# Design Data

by the National Mechanical Insulation Committee (NMIC)

Updated:
09-22-2011

## Introduction

This section of the Mechanical Insulation Design Guide is a collection of information and data that are useful to designers and end-users of mechanical insulation systems. The section contains some simple calculators that allow the calculation of heat flow and surface temperatures. Discussion of and links to other more sophisticated computer programs for performing these calculations are included.

## Estimating Heat Loss / Heat Gain

Steady-state, one dimensional heat flow through insulation systems is governed by Fourier's law:

 q = - k·A·dT/dx (1)

where:

q = rate of heat flow, Btu/hr

A = cross sectional area normal to heat flow, ft2

k = thermal conductivity of the insulation material, Btu-in/h ft2°F

For flat geometry of finite thickness, the equation reduces to:

 q = k ·A· (T1–T2)/X (2)

where:

X = thickness of the insulation, in.

For cylindrical geometry, the equation becomes:

 q = k·A2·(T1–T2)/(r2·ln (r2/r1)) (3)

where:

A2= area of outer surface, ft2

The term r2 ln (r2/r1) is sometimes called the "equivalent thickness" of the insulation layer. Equivalent thickness is that thickness of insulation, which, if installed on a flat surface, would yield a heat flux equal to that at the outer surface of the cylindrical geometry.

Heat transfer from surfaces is a combination of convection and radiation. Usually, it is assumed that these modes are additive, and therefore a combined surface coefficient can be used to estimate the heat flow to/from a surface:

 hs = hc + hr (4)

where:

hs = combined surface coefficient, Btu/h ft2 °F

hc = convection coefficient, Btu/h ft2 °F

hr = radiation coefficient, Btu/h ft2 °F

Assuming the radiant environment is equal to the temperature of the ambient air, the heat loss/gain at a surface can be calculated as:

 q = hs·A·(Tsurf–Tamb) (5)

The radiation coefficient is usually estimated as:

 hr = ε·σ·(Tsurf4 –Tamb4)/(Tsurf–Tamb) (6)

where:

ε = emittance of the surface

σ = Stephen-Boltzmann constant (=0.1714 x 10-8 Btu/(h·ft2·°R4)

Tx = Temperature, °R

The emittance (or emissivity) of the surface is defined as the ratio of radiation emitted by the surface to the radiation emitted by a black body at the same temperature. Emittance is a function of the material, its surface condition, and its temperature. A table giving the approximate emittance of commonly used materials is given in Table 1.

Table 1. Emittance Data of Commonly Used Materials

Material Emittance (~80 °F)
All Service Jacket 0.9
Aluminum paint 0.5
Aluminum, anodized 0.8
Aluminum, commercial sheet 0.1
Aluminum, embossed 0.2
Aluminum, oxidized 0.1-0.2
Aluminum, polished 0.04
Aluminum-zinc coated steel 0.06
Canvas 0.7-0.9
Colored mastic 0.9
Copper, highly polished 0.03
Copper, oxidized 0.8
Elastomeric or Polyisobutylene 0.9
Galvanized steel, dipped or dull 0.3
Galvanized steel, new, bright 0.1
Iron or steel 0.8
Painted metal 0.8
Plastic pipe or jacket (PVC, PVDC, or PET) 0.9
Roofing felt and black mastic 0.9
Rubber 0.9
Silicon impregnated fiberglass fabric 0.9
Stainless steel, new, cleaned 0.2

©American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Convection is energy transport by the combined action of heat conduction, energy storage, and mixing action. It is classified as either forced convection (when the mixing motion is induced by some external agency) or natural convection (when the mixing action takes place as a result of density differences caused by temperature gradients). Convection coefficients (hc) may be estimated for a number of simple geometries utilizing correlations of data from experimental studies. These studies utilize appropriate dimensionless parameters to correlate results. Incropera and DeWitt present a number of these correlations in their text "Fundamental of Heat and Mass Transfer". These correlations are also summarized in the ASTM Standard Practice C 680 and in the 2013 ASHRAE Handbook—Fundamentals.

## Controlling Surface Temperatures

A common calculation associated with mechanical insulation systems involves determining the thickness of insulation required to control the surface temperature to a certain value given the operating temperature of the process and the ambient temperature. For example, it may be desired to calculate the thickness of tank insulation required to keep the outside surface temperature at or below 140 F when the fluid in the tank is 450 F and the ambient temperature is 80 F.

At steady state, the heat flow through the insulation to the outside surface equals the heat flow from the surface to the ambient air. In equation form:

 qins = qsurf (7)

Or

 (k/X)·A·(Thot–Tsurf) = h·A·(Tsurf–Tamb) (8)

Rearranging, this equation yields:

 X = (k/h)·[(Thot–Tsurf)/(Tsurf–Tamb)] (9)

Since the ratio of temperature differences is known, the required thickness can be calculated by multiplying by the ratio of the insulation material conductivity to the surface coefficient.

