Radial heat transfer

Radial heat transfer Slow Fast Fast Fast... 

Weekman and Myers (W3) measured wall-to-bed heat-transfer coefficients for downward cocurrent flow of air and water in the column used in the experiments referred to in Section V,A,4. The transition from homogeneous to pulsing flow corresponds to an increase of several hundred percent of the radial heat-transfer rate. The heat-transfer coefficients are much higher than those observed for single-phase liquid flow. Correlations were developed on the basis of a radial-transport model, and the penetration theory could be applied for the pulsing-flow pattern. 

Bunimovich et al. (1995) lumped the melt and solid phases of the catalyst but still distinguished between this lumped solid phase and the gas. Accumulation of mass and heat in the gas were neglected as were dispersion and conduction in the catalyst bed. This results in the model given in Table V with the radial heat transfer, conduction, and gas phase heat accumulation terms removed. The boundary conditions are different and become identical to those given in Table IX, expanded to provide for inversion of the melt concentrations when the flow direction switches. A dimensionless form of the model is given in Table XI. Parameters used in the model will be found in Bunimovich s paper. 

Equations 12.7.28 and 12.7.29 provide a two-dimensional pseudo homogeneous model of a fixed bed reactor. The one-dimensional model is obtained by omitting the radial dispersion terms in the mass balance equation and replacing the radial heat transfer term by one that accounts for thermal losses through the tube wall. Thus the material balance becomes... 

KATAPAK s are applied in catalytic distillation and in some gas-phase exothermic oxidation processes traditionally carried out in fixed beds. In these processes KATAPAK s exhibit very good radial heat transfer characteristics (37). 

Mechanistic equations describing the apparent radial thermal conductivity (kr>eff) and the wall heat transfer coefficient (hw.eff) of packed beds under non-reactive conditions are presented in Table IV. Given the two separate radial heat transfer resistances -that of the "central core" and of the "wall-region"- the overall radial resistance can be obtained for use in one-dimensional continuum reactor models. The equations are based on the two-phase continuum model of heat transfer (3). 

The theoretical model assumes a line heat source dissipating heat radially into an infinite solid, initially at uniform temperature. The fundamental heat conduction equation in cylindrical coordinates, assuming uniform radial heat transfer, is [3] ... 

Considering the models in Table I, it follows that the response of model III-T will be more close to reality due to (i) the correct way the transfer phenomena in and between phases is set up, and (ii) radial gradients are taken into account. Therefore, the responses of the different models will be compared to that one. It is obvious that the different models can be derived from model III-T under certain assumptions. If the mass and heat transfer interfacial resistances are negligible, model I-T will be obtained and its response will be correct under these conditions. If the radial heat transfer is lumped into the fluid phase, model II-T will be obtained. This introduces an error in the set up of the heat balances, and the deviations of type II models responses will become larger when the radial heat flux across the solid phase becomes more important. On the other hand, the one-dimensional models are obtained from the integration on a cross section of the respective two-dimensional versions. In order to adequately compare the different models, the transfer parameters of the simplified models must be calculated from the basic transfer... 

From the analysis of Equation 18> it follows that the main variables that affect the error in the reaction rate are E and P due to their effect on T and TC Thus, very good responses are obtained from a one-dimensional model when reaction conditions are mild (moderate values of E and P). It can also be seen that for these conditions, the influence of the distribution of the radial heat transfer resistances between the bed and the wall, given by the Biot number, is small. E.g., for T = 673°K, Tw = 643°K and E = 12.5 kcal/mol, the maximum er, found for Big -> < is 2.8%. 

When Re and dp/dt vary, while both the activation energy and the ratio between the radial heat transfer and heat generation rate at the inlet are kept constant, the values of 7 and T do not vary significantly. On the other hand, since the effect of the Biot number on the error is small, no variations in the difference between models are expected. 

The first three types (pellets, extrudates and granules) are primarily used in packed bed operations. Usually two factors (the diffusion resistance within the porous structure and the pressure drop over the bed) determine the size and shape of the particles. In packed bed reactors, cooled or heated through the tube wall, radial heat transfer and heat transfer from the wall to the bed becomes important too. For rapid, highly exothermic and endothermic reactions (oxidation and hydrogenation reactions, such as the ox-... 

