Heat transfer resistance, effect uptake curves

Figure 4,7 Effect of heat transfer resistance on uptake of adsorbates. The figures on the curves represent the parameter y. The left-hand diagram is for 6 = 0.5 and the right-hand diagram is for S = 0.2 (see text) (source Ruthven etal. 1980).

FIGURE 6.12. Theoretical uptake curves calculated according to Eqs. (6.67) and (6.68) showing the effect of heat transfer resistance. As oo the curves approach the limiting isothermal curve calculated from Eq. (6.4) (—) while for ->0 the curves approach the limiting case of heat transfer control given by Eq. (6.70) (- ) (From ref. 20, with permission.)... 

When heat transfer is controlling, the uptake curyes commonly show a rapid initial uptake followed by a slow approach to equilibrium and the observation of a distinct break in an experimental uptake curve therefore provides a useful clue that heat transfer resistance may be important. For all values of the parameters a and the uptake curves in the long time region show a simple exponential approach to equilibrium and so give straight lines when plotted as ln(l-m,/m ) versus t. If the process is substantially isothermal the intercept of such a plot should be 6/ir, and a significant deviation from this value can provide useful evidence of the intrusion of heat transfer effects. However, it is clear from Eq. (6.70) that when / is 1.5 the same intercept will be obtained under conditions of complete heat transfer control. It is therefore not possible to determine unequivocally the significance... 

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