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The three-dimensional structure of monolithic networks such as ceramic sponges and their geometrical dimensions are part of the fundamentals necessary for investigation in most possible applications in chemical engineering. A volume imaging method must be applied to determine this structure and to measure features such as the specific surface area and the pore diameter. Magnetic Resonance Imaging was chosen for such measurements in this study. The analysis of volume images is performed with various methods based on different principles, which are compared with each other as well as with data generated by conventional techniques and from literature models.

Passive sampling is a technology that is gaining more and more importance in the field of environmental monitoring. Sampling with ceramic dosimeters (passive samplers) is a new method which is being developed for long-term, time-integrated monitoring of organic pollutants in groundwater. The concept of time-integrated concentration measure ments can theoretically be used for contaminant monitoring in groundwater, rivers, lakes, wastewater sewers, and so on, and can be used to quantify exposures to contaminants for a range of contaminants such as polycyclic aromatic hydrocarbons (PAHs) and volatile aromatic compounds such as benzene, toluene, and xylenes (BTEX), and volatile chlorinated hydrocarbons. This paper presents (1) results from laboratory tests for recovery rates for the extraction of analytes from the adsorbent material Dowex Optipore L-493; (2) tests on the long-term stability of adsorbed BTEX and naphthalenes in ceramic dosimeters; and (3) results from field tests in groundwater wells comparing...

Based on the generalized Leveque equation (GLE) a new type of analogy between pressure drop and heat transfer has been discovered, that may be used in the cross corrugated channels of chevron type plate heat exchangers, in packed beds, in tube bundles, in crossed rod matrices or in many other spacewise periodic arrangements. Experimental data on heat transfer in tube bundles in crossflow, both inline, and staggered arrangements, had been recently tested in greater detail. Using an empirical correlation for pressure drop in these arrangements from the literature that has been successfully tested against a large number of experimental pressure drop data, heat transfer data collected earlier could be very well represented from the pressure drop correlation and the GLE. The data for staggered bundles have been shown to be in better agreement with this new method, than with the existing empirical heat and mass transfer correlations. Somewhat larger deviations for inline tube bundles had been found at lower Reynolds numbers. Here a simple and physically reasonable correction function of Re is presented, which leads to a better agreement for the inline bundles, too. Additionally, it can be shown for a number of literature data on tube bundles and on crossed rod matrices that the agreement with the GLE prediction is even better if original pressure drop data from the same sources are available in place of a pressure drop correlation. The method results in reasonable heat or mass transfer predictions from frictional pressure drop, which may be widely used in chemical engineering applications.

Spray coating or granulation is used to produce coarse granular solid particles by spraying solutions or suspensions in the form of fine droplets on fluidized particles followed by drying in a stream of fluidizing air. The quality and thickness of granulation or coating on the particle should be uniform. A part of the liquid-droplets from the spray-nozzle collide with the particle, of which, a part bounces back and the remaining part adheres on the surface of the particle giving layered-growth. In this work, the granulation process is carried out on a single spherical particle. Experiments are conducted to study the influence of process parameters, drying conditions, impact velocities and physical properties of sprayed solutions on the kinetics of granulation and on the morphology of the end product. A change in the drying condition changes the viscosity and surface tension of the sprayed solution. With increase in droplet velocity, the growth rate decreases. The results are useful to model the droplet deposition behaviour in fluidized bed granulation.

Large scale recirculation due to unwanted free convection currents of the fluids in a vertical countercurrent shell-and-tube heat exchanger in industry obviously was the reason of severe reductions in heat transfer performance by up to 40% against the design expectations. The apparatus was operated with the cold end on top. Applying a simple one dimensional calculation of flow and heat ransfer, with backflow of the tube side fluid in some of the tubes, shows that the reductions predicted from the model are not too far from the observed ones. In comparing experimental plant data to the predictions of the model, it became obvious, that the influence of free convection on the shell side heat transfer needs to be taken into account additionally to fully explain the experimental observations. An effective remedy, as earlier suggessted is to change flow directions in shell and tubes, i.e. to operate the heat exchanger with the hot side on top. In case of the industrial heat exchanger presented in the paper, the change of flow directions in shell and tube side has been carried out in the meantime. This change actually solved the problem, and resulted in the designed performance with efficiencies around 95%.

