Course 11 What is film heat transfer coefficient , hi?

Well, here is a trial production experiment building of a certain chemical company again. Current recipe of the prototype is, a low viscosity monomer raw material becomes a high viscosity polymer (about 20 Pa·s) in the final stage. Then it will be cooled from 150 °C to 80 °C and be transferred to the following processes.

They checked mixing condition of the viscosity increased polymer solution through the observation glass. The photos and video clip are below. (For the sake of convenience, simulant mixing condition from our 200 litter testing apparatus is posted.) Check it out.

< Mixing Conditions >
Impeller types:
3 stages pitched blade paddle
Fluid types:
non-Newtonian fluid (CMC aqueous solutions, viscosity: 20 Pa·s)
Diameter of the vessel: 600 mm
Fluid volume: 130 L

< Mixing Conditions >

Hi everyone, how was it? As you can see, the two people are shocked to see the fluid stopping phenomenon of non-Newtonian fluids for the first time.
The photos and video clip above show test examples with 3 stages pitched paddle impellers in CMC solutions of about 20 Pa·s.
For example, when cooking curry or stew, you may want to scrape the bottom or sides of the pod with a ladle. That is because the target liquid is close to the fluid as shown.
As with miso soup and stew, the tools for mixing are different. Similarly, it is very important to select the best mixing impellers depending on the objects and operation methods. It is extremely difficult to estimate mixing times and heat transfer coefficients for a mixing vessel when the overall circulation flow has not yet been formed.

The example we introduced here may be a little extreme, but in an actual industrial setting, situations similar to these phenomena sometimes occur during manufacturing.
With this in mind, look at the equation for calculating film heat transfer coefficients. The basic formula is shown in Equation 1 below.

Other symbols are as follows:

Oh No! Nusselt number, Prandtl number, again, you see words that may be unfamiliar. We will leave the detailed explanation to technical books. Understand the meaning of each dimensionless number in the following way.

What is the Nusselt number (Nu)?:
It is the ratio of convection heat transfer to fluid conduction heat transfer.

In case of mixing operation, it is the ratio of the amount of heat transferred by forced convection with impellers to the amount of heat transferred by heat conduction of the fluid itself.
Therefore, Nu = 1 is a completely stationary fluid (heat is transferred only by heat conduction).
Note that characteristic length D is included as expressed for Np values and Re number. Therefore, when geometric similarity conditions cannot be kept, we cannot discuss the magnitude of heat transfer performance depending on the Nusselt number, similar to the Np value.
In addition, the inner diameter D is usually used as characteristic length for jacket heat transfer in the mixing vessel.

What is the Prandtl number (Pr)?:
It indicates the ratio of thickness of velocity boundary layer to thickness of temperature boundary layer.

Well, it is difficult. Considering jacket heat transfer in a mixing vessel, it can be explained as follows.
Thickness of velocity boundary layer means the radial dimension from the vessel inner wall surface where the flow velocity is zero to bulk flow velocity in the vessel.
Thickness of temperature boundary layer is defined as the radial dimension from the vessel wall to a position where the temperature has reached to a stable temperature.
Therefore, it indicates that the smaller the Prandtl number, the faster the heat diffuses compared to the fluid momentum.
Prandtl number is a dimensionless number determined only by physical property (viscosity, specific heat, and thermal conductivity). Try to memorize the approximate value for typical ones.
Examples at a temperature of 20 °C are as follows: Air is 0.71, Water is about 7.1, and Spindle Oil is about 168. As the fluid becomes sticky (high viscosity), the Prandtl number steadily increases.

Now, from basic equation (1), the relationship with each factor of the film heat transfer coefficient hi of a mixing vessel is as follows:

Therefore, the contribution ratio for each factor is as follows:

With equation 3, we will explain some important points when considering the film heat transfer coefficient hi of a mixing vessel.

That is all for this session. We introduced important design points regarding film heat transfer coefficients for inside of a vessel (hi), which can be critical to heat transfer while mixing.
In general, hi calculation formula is organized as a function of the Reynolds number and the Prandtl number; however, circulating flow reaching the overall area of a vessel must be formed by mixing impellers.
However, for highly viscous liquids with high non-Newtonian properties, hi suddenly decreases in some cases due to the fluid stopping phenomenon. In such a condition, it is also necessary to consider other options, such as special large impellers and complex, multi-shaft mixers.

We will summarize the mixing course (beginners' course) in the next session. Also, we will review what we have discussed over the past year.
Not the overall heat transfer coefficients, U values, it will be about the overall summary of mixing course!
A variety of unit operations, such as reaction, dissolution, heat transfer, and extraction, are occurring inside a mixing vessel. What is rate limiting in the mixing device you are studying? It may be the same as identifying the maximum resistance factor of the overall heat transfer coefficient.
The ability to notice the most important thing is needed for a true engineer!