend to Hberate such large amounts of heat when they are absorbed into a solvent that the operation caimot be assumed to be isothermal, as has been done thus far. The resulting temperature variations over the tower will displace the equiUbrium line on 2tj—x diagram considerably because the solubiUty usually depends strongly on temperature. Thus nonisothermal operation affects column performance drastically. 

Fig. 9. Simple model of adiabatic gas absorption. A, nonisotherm a1 equihbrium line for overall gas-phase driving force y = B, nonisotherm a1...

Fig. 15. Correlation of effective average slope m of nonisothermal equilibrium line (concentrated part of absorber) equilibrium line concave downward. The...

Fig. 16. Correlation of the Hquid concentration at which the inflection point of the nonisothermal equihbrium occurs (45).

Nonisothermal Gas Absorption. The computation of nonisothermal gas absorption processes is difficult because of all the interactions involved as described for packed columns. A computer is normally required for the enormous number of plate calculations necessary to estabUsh the correct concentration and temperature profiles through the tower. Suitable algorithms have been developed (46,105) and nonisothermal gas absorption in plate columns has been studied experimentally and the measured profiles compared to the calculated results (47,106). Figure 27 shows a typical Hquid temperature profile observed in an adiabatic bubble plate absorber (107). The close agreement between the calculated and observed profiles was obtained without adjusting parameters. The plate efficiencies required for the calculations were measured independendy on a single exact copy of the bubble cap plates installed in the five-tray absorber. 

A general, approximate, short-cut design procedure for adiabatic bubble tray absorbers has not been developed, although work has been done in the field of nonisothermal and multicomponent hydrocarbon absorbers. An analytical expression which will predict the recovery of each component provided the stripping factor, ie, the group is known for each component on each tray of the column has been developed (102). This requires knowledge... 

For an isothermal system the simultaneous solution of equations 30 and 31, subject to the boundary conditions imposed on the column, provides the expressions for the concentration profiles in both phases. If the system is nonisotherm a1, an energy balance is also required and since, in... 

This development has been generalized. Results for zero- and second-order irreversible reactions are shown in Figure 10. Results are given elsewhere (48) for more complex kinetics, nonisothermal reactions, and particle shapes other than spheres. For nonspherical particles, the equivalent spherical radius, three times the particle volume/surface area, can be used for R to a good approximation. 

Because the system likely is nonisothermal, the analysis of a closed-desiccant system requites knowledge of the temperature of the desiccant as well as the dew point (ice point) or water concentration (partial pressure) specification. Indeed, the whole system may undergo periodic temperature transients that may compHcate the analysis. Eor example, in dual-pane windows the desiccant temperature is approximately the average of the indoor and outdoor temperatures after a night of cooling. However, after a day in the sun, the desiccant temperature becomes much warmer than the outdoor temperature. When the sun sets, the outdoor pane cools quickly while the desiccant is still quite warm. The appropriate desiccant for such an appHcation must have sufficient water capacity and produce satisfactory dew points at the highest temperatures experienced by the desiccant. 

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

For nonisothermal flow of liquids across tube bundles, the fric tion factor is increased if the liquid is being cooled and decreased if the liquid is being heated. The factors previously given for nonisotherm flow of liquids in pipes ( Tncompressible Flow in Pipes and Channels ) should be used. 

Computational fluid dynamics (CFD) emerged in the 1980s as a significant tool for fluid dynamics both in research and in practice, enabled by rapid development in computer hardware and software. Commercial CFD software is widely available. Computational fluid dynamics is the numerical solution of the equations or continuity and momentum (Navier-Stokes equations for incompressible Newtonian fluids) along with additional conseiwation equations for energy and material species in order to solve problems of nonisothermal flow, mixing, and chemical reaction. 

Phenomena of multiple steady states and instabilities occur particularly with nonisothermal CSTRs. Some isothermal processes with hyperbohc rate equations and processes with porous catalysts also can have such behavior. 

Minimum reactor volumes of isothermal and nonisothermal cascades by dynamic programming... 

Coil-in-Tank or Jacketed Vessel Nonisothermal Heating Medium... 

External Exchanger with Liquid Continuously Added to Tank Nonisothermal Cooling Medium... 

The downflow condenser is used mainly for nonisothermal condensation. Vapors enter through a header at the top and flow downward. The refliix condenser is used for isothermal and small-temperature-change conditions. Vapors enter at the bottom of the tubes. 

Local equilibrium theory Shows wave character—simple waves and shocks Usually indicates best possible performance Better understanding Mass and heat transfer very rapid Dispersion usually neglected If nonisothermal, then adiabatic... 

Nonisothermal hquid-phase processes may be driven by changes in feed temperature or heat addition or withdrawal through a column wall. For these, heats of adsorption and pressure effects are generally of less concern. For this case a suitable energy balance is... 

Simulritiun of a nonisothermal batch reactor Concentration versus time... 

Nonisothermal reaction in a batch reactor Acetylated Castor Oil Hydrolysis... 

Omoleye, J. A., Adesina, A. A., and Udegbunam, E. O., Optimal design of nonisothermal reactors Derivation of equations for the rate-temperature conversion profile and the optimum temperature progression for a general class of reversible reactions, Chem. Eng. Comm., Vol. 79, pp. 95-107, 1989. 

To characterize the relationship between the buoyancy forces and momentum flux in different cross-sections of a nonisothermal jet at some distance x, Grimitlyn proposed a local Archimedes number ... 

Introduction of the local Archimedes criterion helped to clarify nonisothermal jet design procedure. Grimitlyn suggested critical local Archimedes number values, Ar , below which a jet can be considered unaffected by buoyancy forces (moderate nonisothermal jet) Ar, 0.1 for a compact jet, Ar, < 0.15 for a linear jet. 

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