Modelling reactor jacket with or without insulation, how to proceed?

I am currently trying to derive a model to help estimate as precisely as possible how much time can be saved by insulating the jacket of a reactor used for eating and cooling.

EDIT: I edited my post so that it is clearer for everybody, I understand it could have be quite confusing. I also corrected a few typos.

Presentation of the system

Let's consider the following reactor: