Stirred-Tank Reactor (STR) Cooling — A coolant is pumped through an internal cooling coil to remove heat. Which statement about improving the rate of cooling is NOT correct?

Introduction:
Removing heat efficiently from an exothermic fermentation or reaction in a stirred-tank reactor (STR) relies on both mixing in the bulk liquid and heat transfer inside the cooling coil. Understanding which operating changes increase or decrease the overall heat removal rate helps operators maintain temperature control and avoid hot spots.

Given Data / Assumptions:

• Internal cooling coil with a flowing coolant.
• Agitated vessel; stirrer speed and baffles affect bulk mixing.
• Coolant flow rate through the coil can be adjusted.
• No fouling changes or phase changes are assumed during the comparison period.

Concept / Approach:

The overall heat-transfer coefficient U depends on the inside (tube-side) and outside (liquid-side) film coefficients, wall resistance, and fouling. Increasing stirrer speed enhances the liquid-side coefficient by thinning the boundary layer and improving circulation around the coil. Adding or using baffles suppresses vortexing and improves top-to-bottom mixing, again raising the liquid-side coefficient. On the tube side, increasing coolant flow raises the Reynolds number, improving the tube-side coefficient; therefore, faster pumping usually increases the cooling rate. Slower pumping reduces the tube-side coefficient and reduces the log-mean temperature driving force along the coil, which is counterproductive when aiming for higher cooling rates.

Step-by-Step Solution:

Verification / Alternative check:

Empirical correlations for agitated vessels (e.g., Nusselt versus Reynolds, Prandtl) and coil-in-tank designs consistently show that increasing agitation and internal flow increases heat-transfer coefficients over practical ranges.

Why Other Options Are Wrong:

A, B, and D describe changes that typically increase heat removal. E is also true: both sides of the interface matter. Only the option claiming faster cooling at slower pumping contradicts standard heat-transfer behavior.

Common Pitfalls:

Assuming infinite coolant capacity or ignoring fouling. Very high speeds may give diminishing returns or create shear issues, but the qualitative trends above still hold.

Final Answer:

Faster cooling rates are achieved at a slower pumping rate of coolant through the coil.