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# Example of Optimal Calculation about Insulation thickness

Using the calculation table of JIS A 9501 Thermal and Cold Insulation Construction Standards, I tried to calculate the optimal insulation thickness.

I think that there are probably quite a few companies that calculate the thickness of heat insulation and design it optimally for their own company.

It will be that the value according to the JIS standard is adopted. Our company is the same.

Even if you want to change the design conditions, there are already many calculation software on the market.

In that sense, there are almost no opportunities to use the contents of this article.

By looking at the JIS standards and performing calculations on your own and checking your answers, I hope that you will deepen your understanding of the standards and use them as references for other engineering calculations.

If you work as an engineering person for a long time, you should be familiar with such calculations.

If you move to manager management work after a certain number of years, the chances of calculating will decrease and the technology will deteriorate.

## Prerequisites for optimal insulation thickness

Organize the calculation target conditions.

• JIS G 3452 Outer diameter of SGP pipe
• Ambient temperature 20℃
• Surface heat transfer coefficient 12W/(m 2・K)
• 5% annual interest rate
• 15 years of use
• Calorie price 5 yen/(kWh)
• Annual use time 4000 hours

These parameters can be used under almost the same conditions in Japan.

If you dare to change it, it will be about changing the ambient temperature for cold regions .

Changing the annual interest rate, years of use, and calorific value will be limited to cases where the conditions are different from those in Japan, such as overseas.

If you care about this range of influence, you will never be able to determine the thickness.

Let’s organize the formulas.

Insulation material construction cost

$$a=10^3×(12×d^{-k}＋300)$$

k=1.00 to 1.30 depending on aperture.

A calcium silicate heat insulator is assumed.

heat transfer coefficient

$$λ=0.0407+1.28×10^{-4}×Θ$$

Annual depreciation rate

$$N=\frac{n×{(1+n)}^y}{{(1+n)}^y-1}$$

## Calculation example of optimum insulation thickness

Calculation of the optimum heat insulation thickness consists of two calculations: heat dissipation calculation and cost calculation.Determining process for optimum insulation thickness

• step1 Heat dissipation calculation
• step2 cost calculation
• step3 Selection of optimum thickness

As a simple example, we will take up insulation of pipes.

There are slightly different calculation formulas for heat insulation and cold insulation, flat surfaces and piping, but the basic idea is the same.

First, let’s calculate the main heat dissipation.

Calculation of the amount of heat dissipation is determined by heat transfer coefficient x temperature difference .

Consider the composite heat transfer coefficient (heat transfer coefficient/heat transmission flow) of the surface heat transfer coefficient and the heat transfer coefficient of the heat insulating material.

Heat dissipation calculation

$$q=\frac{1}{R_t}(Θ_{si}-Θ_a)$$

Thermal resistance calculation

$$R_t=\frac{1}{2πλ}ln\frac{D_e}{D_i}+\frac{1}{h_{se}πD_e}$$

Here, assumptions are made about the outer shape of the insulation material D e .

It is a process of calculating the optimum insulation thickness by calculating the economic efficiency for the assumed insulation thickness.Insulation Thickness Calculation Process

• step1 Assumption of insulation thickness
• step2 Economic evaluation
• step3 Selection of optimum thickness

Let’s calculate under the conditions of ambient temperature 20°C, heat insulation material temperature 100°C, heat insulation thickness 20 mm at 20 A.

It means that you want to keep the piping at 100°C against the outside air temperature of 20°C, so let’s start with a heat insulation thickness of 20mm.

### Insulation average temperature

First find the average insulation temperature Θ.

This takes the average temperature inside and outside the insulation.

Since the inside is 100°C and the outside is 20°C, (100+20)/2 = 60°C .

Strictly speaking, the ambient temperature and the outside temperature of the heat insulator are not the same, and the outside temperature of the heat insulator should be slightly higher, but we will ignore it here.

Calculations are complicated.

### Insulation heat transfer coefficient

Next, calculate the heat transfer coefficient of the insulation.

The heat transfer coefficient of insulation depends on the temperature of the insulation.

Here, use the average temperature Θ of the heat insulating material obtained earlier.

0.0407+1.28×10-4 × 60 = 0.0484 W/(m・K).

Temperature has little effect on the heat transfer rate.

### overall thermal resistance

Let’s calculate the overall thermal resistance.

1/(2×π×0.0484)×ln(61.7/21.7) = 3.4 (m・K)/W

here

• The 20mm SGP has an outer diameter of 21.7mm .
• The insulation thickness is 20mm, so the outer diameter of the insulation is 21.7+20×2= 61.7mm .

Again, if the thickness of the insulation changes, the calculation results here will change.

Calculate the surface heat transfer coefficient in the same way.

1/(12×π×0.0617) = 0.5 (m・K)/W

Don’t forget to set the unit of the outer diameter of the insulation to m.

Finally, calculate the overall thermal resistance.

t =3.4+0.5 = 3.9 (m・K)/W

From here, calculating the amount of heat dissipation is easy.

1/3.9 x (100-20) = 20.7 W/m

I’m not sure what this number means.

## cost

Let’s take a look at the cost calculation for insulation.

### depreciation rate

Apply the depreciation rate calculation directly.

{0.05×(1+0.05) 15 }/{(1+0.05) 15 -1} = 0.096

### Insulation material installation unit price

The construction unit price of the insulation material is the same as the calculation formula.

12×0.020 -1.3 +300= 2,240 yen

### Economic insulation thickness calculation

To calculate the economic insulation thickness, add the following two:

• Insulation material installation price
• Heat dissipation unit price

Insulation material installation price

π/4*(0.0617 2 -0.0217 2 )×2240×0.096/1000 = 565 thousand yen

The weight of the insulation is calculated as concentric cylinders and multiplied by the depreciation rate.

Units are summarized in thousand yen.

The heat dissipation unit price is

5×4000×20.7/1000 = 414,000 yen

It is the amount of heat dissipation and time multiplied by the heat unit price.

Note that calculations are performed in units of m.

565+414= 979 thousand yen/m

## Comparison of ambient temperature and optimum insulation thickness

This calculation is for calculating the insulation thickness to maintain the inside of a 20A pipe at 100°C at an ambient temperature of 20°C .

The calculations so far have shown that a heat insulation thickness of 20 mm costs 979,000 yen/m .

Insulation thicknesses of 30 mm and 40 mm are calculated in the same way.

Just put the data.

• Thermal insulation thickness 20mm 979,000 yen
• Thermal insulation thickness 25mm 991,000 yen
• Insulation thickness 30mm 1,020,000 yen

From this result, 20mm is optimal.

It is 25 mm when compared with the table of JIS .

It’s a little different.

There is a comment on JIS, but the difference comes out depending on the rounding of the program.

It would be nice if it was roughly OK.

## reference

Widely known standards such as JIS tend to be used without knowing the basis for them.

The way of thinking is only using the basics of heat transfer, so if you study with the following books, you will deepen your understanding.

created by Rinker
¥2,310 (2024/03/16 12:34:45時点 楽天市場調べ-詳細)

Related article

## lastly

Introduced an example of calculating the optimum insulation thickness of JIS.

When I try to make this calculation in Excel and compare the results, I find that they are almost the same, which gives me confidence as an engineer.

For example, it is possible to freely calculate what would happen if the ambient temperature were set to 0°C.