# Calculating the Maximum Volume of Fermentor that can be used without Additional Cooling

The heat generated by fermentor is 60 kcal/hr L. The cooling capacity of jacket is 10,000 kcal/hr m^2. For a cylindrical fermentor with H/D of 3, the jacket area (m^2) is porportional to fermentor volume (m^3) to the 2/3 power.

Area of Jacket (m^2) = 7*v^(2/3) (m^3)

What is the maximum volume of the fermentor that can be used without additional cooling capacity?

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#### Solution Preview

The heat generated by a fermentor with volume v [L] is

Qgen=60*v ...

#### Solution Summary

Using equalites relating heat generated and heat removed, the maximum volume of the fermentor that can be used without additional cooling is calculated. The calculation steps are shown.

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