Design Data

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
dT/dx = temperature gradient, °F/in

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:

r₂ = outer radius, in
r₁ = inner radius, in
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:

h_s = combined surface coefficient, Btu/h ft² °F
h_c = convection coefficient, Btu/h ft² °F
h_r = 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)
T_x = 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 (h_c) 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).

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

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.