In the example above, assume the surface coefficient can be estimated as 1.0 Btu/h ft2 F, and the conductivity of the insulation to be used is 0.25 Btu-in/h ft2 F. The required thickness can then be estimated as:

X = (0.25/1.0) [(450-140)/(140-80) = 1.29 in.

This estimated thickness would be rounded up to the next available size, probably 1–½".

For radial heat flow, the thickness calculated would represent the equivalent thickness; the actual thickness (r2-r1) would be less (see equation (8) above).

This simple procedure can be used as a first-order estimate. In reality, the surface coefficient is not constant, but varies as a function of surface temperature, air velocity, orientation, and surface emittance.

When performing these calculations, it is important to use the actual dimensions for the pipe and tubing insulation. Many (but not all) pipe and tubing insulation products conform to dimensional standards originally published by the military in MIL-I-2781 and since adopted by other organizations, including ASTM. Standard pipe and insulation dimensions are given for reference in Table 2. Standard tubing and insulation dimensions are given in Table 3. Corresponding dimensional data for flexible closed cell insulations are given in Tables 4 and 5.

For mechanical insulation systems, it is also important to realize that the thermal conductivity (k) of most insulation products varies significantly with temperature. Manufacturer's literature will usually provide curves or tabulations of conductivity versus temperature. When performing heat transfer calculations, it is important to utilize the "effective thermal conductivity", which can be obtained by integration of the conductivity vs. temperature curve, or (as an approximation) utilizing the conductivity evaluated at the mean temperature across the insulation layer. ASTM C 680 provides the algorithms and calculation methodologies for incorporating these equations in computer programs.

These complications are readily handled for a variety of boundary conditions using available computer programs, such as the NAIMA 3E Plus® program (www.pipeinsulation.org). The NAIMA 3E Plus program may also be accessed through the Department Of Energy Industrial Technology Program website at https://ecenter.ee.doe.gov/Pages/default.aspx

An example printout of the 3E Plus® program is shown in Figure 1.

Figure 1. Sample Printout from NAIMA 3E Plus® Program.

Estimates of the heat loss from standard pipe and tube sizes are given in Tables 6 and 7. These are useful for quickly estimating the cost of lost energy due to uninsulated piping.

## Dimensions of Standard Pipe and Tubing Insulation

Table 2. Inner and Outer Diameters of Standard Pipe Insulation

Pipe Size, NPS Pipe OD, in. Insulation ID, in. Insulation Nominal Thickness
1 1–½ 2 2–½ 3 3–½ 4 4–½ 5
½ 0.84 0.86 2.88 4.00 5.00 6.62 7.62 8.62 9.62 10.75 11.75
¾ 1.05 1.07 2.88 4.00 5.00 6.62 7.62 8.62 9.62 10.75 11.75
1 1.315 1.33 3.50 4.50 5.56 6.62 7.62 8.62 9.62 10.75 11.75
1–¼ 1.660 1.68 3.50 5.00 5.56 6.62 7.62 8.62 9.62 10.75 11.75
1–½ 1.900 1.92 4.00 5.00 6.62 7.62 8.62 9.62 10.75 11.75 12.75
2 2.375 2.41 4.50 5.56 6.62 7.62 8.62 9.62 10.75 11.75 12.75
2–½ 2.875 2.91 5.00 6.62 7.62 8.62 9.62 10.75 11.75 12.75 14.00
3 3.500 3.53 5.56 6.62 7.62 8.62 9.62 10.75 11.75 12.75 14.00
3–½ 4.000 4.03 6.62 7.62 8.62 9.62 10.75 11.75 12.75 12.75 14.00
4 4.500 4.53 6.62 7.62 8.62 9.62 10.75 11.75 12.75 14.00 15.00
4–½ 5.000 5.03 7.62 8.62 9.62 10.75 11.75 12.75 14.00 14.00 15.00
5 5.563 5.64 7.62 8.62 9.62 10.75 11.75 12.75 14.00 15.00 16.00
6 6.625 6.70 8.62 9.62 10.75 11.75 12.75 14.00 15.00 16.00 17.00
7 7.625 7.70   10.75 11.75 12.75 14.00 15.00 16.00 17.00 18.00
8 8.625 8.70   11.75 12.75 14.00 12.00 16.00 17.00 18.00 19.00
9 9.625 9.70   12.75 14.00 15.00 16.00 17.00 18.00 19.00 20.00
10 10.75 10.83   14.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00
11 11.75 11.83   15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00
12 12.75 12.84   16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00
14 14.00 14.09   17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00

