Mass and Heat Transfer Coefficients

1 Heat and Mass Transfer Coefficients - While one-dimensional models are relatively easy to solve and offer the attraction of a substantial reduction in the 

1970-80 Hegedus (L), (S) Solid overtemperature can occur by the nature of the fuel and channel geometry 

1980-90 T ien (L), (T) Study of transient response in monolith combustors. Response delay due to substrate inertia 

Groppieta/. (L),(S) Parametric study of the influence of design variables in particular hybrid reactors 

Markatou et (D), (S) Detailed gas-phase chemistry for oxidation of methane. Both catalytic and non-catalytic surfaces were investigated 

The following section renders correlations, with which it is possible to determine heat and mass transfer coefficients for some cases significant to thermal process engineering. 

A reliable literature source for heat and mass transfer coefficients is the VDI-Heat Atlas (2010). 

For better clarity, only correlations for a-values or -numbers are given in the following sections. With (4.3-19) y -values can be derived and Sh -eorrelations ean then be derived from -correlations by exchanging the Prandtl nnmber Pr with the Schmidt number Sc. 

If a fluid flows past a plate at bulk velocity w, then close to the surface a velocity, temperature and concentration profile develops. These profiles are approximated by laminar boundary layers, of characteristic thickness. In these boundary layers the resistances to momentum, heat and mass transfer are located. As long as the Reynolds number Re = w L p/ rj, calculated with plate length L, is smaller than 10 , the flow is laminar. 

Solving the system of equations for conservation of energy, momentum, and mass for the longitudinal flow past a plate at constant wall temperature results in the following equation for the heat transfer coefficient (Pohlhausen 1921)  

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Thus, the enthalpy and temperature of the vapor—Hquid interface are related to the Hquid temperature and gas enthalpy at any point in the column through a ratio of heat- and mass-transfer coefficients. 

Not only is the type of flow related to the impeller Reynolds number, but also such process performance characteristics as mixing time, impeller pumping rate, impeller power consumption, and heat- and mass-transfer coefficients can be correlated with this dimensionless group. 

Stewart, W. S., Heat and Mass Transfer Coefficients for the System Air-Water in a Perforated Plate Column, thesis presented in partial fulfillment of Master s Degree in chemical engineering, Louisiana State University (1958). 

The heat and mass transfer coefficients are given in the literature usually in terms of the Sherwood and Nusselt numbers... 

When the gas velocities are increased, both the Reynolds number and the Nusselt number would increase, while the ratio Nu/Re decreases with (Re) to the —0.4 to —0.6 power. An increase in gas velocities would improve on the heat and mass transfer coefficients from gas to wall, but would also increase the fraction of heat that is not given up to the wall and the fraction of benzene that never goes near the wall due to the reduction in residence time. 

In addition, it was concluded that the liquid-phase diffusion coefficient is the major factor influencing the value of the mass-transfer coefficient per unit area. Inasmuch as agitators operate poorly in gas-liquid dispersions, it is impractical to induce turbulence by mechanical means that exceeds gravitational forces. They conclude, therefore, that heat- and mass-transfer coefficients per unit area in gas dispersions are almost completely unaffected by the mechanical power dissipated in the system. Consequently, the total mass-transfer rate in agitated gas-liquid contacting is changed almost entirely in accordance with the interfacial area—a function of the power input. 

Second, it is necessary to take account of non-Newtonian behaviour in the design of process plant and pipelines. Heat and mass transfer coefficients are considerably affected by the behaviour of the fluid, and special attention must be devoted to the selection of appropriate mixing equipment and pumps. 

Thus Sh and therefore decreases rapidly as the velocity is increased, and heat and mass transfer coefficients are therefore considerably influenced by the velocity. 

In addition to momentum, both heat and mass can be transferred either by molecular diffusion alone or by molecular diffusion combined with eddy diffusion. Because the effects of eddy diffusion are generally far greater than those of the molecular diffusion, the main resistance to transfer will lie in the regions where only molecular diffusion is occurring. Thus the main resistance to the flow of heat or mass to a surface lies within the laminar sub-layer. It is shown in Chapter 11 that the thickness of the laminar sub-layer is almost inversely proportional to the Reynolds number for fully developed turbulent flow in a pipe. Thus the heat and mass transfer coefficients are much higher at high Reynolds numbers. 

