Graetz-Nusselt model

As a consequence of the calibration of the Graetz-Nusselt problem to give exactly the same value of the initial Sherwood number, both models behave in A similar way. There is a slight difference in the dynamics of the dissolution as the spherical blobs model by Powers et al. (1994) gives stronger TCE flux than the Graetz-Nusselt model. However, the complete dissolution time of the residual TCE content is the same for both models as it is shown in Figure 15.10. 

It has been demonstrated that kg can be estimated by analogy with the Graetz-Nusselt problem governing heat transfer to a fiuid in a duct with constant wall temperature (SH= Nut) [30] and that the axial concentration profiles of NO and of N H 3 provided by the 1D model are equivalent and almost superimposed with those of a rigorous multidimensional model of the SCR monolith reactor in the case of square channels and of ER kinetics, which must be introduced to comply with industrial conditions for steady-state applications characterized by substoichiometric NH3 NO feed ratio, that is, a[Pg.401]

In many situations, solution for the Graetz-Nusselt problem is closely approximated by the "film model". In this model, radial temperature and concentration profiles are assumed to be uniform in the bulk fluid, whereas heat and mass transfer resistances are assumed to be close to the solid surface. Surface and bulk fluid properties being different, the specific radial mass and heat fluxes are given respectively by... 

V is the kinematic viscosity, u the mean gas velocity in the channel, a the thermal diffusivity, Po the gas density, Cpo the heat capacity of the gas, and its thermal conductivity. Correlations (2.1) and (2.2) indicate a strong flowrate dependence. For standard monoliths and operating conditions, Sh ranges from 0.7 to 1.6, and Nu from 0.6 to 2.7 according to the correlations above. These correlations contradict the results of Heck et al. (1974) and other earlier authors on one hand, and the results of the comparison between the Graetz-Nusselt and film models on the other hand. There are several explanations to this discrepancy. As mentioned above, wall irregularity may be invoked. However, we may also invoke a non-uniform flow distribution in the monolith sample (Martin (1978)), or the effect of the small L/Dj, ratio (less than 10) and the small diameter of the monolith sample used by Votruba et al.. Here again, we see that the gas-solid transfer process is not fully understood, and that a refined and detailed description of this process is not presently possible. Consequently, we think that the Nusselt and Sherwood numbers must be considered adjustable parameters. 

As introduced in Equation 15.29, the Graetz-Nusselt closed-form solution for the Sherwood number models dissolving walls of a single tubular TCE entrapment. In... 

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