Table 3. Inner and Outer Diameters of Standard Tubing Insulation

Tube Size, CTS Tube OD, in. Insulation ID Insulation Nominal Thickness
1 1–½ 2 2–½ 3 3–½ 4 4–½ 5
3/8 0.500 0.52 2.38 3.50 4.50 5.56 6.62
½ 0.625 0.64 2.88 3.50 4.50 5.56 6.62
¾ 0.875 0.89 2.88 4.00 5.00 6.62 7.62 8.62 9.62 10.75 11.75
1 1.125 1.14 2.88 4.00 5.00 6.62 7.62 8.62 9.62 10.75 11.75
1–¼ 1.375 1.39 3.50 4.50 5.56 6.62 7.62 8.62 9.62 10.75 11.75
1–½ 1.625 1.64 3.50 4.50 5.56 6.62 7.62 8.62 9.62 10.75 11.75
2 2.125 2.16 4.00 5.00 6.62 7.62 8.62 9.62 10.75 11.75 12.75
2–½ 2.625 2.66 4.50 5.56 6.62 7.62 8.62 9.62 10.75 11.75 12.75
3 3.125 3.16 5.00 6.62 7.62 8.62 9.62 10.75 11.75 12.75 14.00
3–½ 3.625 3.66 5.56 6.62 7.62 8.62 9.62 10.75 11.75 12.75 14.00
4 4.125 4.16 6.62 7.62 8.62 9.62 10.75 11.75 12.75 14.00 15.00
5 5.125 5.16 7.62 8.62 9.62 10.75 11.75 12.75 14.00 15.00 16.00
6 6.125 6.20 8.62 9.62 10.75 11.75 12.75 14.00 15.00 16.00 17.00

Table 4. Inner and Outer Diameters of Standard Flexible Closed Cell Pipe Insulation

Pipe Size, NPS Pipe OD, in. Insulation ID, in. Insulation OD, Inches
Insulation Nominal Thickness
½" ¾" 1"
½ 0.84 .97 1.87 2.47 2.97
¾ 1.05 1.13 2.03 2.63 3.13
1 1.315 1.44 2.44 2.94 3.44
1–¼ 1.660 1.78 2.78 3.38 3.78
1–½ 1.900 2.03 3.03 3.63 4.03
2 2.375 2.50 3.50 4.10 4.50
2–½ 2.875 3.00 4.00 4.60 5.00
3 3.500 3.70 4.66 5.26 5.76
3–½ 4.000 4.20 5.30 5.90 6.40
4 4.500 4.70 5.88 6.40 6.90
4–½ 5.000
5 5.563 5.76 6.86 7.46 7.96
6 6.625 6.83 7.93 8.53 9.03
7 7.625
8 8.625 8.82 9.92 10.52

Table 5. Inner and Outer Diameters of Standard Flexible Closed Cell Tubing Insulation

Tube Nominal Size, in. Tube OD Insulation ID, in. Insulation OD, Inches
Insulation Nominal Thickness
½" ¾" 1"
3/8 0.500 .600 1.500 1.950
½ 0.625 .750 1.650 2.150 2.750
¾ 0.875 1.000 1.950 2.500 3.000
1 1.125 1.250 2.220 2.850 3.250
1–¼ 1.375 1.500 2.500 3.100 3.500
1–½ 1.625 1.750 2.750 3.350 3.750
2 2.125 2.250 3.250 3.850 4.250
2–½ 2.625 2.750 3.750 4.350 4.750
3 3.125 3.250 4.250 4.850 5.250
3–½ 3.625 3.750 4.850 5.450 5.950
4 4.125 4.250 5.350 5.950 6.450

## Heat Loss from Bare Pipe and Tubing

Table 6. Heat Loss from Bare Steel Pipe to Still Air at 80 °F, Btu/h·ft

Nominal Pipe Size, in. Pipe Inside Temperature, °F
180 280 380 480 580
½ 56.3 138 243 377 545
¾ 68.1 167 296 459 665
1 82.5 203 360 560 813
1–¼ 102 251 446 695 1010
1–½ 115 283 504 787 1150
2 141 350 623 974 1420
2–½ 168 416 743 1160 1700
3 201 499 891 1400 2040
3–½ 228 565 1010 1580 2310
4 254 631 1130 1770 2590
4–½ 281 697 1250 1960 2860
5 313 777 1390 2180 3190
6 368 915 1640 2580 3770
7 421 1040 1880 2950 4310
8 473 1180 2110 3320 4860
9 525 1310 2340 3680 5400
10 583 1450 2610 4100 6000
12 686 1710 3070 4830 7090
14 747 1860 3340 5260 7720
16 850 2120 3810 6000 8790
18 953 2380 4270 6730 9870
20 1060 2630 4730 7460 10950
24 1260 3150 5660 8920 13100

©American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Table 7. Heat Loss from Bare Copper Tube to Still Air at 80 °F, Btu/h·ft

Nominal Tube Size, in. Tube Inside Temperature, °F
120 150 180 210 240
3/8 10.6 20.6 31.9 44.2 57.5
½ 12.7 24.7 38.2 53.1 69.2
¾ 16.7 32.7 50.7 70.4 91.9
1 20.7 40.5 62.9 87.5 114
1–¼ 24.6 48.3 74.9 104 136
1–½ 28.5 55.9 86.9 121 158
2 36.1 71.0 110 154 201
2–½ 43.7 86.0 134 187 244
3 51.2 101 157 219 287
3–½ 58.7 116 180 251 329
4 66.1 130 203 283 371
5 80.9 159 248 347 454
6 95.6 188 294 410 538
8 125 246 383 536 703
10 154 303 473 661 867
12 183 360 562 786 1031

©American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.