Lesson 10 - Jacketed Vessels

In this section, we will recall a number of heat transfer equations and explain how these can be used in the design and sizing of a jacketed vessel.

The design and sizing of jacketed vessels is a highly specialised field. The methods shown in this section are thus for approximation purposes only.

Vessel manufacturers will have their own design information, based on a combination of theoretical and empirical data. For detailed and accurate sizing, it is always best to seek their assistance.

Heat transfer in a single fluid

In the lesson on Conduction, we learned about two equations relating to heat transfer to or from a single fluid. These were:

1. The heat transferred when heating or cooling a mass of fluid is defined as:

2. The heat transferred when changing the state of a mass of fluid is defined as:

As you will recall, the ΔT shown in the first equation represents the difference in temperature between when the utility fluid enters and leaves the jacket or the product fluids initial and final temperature.

These equations can be applied to either the product or utility fluid of a jacketed vessel. Based on the law of conservation of energy, the two equations can be used to determine any one of the following: 

• The temperature change that can be achieved in the product fluid by a known mass of condensing or evaporating utility fluid.

• The mass of product that can be heated or cooled by a known amount of condensing or evaporating utility fluid.

• The mass of utility fluid required to heat or cool a known mass of product.

Steady state heat transfer

In the lesson on Radiation and Combined, we learned that in steady state heat transfer:

As you will recall, the ΔT shown in this equation represents the difference between the product and utility fluid temperatures (also known as the temperature driving force).

This equation can be used to determine the required heat transfer area of a jacket, where the temperature between the product and utility fluid remains constant over time.

Unsteady state heat transfer

In addition to the above equations, in the previous section we learned that in unsteady state heat transfer, the following equation applies:

We can use this relationship in two different ways when sizing jacketed vessels:

• To determine the required heat transfer surface area (A) of a jacketed vessel to achieve a specified temperature change in a required time. Once the vessel area is known, then by using the vessel diameter, we can estimate the height of the jacket around the vessel.

• If we have an existing vessel, and we know its jacket area, we can use this relationship to determine the time (t) required to heat or cool the product to a specified temperature, or the mass of fluid that can be heated or cooled (M) within an available timescale.

In the case where a jacketed vessel has multiple heating or cooling steps, the vessel jackets must be sized for the step that has the largest heat transfer area requirements.

For example, in a fermentation vessel, the heat transfer area for fermentation can be calculated using the equation for steady state heat transfer. The area required for cool down can then be calculated using the equation for unsteady state heat transfer. The greater of these two will be the required heat transfer area of the vessel.

This means that for the other steps, the jackets will be over-sized. This in turn means that the heat transfer rates will be faster than required. This can be managed with proper control, which is explained in more detail at the end of this lesson.

Once an initial heat transfer area is determined, a designer will optimise this further, based on the following factors:

• Optimal jacket configuration

• Pressure drop across the jacket versus utility fluid flow rate

• Heat transfer versus utility fluid flow rate and agitator design

• Need for multiple jackets

Let’s now look at a worked example for sizing a jacketed vessel.