Many investigators (1-9) have attempted to explain the sintering of catalysts which is frequently found during coke burn-off. It is known that this sintering is associated with the anomalous temperature rise which occurs during exothermic reactions (1-3). Cusumano and Low ( 4 ) have recently used an infrared radiometric method to show such high temperature rises during the sorption of O2 on Si02-supported Ni.The early work of Damkohler ( 5 ) determined the maximum steady state temperature rise of a bulk catalyst. Subsequent work by Prater (6) predicted a maximum temperature rise of only 2"C., while the study by Wei (7) predicted a possible rise of 34°C. for a 2 A hot spot. Such small temperature rises do not appear to be comparable to the experimental observations ( 4 ) . More recently, Luss and Amundson (8) employed a shell progressive model to predict a rise of 250°C. for a typical cracking catalyst. Luss (9) has recently proposed two simple analytical models which will give upper and lower bounds on the temperature rise. It appears that the predicted values of the temperature rise tend to be more realistic, but it also seems that they cannot successfully explain the catastrophic catalyst sintering which is occasionally encountered.It is possible that all of these analytical studies may have a fundamental flaw in that they have been based on the conventional Fourier and Fick laws which result in the conventional heat conduction and mass diffusion equation of the parabolic type __ ae + av2e = S at 8, CY and S can be interpreted respectively as temperature, thermal diffusivity, and heat of reaction in the case of energy transport and as concentration, mass dausivity, and rate of reaction in mass transport. The propagation velocities of heat and mass resulting from such a parabolic formulation are infinite, which is of course unrealistic. In fact, Morse and Feshbach (10) --which is a hyperbolic type of equation. The latter equation can also be derived (11) using a truncation of the more general Maxwell equation (12) for an ideal gas. The basic difference between the parabolic and hyperbolic equations is that the latter has an additional term which involves a finite propagation speed. Other differences between these two types of equation were recently demonstrated by Baumeister and Hamill (13). The effect of the finite propagation speed may become important when the system is at very low temperature or when the time of interest is very short. In the present problem of exothermic catalytic reactions, the maximum temperature may occur in a very short time. For example, time periods as short as sec. after reaction were considered by Luss (9). Under such circumstances the hyperbolic type equation may give significantly different results than the parabolic equation. It is the purpose of this paper to investigate the effect of finite speed of heat transfer on the temperature rise of catalytic supported crystallites. AN A LY S I SThe simple yet interesting physical model employed by Luss (9) is adopted here to demonstrat...

Approximate analytical solutions are presented for constant-property laminar free- and forced-convection flows between finite vertical parallel plates. For free convection, the thermal boundary conditions considered include the thermally symmetric channel with uniform wall temperature or step change in wall temperature and the unsymmetric channel with uniform but unequal wall temperatures. For forced convection and combined free and forced convection, the thermally symmetric and uniform thermal boundary condition is considered. Where possible, results are compared with available numerical and experimental results. Particular attention is given to heat-transfer results, which cover a wide range of Rayleigh and Prandtl numbers. For combined convection the heat-transfer results are related to the impressed pressure difference and flow rate.

No abstract

No abstract

Two features distinguish vapor nucleation in multicomponent liquids from the single component case. Both result from the unequal volatilities of the species. One is that the vapor phase may contain several components; the other is that nucleus formation alters the composition of the nearby liquid. These two features are incorporated into the classical theory of homogeneous nucleation to yield a general theory applicable to multicomponent liquids. The theory is applied to binary hydrocarbon mixtures by using an equation of state extrapolated into the metastable region. Superheat limits thus calculated are compared with published experimental results.