External heat transfer criterion

Criterion Biot determines the ratio of intensity of external heat exchange processes (numerator) and effective thermal conductivity of a hydride layer (denominator). To carry out frontal chemical reactions of hydrogen sorption -desorption, small numbers Biot (Bi<0.1) are preferable. Number Bi can be decreased by several ways 1) decreasing of the characteristic layer size 2) decreasing of intensity of an external heat transfer (but time of non-stationary processes is growing) 3) increasing of effective hydride bed thermal conductivity. 

Note that criterion 7.186 requires a knowledge of the apparent activation energy for the reaction. Criterion 7.186 holds whether internal diffusion limitations exist or not. When the criterion concerning external heat transfer is compared to criterion 7.167 concerning radial heat transport limitations through the bed, it can been seen that the latter are more critical unless ... 

The criterion for external heat transfer was proposed by D.E. Mears (J. Catal. 20 (1970) 127). 

The advantage of applying different criteria is that observed values of reaction rates are used, but not kinetic constants, such as in the Thiele modulus, which are often unknown. The criterion for external heat transfer was proposed by Mears [8] ... 

Mears Criterion for External Fleat Transfer Effects There is an analogous Mears criterion for predicting possible heat transfer effects [26-28] ... 

The Biot number was originally established as a criterion for gauging relative resistances for fhe analogous heat transfer case. Here the span of Biot numbers extends into both regions of controlling resistances. This is in large part due to the wide range of thermal conductivities of solids seen in practice. Thus, heat transfer from a turbulent stream of air to a sheet of copper k = 390 W/mK) would have external (air) resistance control, while in heat transfer fo a sheef of asbestos k = 0.15 W/mK) under the same conditions the principal resistance would reside in the solid. The reach of the Biot number in mass transfer is more limited but still of some importance. 

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