The prediction of the conductivity of a random distribution of spheres in a continuum of different material is addressed in this work. The approach of Ohm's law based on the unit cell is the starting point. Firstly, it is shown that the approach is compatible with the Fourier law approach which until now was considered irreconcilable. It is then demonstrated how one may use this result to model non-Maxwell interactions and thereby arrive at an equation for the conductivity of disperse media which predicts the property simply and in a physically clear fashion. Comparisons are made with existing models. The new equation is easy to use and can accommodate extensions to account for secondary effects. ? 1995 Elsevier Science S.A. All rights reserved.

The well-known series solutions, developed in the early 19th century by Fourier (1822) in order to describe the transient process of heat conduction in a solid have since become standard tools of engineering science. Attempts have often been made to facilitate the practical use of that first mathematical theory of an irreversible process by the provision of charts and simpler approximate equations and thus avoid the cumbersome calculations involved in the series. Some of the more recent approaches to simplifying the application of Fourier's theory are briefly reviewed. Three degrees of approximation, essentially based on the same ideas have been developed by Hausen (1942) and Elgeti (1969), by Schlunder (1972), and by the authors of this paper in 1992. Our own improved version of the approximate equations provides higher accuracy, and the additional possibility to obtain centre and surface temperatures (concentrations), not merely volumetric average values as in the earlier versions.

A summary of the available literature on heat transfer to liquid—solid fluidized beds is presented. The influence of process parameters such as bed geometry, flow velocity, and fluid and particle properties on heat transfer is discussed. 36 correlations based on various models or empirical assumptions are presented. The predictions of the correlations are compared with a database comprising 2665 measured data for a variety of fluids and particles. A new empirical correlation is developed which predicts the measurements better than published correlations.

Experiments on heat transfer in cylindrical monoliths are presented. The monoliths were heated at the wall, thus warming up cold air passing through their channels. Measurements of the solid-phase temperatures of different monoliths in the radial and axial directions show how heat transfer in such bodies is influenced by the void fraction. Two models describing the heat transfer are developed and a comparison of the calculated and measured temperatures is given.

Radial conduction of heat in packed tubes has a crucial influence on yield and selectivity of many heterogeneously catalyzed reactions. In spite of many years of intensive research in the field, there are still tremendous discrepancies between correlations of different origin. Even the standard model using two constant heat transport parameters, which was introduced in the fifties and has since become most widely accepted, has been controversially discussed and called into question. The unsatisfactory state of the art has been an incentive for several groups of researchers to take up this old topic once again. Three parallel experimental investigations on heat transport with air flowing in packed tubes of similar dimensions, electrically heated, steam-heated, or water-cooled, were completed in 1991. Comparative evaluation of the results of these three investigations, together with other data from the relevant literature, now provides the first clear answers to some of the questions so controversially discussed in the past

Pressure drop and heat transfer characteristics, in the form of fRe and Nu respectively, of hydrodynamically developed laminar flow through a cylindrical shell containing a bundle of seven tubes with a uniform tube-wall temperature are determined by solving the momentum and energy balance equations in finite difference forms, using a forward-marching, implicit method. Correlations suitable for predicting fRe are derived as functions of the tube-to-shell radius ratio (rt/rs) and the non-dimensional pitch radius (rp/rs). Local Nusselt numbers and logarithmic-mean Nusselt numbers are presented graphically for Graetz numbers up to 105. Nusselt numbers in the thermally developing range are also obtained from the mean velocity gradients at the tube walls applying the asymptotic solution due to Levěque.

By the method of mechanical manufacture of microstructures jointly developed by the Karlsruhe Nuclear Research Center (KfK) and Messerschmitt-Bolkow-Blohm (MBB) very compact cross-flow micro heat exchangers have been fabricated whose active volumes are 1 × 1 × 1 cm3 and whose typical channel cross-sections are 75 × 90 μm2. Measurements with nitrogen, argon and helium as heat transfer fluids were performed on two copper and stainless steel finned plate heat exchangers. With the stainless steel heat exchanger overall heat transfer coefficients up to 1700 W m−2 K−1 have been attained in the range investigated using helium as the fluid. For low flow rates greatly reduced overall heat transfer coefficients have been measured compared with the values to be anticipated for laminar flow. In some ranges higher heat transfer rates have been achieved with the stainless steel heat exchanger compared with the system made from copper. This leads to the conclusion that the heat transfer behavior for low gas flow rates is largely determined by heat conduction in the longitudinal direction within the wall and fin materials. With a homogeneous model the influence of longitudinal heat conduction in the stationary walls can be explained and is in fairly good agreement with the experimental data.

