Heat Transfer in Mechanically Agitated Tanks

This article summarizes the methodology for heat transfer design in the most common mechanically agitated vessels.

Heat transfer in agitated tanks is an important part of many applications in the chemical process industries (CPI) (1). Though not always obvious, the basic concept for agitated heat transfer is to solve two equations simultaneously. The principle is that the heat transferred into or out of the process fluid must equal the heat gained or lost by the heating or cooling medium under steady state conditions.

This article describes the necessary heat transfer calculations for vessels with turbine agitators. Heat transfer coefficients and overall heat transfer rates are demonstrated, which will help ensure that the heat transfer rate of your process is adequate for process needs. Those who will find this article useful include process engineers and engineers responsible for specifying tank internals and ancillary equipment such as chilled water supply, hot water supply, or thermal fluid supply.

Basic concept of steady state heat transfer in an agitated tank

The two aforementioned heat transfer equations may be represented mathematically with Equations 1 and 2:

where Q_t is the rate of heat transferred through a heat exchange surface, U is the overall heat transfer coefficient, A is the heat transfer surface area, and ∆θ_LM is the log mean temperature difference.

where Q_m is the rate of heat transferred to or from the medium, F is the flowrate of the cooling medium, C_Pm is the cooling medium’s heat capacity at constant pressure, θ_out is the exit temperature of the heat transfer medium, and θ_in is the inlet temperature of the heat transfer medium.

Because the log mean temperature difference depends on the exit temperature of the heat transfer medium, Equations 1 and 2 must be solved iteratively. A typical procedure would be to estimate the outlet temperature of the medium, use that in Eq. 1 to calculate the heat transferred (Q_t), and then use Eq. 2 to calculate the medium’s outlet temperature. If the numbers differ, repeat with a new estimate of the medium outlet temperature until the numbers agree closely.

Some engineers may specify that the agitator must be designed to meet a target heat transfer coefficient. But that would be unwise, as the process-side coefficient is only proportional to the agitator power input to an exponent of 0.22–0.26, depending on whether impeller diameter or shaft speed is used to adjust power. The best approach is to design the agitator for the intended mixing job, and then select the heat transfer media flow, temperature, and exchange surfaces to meet the desired heat transfer rate.

The rest of this article focuses on determining the U value — the overall heat transfer coefficient — and exploring the specifics of several heat transfer surfaces commonly used. A sample problem is used to illustrate the concepts...