Parameter heat transfer

Dixon, A. G. and Cresswell, D. L., Theoretical prediction of effective heat transfer parameters in packed beds, AIChE /., 25, 663-676 (1979). 

Figure 34 Experimental vial heat transfer parameters. Accommodation coefficient = 0.67 vial top emissivity = 0.84. (Data from Ref. 5.)...

The three unitary heat transfer parameters descriptive of equipment efficiency can now be redefined in terms of the above dimensionless integrals ... 

From this illustration we can see that the added detail of the radial temperature profile near the wall that could be provided by CFD simulations does not help in obtaining better estimates for the standard heat transfer parameters. It also implies that experimental efforts to measure temperatures closer to the wall are, in fact, counter-productive. Finally, it is clear that the standard model with plug flow and constant effective transport parameters does not fit satisfactorily to temperature profiles in low-Abeds. These considerations have led us to look for improved approaches to near-wall heat transfer. 

It should be noted that the importance of the continuity equation is in evaluating actual velocities within the reactor bed as influenced by the mole, temperature, and pressure changes. Because of the use of mass velocities (pgug), the importance of the actual velocities is really restricted to cases where pressure relationships such as the Blake-Kozeny equation or velocity effects on heat transfer parameters are considered. As will be shown later, very little increased computational effort is introduced by retaining the continuity equation, since it is solved as a set of algebraic equations. 

De Wasch and Froment (1971) and Hoiberg et. al. (1971) published the first two-dimensional packed bed reactor models that distinguished between conditions in the fluid and on the solid. The basic emphasis of the work by De Wasch and Froment (1971) was the comparison of simple homogeneous and heterogeneous models and the relationships between lumped heat transfer parameters (wall heat transfer coefficient and thermal conductivity) and the effective parameters in the gas and solid phases. Hoiberg et al. (1971)... 

Material Bulk Density (kg/m3) Heat Transfer Parameter [k/pCp]1/2... 

From the literature it is not possible to deduce a kinetic scheme suitable for modeling the reaction, since the majority of publications (10-39) do not present an unequivocal picture. Also the fundamental difficulties of estimating from independent measurements heat transfer parameters for a packed-bed reactor are well known (5,6,7). 

Heat Transfer Parameters. Attempts in this investigation to use heat transfer parameters ( X. h ) calculated from correlations based on data without reactidn 6,7) led to the result that the energy balance of the reactor at the measured temperatures was not satisfied. On the other hand, the simultaneous estimation of heat transfer and kinetic parameters by regression analysis of polytropic measurements allows these parameters to influence each other. It was observed that the parameters calculated by these two methods were quite different (5,46). Therefore in this report the heat transfer parameters were determined from experimental results by a third method with a minimum of additional assumptions ... 

These heat transfer parameters were used for all experiments (Table IV) they are distinctly higher than those which can be calculated from (7) for the case without reaction. This agrees with investigations of the oxidation of CO (5). 

The results of the steady-state model for the reactor under the same operating conditions are displayed as the solid lines in Figure 2. The predicted catalyst and gas temperatures are shown at each of the axial collocation points. As discussed earlier, a priori values of kinetic parameters were used ( 1, 2) similarly, heat and mass transfer parameters (which are listed in Table II) were taken from standard correlations (15, 16, 17) or from experimental temperature measurements in the reactor under non-reactive conditions. The agreement with experimental data is encouraging, considering the uncertainty which exists in the catalyst activity and in the heat transfer parameters for beds with such large particles. 

The heat transfer coefficient h was calculated according to Hand-ley and Heggs (24) with the Reynolds number based upon an equivalent diameter, namely that of a sphere with the same volume as the actual particle. The overall heat transfer coefficient U was calculated from the heat transfer parameters of the two dimensional pseudohomogeneous model (since the interfacial At was found to be negligible), to allow for a consistent comparison with two dimensional predictions and to try to predict as closely as possible radially averaged temperatures in the bed (25). Therefore ... 

The outside tubeskin temperature was taken to be identical to that generated in the previous simulation. The input data were also identical. Radial process temperature profiles are given in Figure 7. The ATg between the bed centerline and the wall amounts to 33°C, which is not excessive and permits the radially averaged temperature to be accurately simulated by means of the one dimensional model with "equivalent" heat transfer parameters, as discussed above. The methane conversion at the wall never differed more them 2% absolute from that in the centerline of the bed. The more detailed description which is possible by the two dimensional model would only be required if thermodynamic s predict possible carbon formation, and therefore catalyst deactivation, at locations different from those simulated by the one dimensional model. 

Note Packed bed heat transfer parameters based upon unit total cross-sectional area normal to direction of heat transfer (solid + void). 

Such a comparison is given in Fig. 7 where the two heat transfer parameters X, and aw plus the external catalyst surface ap, the bed void fraction e and the pressure drop Ap are given for a selection of different random and regular catalyst packings in a tube of 50 mm internal diameter and a mass flow velocity of G. = 1 kg/(m2 s). 

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