La formule bien connue pour l'efficacite et la difference de temperature moyenne d'un echangeur de chaleur, en fonction de ces nombres d'unite de transfert, ou de longueur adimensionnelles, peut etre ecrite dans une forme plus compacte en introduisant la fonction auxilliaire φ (x)=x/(1-e -x ). Les nouvelles formules resultantes presentent de nombreux avantages: plus courtes, plus faciles a memoriser et dans certains cas, les valeurs limitantes sont observees directement. Elles contribuent ainsi a faciliter et a accelerer la conception des echangeurs, et a reduire la probabilite d'erreurs dans les principaux calculs

For low Peclet numbers most of the experimentally obtained particle-to-fluid heat and mass transfer coefficients in packed beds were found to be some orders of magnitude below the values predicted for a single sphere in cross flow. From theoretical considerations one should expect the transfer coefficients in packed beds to exceed the single sphere predictions as they actually do for higher Peclet numbers. The obvious discrepancy between theory and experiment can be cxplained by a simple model accounting for a nonuniform distribution of the void fraction. The model consists of a packed bed of uniformly sized particles with an average void fraction ψ, where a small part ϕ of the total cross-sectional area f is assumed to have a larger void fraction ψ 2 . Since the same pressure drop applies to both parts of the bed, the superficial velocity will be much larger in the section with the larger void fraction, especially in the range of low Reynolds numbers. Even though in both parts of the packed bed the individual transfer coefficients are taken from a correlation which is based on the single sphere predictions (as it is valid in the range of high Peclet numbers), the apparent overall transfer coefficients for the nonuniform system become much lower, and show the same characteristic variation with Peclet number and the ratio of particle diameter to bed height as the majority of the experimental data.

Heat transfer from a rigid wall to gas-solid particulate systems. Considerable progress made in the last twenty years now permits a better understanding of heat transfer between a rigid wall and gas/solid particulate systems. The following paper reviews this progress. The heat transfer from a rigid wall to fixed, agitated, and fluidized beds as well as to fixed beds with fluid flow is discussed, and an example of indirect cooling of high-capacity computers is given. In modelling, the concept of a contact and a penetration resistance in series is applied. The physical significance and the calculation of these resistances are discussed.

A solution to the momentum and continuity equations in stratified and annular two-phase laminar flow is presented for the cases of parallel plates, round and elliptical tubes. The velocity distribution, mean velocity, void fraction and pressure drop are evaluated in each geometry. It is shown that the pressure drop in elliptical tubes with the main axis of the ellipse in a vertical position is smaller than in a horizontal position. In general, the pressure drop is lower when the channel geometry is such that the contact area between the phases is smaller. The effect of liquid viscosity upon the pressure drop is stronger for low flow quality and decreases rapidly with an increase of the gas flow rate.

The temperature distribution in spiral plate heat exchangers has been calculated numerically to obtain the efficiency and the logarithmic mean temperature difference (LMTD) correction factors F as a function of the number of transfer units N, the number of turns n, and the heat capacity rate ratio C. It has been found that the LMTD correction factors, when plotted against the number of transfer units per turn N/n, fall approximately on a single curve. That curve for balanced countercurrent operation (C = −1) can be very closely represented by the simple formula F = (n/N)tanh(N/n). From that simple analytic representation of our numerical results it was concluded that a simpler physical model might exist to represent the overall behaviour of a spiral plate heat exchanger equally well. In fact, a countercurrent cascade of n cocurrent heat exchangers does result exactly in the above-mentioned formula for the LMTD correction factor. From that model the F-factors for other heat capacity rate ratios C (−1 < C ⩽ 0) can also be calculated and they are in sufficient agreement with the numerical results.

A new model is presented for the wall-to-bed heat transfer from solid surfaces immersed in fluidized beds. This model makes use of some basic ideas adopted from the kinetic theory of gases in order to describe the mechanism of energy transfer through the moving particles (“particle convection”). The parallel—and in most cases less important—gas convective and radiative contributions to the total heat transfer coefficient are calculated from well known equations from the literature. The predictions of the new model are in good agreement with many experimental observations, in particular as to the non-monotoneous variation of heat transfer coefficients with gas velocity and particle diameter. Literature data for particle diameters from 0.01 to more than 10 mm, various particle materials, some different gases, various pressures, and temperatures up to more than IOOO°C are compared with the model calculations.

