Heat transfer controlling resistance

The approximate temperature distribution in a multiple-effect evaporator is under the control of the designer, but once built, the evaporator establishes its own equilibrium. Basically, the effects are a number of series resistances to heat transfer, each resistance being approximately proportional to The total available temperature... 

The approximate temperature distribution in a multiple-effect evaporator is under the control of the designer, but once built, the evaporator estabhshes its own equilibrium. Basically, the effects are a number of series resistances to heat transfer, each resistance being approximately proportional to 1/Ur. The total available temperature drop is divided between the effects in proportion to their resistances. If one effect starts to scale, its temperature drop will increase at the ejq)ense of the temperature drops across the other effects. This provides a convenient means of detecting a drop in heat-transfer coefficient in an effect of an operating evaporator. If the steam pressure and final vacuum do not change, the temperature in the effect that is scaling will decrease and the temperature in the preceding effect will increase. 

The drying model for a single wet particle/slurry droplet is based upon a two-stage drying process [50,51]. In the first drying period, the gas phase resistance controls the evaporation rate. Similarly to heat transfer, this resistance is between the gas and the wet envelope of the particle. This may be expressed by... 

In the case of a desorption process all these resistances must be overcome in the reverse order. At first the heat of desorption to be added results in a detachment of the molecules which pass then through the micro- and macroporous system and finally through the concentration boundary layer into the bulk fluid around an adsorbent pellet. The heat of adsorption (in most cases exothermic) and the heat of desorption (endothermic as a rule) lead to the result that these processes cannot be carried out in an isothermal field. The increase of temperature of the adsorbent by adsorption and the decrease of temperature of the sohd phase are the reason that the driving force is reduced and the mass transfer is retarded. It can happen that the mass transfer rates of adsorptives with great heats of adsorption result in such tem-peratrue changes that additional adsorptive can only be adsorbed after a removal of heat combined with a temperatrrre loss. The kinetics in the adsorber is limited by heat transfer (heat transfer controlled). 

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... 

A perfect temperature-controlled heat-transfer surface is difficult to achieve, but it is closely simulated in practice by using a control fluid on one side of, for example, a metal tube. The tube wall should be thin and, ideally, the heat-transfer resistance comparatively large for the other fluid on the working side of the tube the latter surface is then effectively temperature-controlled and responds only to changes in the control fluid. 

Empirical methods approximate methods, in which the resistance to heat transfer is considered to control the rate of condensation, and the mass transfer resistance is neglected. Design methods have been published by Silver (1947), Bell and Ghaly... 

The temperature of the reactor could theoretically be controlled by changing the flow rate or the temperature of the water in the jacket. It will now be shown that the former is impractical. The over-all heat transfer coefficient is given in the major equipment section as around 50 BTU/hr ft2°F or greater. This means that the major resistance to heat transfer is the film on the inside of the reaction vessel. 

Heat transfer from the shelves to the sublimation front depends on the pressure and the distance between shelf and product (Fig. 1.58). Mass transfer (g/s) increases with the pressure, but also depends on the flow resistance of the already dry product and of the packing of the bones. If the maximum tolerable Tke is defined, the drying time depends only on the two processes mentioned above. It cannot be shortened under a given geometric situation and the chosen Tke. This method of Tkt control does not require thermocouples, and does not contaminate the product. 

A significant feature of physical adsorption is that the rate of the phenomenon is generally too high and consequently, the overall rate is controlled by mass (or heat transfer) resistance, rather than by the intrinsic sorption kinetics (Ruthven, 1984). Thus, sorption is viewed and termed in this book as a diffusion-controlled process. The same holds for ion exchange. 

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