The requirements for approximating the radial heat transfer in a packed reactor with a constant over-all heat-transfer coefficient are discussed in Section III, above. When these requirements are met, Eqs. (3-32), (3-33), and (3-34) are used to describe conditions in the reactor. With the substitution of Eq. (7-1), these equations take the form... 

Monolithic catalysts for two-phase processes are characterized by (1) poor heat and mass transfer between the gas and the outer surface of the catalyst, and (2) no mass exchange between adjacent channels and consequently zero mass transport in the direction perpendicular to flow. The latter, being the predominant contribution to the overall mechanism of radial heat transfer inside the catalyst bed, results in rather poor heat transfer between the monolith and the surroundings. If more intensive heat and mass transfer within the catalyst bed is needed, arranged catalysts are one of the most effective solutions. 

Since there is no radial bulk transport of fluid between the monolith channels, each channel acts basically as a separate reactor. This may be a disadvantage for exothermic reactions. The radial heat transfer occurs only by conduction through the solid walls. Ceramic monoliths are operated at nearly adiabatic conditions due to their low thermal conductivities. However, in gas-liquid reactions, due to the high heat capacity of the liquid, an external heat exchanger will be sufficient to control the reactor temperature. Also, metallic monoliths with high heal conduction in the solid material can exhibit higher radial heat transfer. 

Usually, an adiabatic operation of MR is assumed in modeling. This seems to be a reasonable assumption, especially for ceramic monoliths of low thermal conductivity and in the absence of significant radial temperature gradients. In practice, there is no convective radial heat transfer because of barriers between the adjacent channels. The radial heat transfer occurs only by conduction through the walls and, to some extent, by convection in liquid plugs. 

Strongly exo- or endothermic processes are generally carried out in multitube configurations, to permit heat removal/supply via a fluid medium. Within the tubes heat must be transferred at right angles to the flow axis this transfer can be described by a radial heat transfer coefficient in the structure itself, and a wall heat transfer coefficient, The overall heat transfer coefficient Oiot is then given, where the radial temperature profile is parabolic (see [9]) ... 

Figure 10 Radial heat transfer coefficient in OCFS and dumped packing (a) Corrugation amplitude 1.7 mm and angle of channel to flow axis 30° (b) corrugation amplitude 4 mm and angle of channel to flow axis 30° (c) corrugation amplitude 4 mm and angle of channel to flow axis 45° (d) 5 mm spheres (e) 2 mm spheres (0 5 mm cylinders.

Reactions that are strongly exothermic, such as selective oxidations, or those that are strongly endothermic, such as oxychlorinations, are usually carried out in multitube reactors. The catalyst is dumped into tubes of limited diameter—typically to 1 in. (25 mm)— such as to permit adequate radial heat transfer to/from the liquid bath surrounding them as a result of their limited cross section, the overall number of such tubes is very large (typically on the order of 25,000). Minimization of pressure drop and maximization of... 

With OCFS, the lower pressure drop in the catalyst bed results in reduction in the energy costs associated with recirculation of gas streams and—in new plants—lower investment costs due to the possibility of using boosters rather than compressors. Further potential for savings lies in the reduction of the number of reactor tubes, due to the increased tube diameter made possible by more efficient radial heat transfer. Of greatest significance, however, for processes such as the oxidation of o-xylene to phthalic anhydride... 

Standard heat pipe is shown on Figure 1. Basic phenomena and equations are related with liquid-vapour interface, heat transport between the outside and the interface ( radial heat transfer), vapour flow and liquid flow. 

A vapour flow (two phase flow) with kinetic reaction rate and pressure, vapour pressure, geometry, conductive and convective heat transport with radial heat transfer inside the sorbent material ... 

In the condenser and evaporator there is a vapour flow, liquid flow, interface position, radial heat transfer with kinetic reaction pressure, liquid pressure, vapour pressure, condensation and evaporation, shear stress, geometry, adhesion pressure, convective heat transport, radial heat transfer under the influence of the gravity field. 

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