After some general remarks about fluidization, and a section on the hydrodynamic behaviour of fluidized beds, the mechanisms of heat transfer between the surfaces of heat exchanger elements and gas—solid fluidized beds are discussed in detail. A theoretical model, presented some years ago, is slightly modified and further developed to improve its applicability within a wide range of variables. The model makes use of some of the basic concepts of molecular kinetic theory as applied to solid particles in a fluidized bed. A complete derivation as well as all the parameters required to apply the model equations are given.

Heat and mass transfer in fluidized beds. Methods of calculation are presented which enable reasonably accurate prediction of heat and mass transfer coefficients in fluidized beds. Some well established equations already given in the literature could be used for estimating the range of existence of the fluidized bed and for calculating maximum fluidization velocities, bed expansion, and particle-to-fluid heat and mass transfer. However, a new model had to be developed for the wall-to-bed heat transfer from solid surfaces immersed in fluidized beds. This model makes use of some basic ideas adopted from the kinetic theory of gases in order to describe the mechanism of energy transfer through the moving particles. Predictions with this new model are in good agreement with most of the experimental observations, particularly regarding the effects of particle diameter, temperature, pressure, physical properties of gas and particles, and gas velocity.

The voluminous literature available on thermal conductivities of packed beds without fluid flow is reviewed. The discussion includes experimental methods as well as theoretical approaches. A classification of predictive models is attempted. One of these models is analysed in detail and recommended for practical use. The predictions of the model are compared with a large amount of experimental data. In the course of this comparison phenomena of physical interest and of technical significance are discussed. Most of the methods presented in this review retain validity for dispersed systems other than gas-filled packed beds and for properties other than the thermal conductivity.

Stoffubergangsmessungen bei Prallstromung aus Schlitzdusenfeldern mit relativen Dusenflachen von 0,9% bis 21% werden in einem weiten Bereich der auseren Einflusgrosen empirisch korreliert. Die gefundene Beziehung wird benutzt, um optimale Dusengeometrien bezuglich der Ventilatorleistung pro m2 Warenflache zu ermitteln. Auserdem gelingt es, durch eine eindimensionale Berechnung der Stromungsverhaltnisse den gemessenen Verlauf der Stoffubergangskoeffizienten uber die Breite der Warenbahn zu erklaren. Die bei einigen Anwendungen gestellte Forderung nach einer hohen Gleichmasigkeit dieses Verlaufs fuhrt zwangslaufig zu aufwendigen Konstruktionen mit sehr hohen Abstromkanalen oder freiem Abzug zwischen den Schlitzen. Daher wird zusatzlich eine andere Moglichkeit untersucht, konstanten Warme- und Stoffubergang uber die Bahnbreite zu erzielen. Diese besteht in einer vorausberechen baren Form der Dusenschlitze mit kontinuierlich vom Bahnrand zur Mitte hin zunehmender Schlitzweite.

Bei Schlitzdusenfeldern mit Abstromung der Dusenluft in Langsrichtung der Schlitze bewirkt das Druckgefalle der Abstromung eine Verminderung der Dusenaustrittsgeschwindigkeit und damit auch des Warme- und Stoffuberganges in Feldmitte. Diese in vielen Anwendungsfallen unerwunschte Erscheinung kann durch die Wahl einer speziellen Schlitzform vermieden werden. Dabei werden die in Feldmitte herrschenden geringeren Austrittsgeschwindigkeiten durch entsprechend grosere Austrittsquerschnitte kompensiert. Die Schlitzform last sich berechnen, wenn man von einer einfachen eindimensionalen Betrachtung der Stromungsverhaltnisse ausgeht.

Die Randubertrocknung, welche in Schlitzdusentrocknern mit Abstromung in Schlitzrichtung beobachtet wird, last sich auf die Verteilung der Austrittsgeschwindigkeit langs der Schlitze zuruckfuhren. Fur Dusentrockner folgt hieraus, das die Abstromflache moglichst das 3,5fache der Dusenaustrittsflache betragen soll, um eine gleichmasige Trocknung zu erhalten.