For flow in a smooth pipe, the friction factor for turbulent flow is given approximately by the Blasius equation and is proportional to the Reynolds number (and hence the velocity) raised to a power of -2. From equations 12.102 and 12.103, therefore, the heat and mass transfer coefficients are both proportional to w 75. 

Lowe and Christie 17 used a 1.3 m square experimental column fitted with a number of different types of packing and measured heat and mass transfer coefficients and pressure... 

Some workers have attempted to base the design of humidifiers on the overall heat transfer coefficient between the liquid and gas phases. This treatment is not satisfactory since the quantities of heat transferred through the liquid and through the gas are not the same, as some of the heat is utilised in effecting evaporation at the interface. In fact, at the bottom of a tall tower, the transfer of heat in both the liquid and the gas phases may be towards the interface, as already indicated. A further objection to the use of overall coefficients is that the Lewis relation may be applied only to the heat and mass transfer coefficients in the gas phase. 

This relationship applies quite closely for the conditions normally encountered in practice. For other systems, the relation between the heat and mass transfer coefficients in the gas phase is given by ... 

GP 9] [R 16[ The extent of external transport limits was made in an approximate manner as for the internal transport limits (see above), as literature data on heat and mass transfer coefficients at low Peclet numbers are lacking [78]. Using a Pick s law analysis, negligible concentration differences from the bulk to the catalyst sur-... 

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). 

Fluidized-bed driers are also widely used due to their large heat- and mass-transfer coefficients. However, materials of even moderate adherence and cohesiveness cannot be dried in a fluid bed. The same applies to materials that are sensitive to oxygen, especially at elevated temperatures. Vacuum drying is often necessary for oxygen sensitive materials and this is not easy to realize in fluid-bed driers, although there are systems to deal with this problem. Fluid-bed driers are not as easy to clean as shelf driers or rotary driers. 

MJ Pikal. Use of laboratory data in freeze drying process design Heat and mass transfer coefficients and the computer simulation of freeze drying. J Parenter Sci Tech-nol 39 115-138, 1985. 

Use the j factor correlations of Section 12.4 to determine appropriate heat and mass transfer coefficients. 

Ideal reactors can be classified in various ways, but for our purposes the most convenient method uses the mathematical description of the reactor, as listed in Table 14.1. Each of the reactor types in Table 14.1 can be expressed in terms of integral equations, differential equations, or difference equations. Not all real reactors can fit neatly into the classification in Table 14.1, however. The accuracy and precision of the mathematical description rest not only on the character of the mixing and the heat and mass transfer coefficients in the reactor, but also on the validity and analysis of the experimental data used to model the chemical reactions involved. 

For heat and mass transfer through a stationary or streamline fluid to a single spherical particle, it has been shown in Volume 1, Chapter 9, that the heat and mass transfer coefficients reach limiting low values given by ... 

It may be seen from equations 10.5 and 10.6 that at high degrees of agitation the ratio of the heat and mass transfer coefficients is almost independent of the speed of the agitator and ... 

Hixson, A. W. and Baum, S. J. Ind. Eng. Chem. 33 (1941) 478, 1433. Agitation mass transfer coefficients in liquid-solid agitated systems. Agitation heat and mass transfer coefficients in liquid-solid systems. 

Another class of derived quantities is represented by the coefficients in diverse physical equations, e.g., transfer equations. They are established by the respective equations and determined via measurement of their constituents (e.g., heat and mass transfer coefficients). 

Transfer coefficients in catalytic monolith for automotive applications typically exhibit a maximum at the channel inlet and then decrease relatively fast (within the length of several millimeters) to the limit values for fully developed concentration and temperature profiles in laminar flow. Proper heat and mass transfer coefficients are important for correct prediction of cold-start behavior and catalyst light-off. The basic issue is to obtain accurate asymptotic Nu and Sh numbers for particular shape of the channel and washcoat layer (Hayes et al., 2004 Ramanathan et al., 2003). Even if different correlations provide different kc and profiles at the inlet region of the monolith, these differences usually have minor influence on the computed outlet values of concentrations and temperature under typical operating conditions. 

For the bulk gas, the spatially ID description with the distributed heat and mass transfer coefficients is used, similarly as in the spatially ID model. 

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