1. Introduction

Vessels with mechanical impellers are largely used by chemical, petrochemical, food, textile, and other industries, operating as extractors, concentrators, flotators, storage vessels, and chemical reactors (producing polymers, paints, fertilizers, and resins, for instance).

The aforementioned processes need heating or cooling, these being provided by jackets, coils, and vertical tube baffles, where the heat transfer area is the target parameter for the project as a function of the overall heat transfer coefficient.

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The jackets are surfaces of heat transfer characterized by encompassing the tank, given that the thermal fluid roams the space between the jacket and the tank. On these equipments, the heat transfer efficiency is low due to the heat source being in the wall, which provokes uneven heating of the fluid within the tank, besides the structural problems in big units. Nevertheless, this system presents advantages as easy cleaning and available project data provided in the current literature [1].

The helical coils are made out of tubes between the impeller center line and the tank's wall. The contact area with the fluid to be heated or cooled is much bigger around the jackets, which end up increasing the heat transfer efficiency; however, the difficulty is in the cleaning of the equipment. Most agitated vessels involving heat transfer operations are projected with helical coils due to the availability of project data [2].

The spiral coils consist of wounded tubes generally placed on the bottom of the tank. They are mostly applied to heating viscous fluids in pumping transport. Spiral coils have as disadvantage the located heat transfer, fostering uneven heating. Another downside is the lack of data in the current literature [3].

The three heating transfer surfaces mentioned above demand baffles alongside the tank's wall to avoid vortex, which is characterized by the development of a bottleneck formed by the agitated fluid around the mechanical impeller. The vortex is an indicator of inefficiency at mixing and low heat transfer, due to the circular and organized stream lines.

The vertical tube baffles are surfaces that provide significant heating transfer rate and also eradicate the development of a bottleneck, due to its spatial structure, which makes necessary to allocate extra baffles alongside the tank's wall. The drawback of this technique is the lack of data project, especially on continuous operation [4].

However, each type of heat transfer surface will present parameters for Nusselt's equation particular to each system in which they were determined, in such a way that it is possible to obtain a general model that covers all surfaces for heat transfer in agitated vessels.

For batch processes the heat transfer area is determined by transient energy balances, while for continuous processes, on the large majority, the area is obtained by energy balances for steadystate operation.
