Effective radial conductivity

FIGURE 9.2 Existing data for the effective radial conductivity,... 

Input of thermal energy by effective radial conduction... 

Schliinder was originally derived to describe the effective radial conductivity in fixed beds. By using a cell concept the heat is assumed to be transferred by molecular conduction both in a pure gas phase with surface fraction 1 —. 77, and through a gas-solid bulk phase with the complimenting portion of the surface fraction, Deviations from sphericity and inter-particle point-... 

R AR pu CpiT-Tf,)] At Input of thermal energy by effective radial conduction ... 

Mears [97] found that the reaction rates in fixed-bed catalytic reactors are highly affected by two heat transfer resistances resistance to radial heat transfer and resistance to particle-to-fluid heat transfer. Considerable effort has therefore been directed toward finding the effective radial conductivity and the fluid-to-wall heat transfer coefficient (which represents the radial heat transport) and particle-liquid heat transfer coefficient (which represents particle-to-fluid heat transport). 

The heat transfer parameters in the two-dimensional model are the effective radial conductivity Xreff and the wall heat transfer coefficient Owaii Reviews of the correlations using the plug-flow assumption can be found in [159] [199] [274] [288]. 

Correlations of the effective radial conductivity usually have the following form ... 

Figure 4.10.70 Effective radial conductivity of a packed bed of spherical particles for different aspect ratios c/r/c/p, gases (Pr = 0.7), and high Rgp values (Rgp = Usdp/v) lines correlation given in VDI (2002), see Eq. (4.10.194), for a value of the static contribution A,bed/ fiuid 4 area range of literature data (Yagi and Kunii, 1960 Yagi and Wakao, 1959 Calderbank and Pogorski, 1957 Demirel, Sharma, and Al-Ali, 2000 Dixon, 1985 Li and Finlayson,...

Figure 4.10.71 Effective radial conductivity of a packed bed without flow. Adapted from VDI (2002).

Neither model showed significant lack of fit to radial temperature profiles when fitted on a depth by depth basis. However, the plug flow model parameters were found to decrease systematically with increasing bed depth. Figure 8 shows this most clearly in the case of the effective radial conductivity, such effect is observed with the axial conduction model, as is apparent from Figure 9. 

It is interesting also to note from Figure (9) that the effective radial conductivity varies linearly with mass velocity and extrapolates to a finite value as Re 0, once more indicating a direct solid contribution. 

Figure 7. Correlation of effective radial conductivity data...

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