Heat Transfer to Jacketed Stirred Tanks

This section is concerned with the CMext(Text -T) term in the energy balance for a stirred tank. The usual and simplest case is heat transfer, typically cooling, from a jacket. Then Aext refers to the inside surface area of the tank that is jacketed on the outside and in contact with the fluid on the inside. The temperature difference Text - T is between the bulk fluid in the tank and the heat transfer medium in the jacket. The overall heat transfer coefficient includes contributions from wall resistance and jacket-side coefficient, but the inside coefficient is normally limiting. A correlation applicable to tanks with turbine, paddle, and propeller agitators is 

Assuming geometric similarity and recalling that Di scales as gives 

For a scaleup with constant power per unit volume. Table 4.1 shows that Sn scales as 5 2/9. Thus, 

If we want - T) to scale as 5, the driving force for heat transfer must be 

These results are summarized in the last four rows of Table 4.1. Scaling the volume by a factor of 512 causes a large loss in Mext per unit volume. An increase in the temperature driving force by a factor of 10 (e.g., by reducing Text if the reactor is being cooled) could compensate, but such a large increase is unlikely to be possible. Also, with cooling at the walls, the viscosity correction term in Equation 5.33 will become important and will decrease Mext still more. 

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