PR

# U-factor | Overall Heat Transfer Coefficient

Introduce an example of data collection and analysis of the overall heat transfer coefficient ( U-factor ) at the factory site .

Calculation formulas are textbook-like, but data collection is often analog.

Engineers may be surprisingly unaware of what is going on at the field level.

In many cases, we only focus on desk calculations and the point that if the operation goes well, we do not analyze the operation results.

Running away from analysis in this way will not lead to improvement in design skills as a result.

There are elements of trial and error, but I definitely want to take on the challenge.

## Formula for U-factor

The following formula is the basis.

$$Q = UAΔt$$

Let’s convert this formula into an expression that is conscious of finding the U value.

$$U = \frac{Q}{AΔt}$$

You can see that the following elements are required to determine the U value from this formula:

• Heat exchange Q
• Heat transfer area A
• Temperature difference Δt

Let’s look at each element in a little more detail.

## Heat exchange Q

The amount of heat exchanged Q varies depending on the operating conditions.

Consider the flow below.

This is a typical batch process.

Since it is a batch operation, the calculation conditions for the U value change according to various conditions.

### Reactor heating

Let’s look at the stages of heating the reactor.

It is easy to collect data on the amount of heat exchanged at this stage.

All you have to do is check the temperature change of the process liquid in the reactor.

Collect the time data of the thermometer and calculate mCΔt from the liquid volume m and the temperature difference Δt.

Specific heat C will have to make some assumptions.

A level gauge is required to measure the process liquid volume, so it may not be a viable option in some cases.

It may be more stable to check the steam side.

Qv F1 can be calculated from the latent heat of vaporization Qv of steam and the flow rate F1.

Pressure data is required to calculate Qv. Since there are few factors that fluctuate greatly during operation, the steam pressure can be assumed to be constant.

A steam flow meter is essential to control the heating conditions.

### Reactor evaporation

When the process liquid finishes heating and evaporates, unlike the heating stage, it is better to focus on the steam flow rate.

Mathematically, calculating the change in the liquid level in the reactor may seem sufficient, but the liquid level generally fluctuates during operation.

This is because the liquid will rise and fall due to stirring and evaporation.

On the other hand, the steam flow rate is stable.

### heat exchanger cooling

Let’s look at the case of cooling the evaporated gas with a heat exchanger.

This will be calculated as gas flow mp × temperature difference Δt.

How do you calculate the gas flow mp?

The amount of heat exchanged in the reactor /the latent heat of process evaporation.

Do the same calculation as Qv m1 calculated in Steam .

Given the latent heat of vaporization Qp gas flow rate mp of the process,

$$Q_vm_1 = Q_pm_p$$

Calculate as Simple to say the least.

The calculation of Δt will rely on a thermometer.

On-site instruments are also acceptable, so let’s incorporate a thermometer as a basic set at the entrance and exit of the heat exchanger.

If you don’t have a thermometer, you’re going to do some pretty miserable calculations.

It measures the temperature by sampling the cooling water at the inlet and outlet while indirectly measuring the flow rate on the cooling water side.

Analog.

It is rare to install an in-line flow meter for cooling water in a heat exchanger, and you will likely rely on a flow meter that can be measured from outside the pipe.

Calculation results change only how much this accuracy is reliable.

In addition, we also pay a lot of attention to sampling.

If you allow yourself to be careful even if you sample, the temperature will drop steadily.

Confidence will plummet.

Even if you use a thermometer that can measure from outside the pipe like a flow meter, the reliability will drop significantly.

However, there are not many examples of severe U-value measurement in heat exchangers.

Even if the U-value is determined for a single product under specific operating conditions, there are many possible cooling water variations at the production level.

• Heat load of other users
• seasonal factor
• Operating status of refrigerator

I think it’s okay to loosely think that it’s OK all year round as long as it’s sufficiently cooled down.

It will be enough if it cools down to about +10°C of the cooling water temperature.

Generally around 30-40°C.

## Heat transfer area A

This is practically just a matter of simple geometric calculations.

The heat transfer area may also be written on the manufacturer’s drawing.

It can be easily calculated even at the field level.

Calculating the heat transfer area of ​​the mirror may be troublesome, but if you search on the internet, you will find many.

We live in a convenient world.

Having said that, this heat transfer area is quite troublesome.

When evaporating, the process liquid level decreases moment by moment, so the heat transfer area also decreases .

When condensing in a heat exchanger, the heat transfer surface that contributes to condensation cannot be measured in the first place.

## Temperature difference Δt

Temperature difference Δt can come up with logarithmic mean temperature difference or arithmetic mean temperature difference.

Arithmetic mean temperature difference is sufficient at field level.

$$t_a – t_b$$

is the world of

• Process Thermometer – Steam Saturation Temperature for Reactor Heating and Evaporation
• If it is a heat exchanger, heat exchanger thermometer – cooling water temperature

It is easy to collect data on the reactor side.

• Calculated from the relationship between saturated steam pressure and saturated temperature assuming a constant steam pressure
• Subtract two data

Only this.

On the heat exchanger side, the temperature of the cooling water is assumed.

U-value measurements for heat exchangers are not very reliable at this moment.

If you’re serious about heat control with an important heat exchanger, you’ll have a proper thermometer, so that doesn’t mean you shouldn’t take U-value calculations seriously for all of your heat exchangers.

Batch means that there are not many such critical heat exchangers.

## U value (U-factor) changes from time to time

The U value changes every moment.

This is because the data of the thermometer and liquid level gauge change from time to time.

When calculating the U value in facility design, it is likely that the instantaneous and maximum conditions are calculated.

If you try to calculate it seriously, it will be a calculus-integral world that tracks changes over time such as changes in the liquid surface.

It’s a little troublesome to calculate that much.

I don’t think there are many mechanical and electrical engineers who can handle that troublesome work.

## reference

Knowledge of heat transfer is a very important area in chemical plants.

To deepen your knowledge about heat, it is important to study the following books.  created by Rinker
¥2,310(2023/09/29 20:48:47時点 楽天市場調べ-詳細)

## Related article

Related information

shell and tube design

shell and tube structure

plate heat exchanger

## lastly

I explained how to collect on-site data for the overall heat transfer coefficient (U value) in a batch chemical plant.

In order to calculate Q=UAΔt, information such as thermometer and flow meter is required.

I realized that I needed instruments to be incorporated into the DCS for proper operation management.

The combination of heat transfer calculations and field measurements gives you confidence in your heat balance design. 