A2<\/sub>= area of outer surface, ft2<\/sup><\/p>\n
r2<\/sub>\u00a0= outer radius, in<\/p>\n
r1<\/sub>\u00a0= inner radius, in<\/p>\n
The term r2<\/sub>\u00a0in (r2<\/sub>\/r1<\/sub>) is sometimes called the \"equivalent thickness\" of the insulation layer. Equivalent thickness is that thickness of insulation that, if installed on a flat surface, would yield a heat flux equal to that at the outer surface of the cylindrical geometry.<\/p>\n
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 (equation #4):<\/p>\n
Assuming the radiant environment is equal to the temperature of the ambient air, the heat loss\/gain at a surface can be calculated (equation #5):<\/p>\n
\u03c3 = Stephen-Boltzmann constant (=0.1714 x 10-8<\/sup>\u00a0Btu\/(h\u00b7ft2<\/sup>\u00b7\u00b0R4<\/sup>)<\/p>\n
Tx<\/sub> = Temperature, \u00b0R<\/p>\n
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. The approximate emittance of commonly used materials is given in Table 1.<\/p>\n
Table 1. Emittance Data of Commonly Used Materials<\/p>\n
\n\n
\n
Material<\/th>\n
Emittance (~80 \u00b0F)<\/th>\n<\/tr>\n
\n
All service jacket<\/td>\n
0.9<\/td>\n<\/tr>\n
\n
Aluminum, anodized<\/td>\n
0.8<\/td>\n<\/tr>\n
\n
Aluminum, commercial sheet<\/td>\n
0.1<\/td>\n<\/tr>\n
\n
Aluminum, embossed<\/td>\n
0.2<\/td>\n<\/tr>\n
\n
Aluminum, oxidized<\/td>\n
0.1\u20130.2<\/td>\n<\/tr>\n
\n
Aluminum, polished<\/td>\n
0.04<\/td>\n<\/tr>\n
\n
Aluminum paint<\/td>\n
0.5<\/td>\n<\/tr>\n
\n
Aluminum-zinc coated steel<\/td>\n
0.06<\/td>\n<\/tr>\n
\n
Canvas<\/td>\n
0.7\u20130.9<\/td>\n<\/tr>\n
\n
Colored mastic<\/td>\n
0.9<\/td>\n<\/tr>\n
\n
Copper, highly polished<\/td>\n
0.03<\/td>\n<\/tr>\n
\n
Copper, oxidized<\/td>\n
0.8<\/td>\n<\/tr>\n
\n
Elastomeric or polyisobutylene<\/td>\n
0.9<\/td>\n<\/tr>\n
\n
Galvanized steel, dipped or dull<\/td>\n
0.3<\/td>\n<\/tr>\n
\n
Galvanized steel, new, bright<\/td>\n
0.1<\/td>\n<\/tr>\n
\n
Iron or steel<\/td>\n
0.8<\/td>\n<\/tr>\n
\n
Painted metal<\/td>\n
0.8<\/td>\n<\/tr>\n
\n
Plastic pipe or jacket (PVC, PVDC, or PET)<\/td>\n
0.9<\/td>\n<\/tr>\n
\n
Roofing felt and black mastic<\/td>\n
0.9<\/td>\n<\/tr>\n
\n
Rubber<\/td>\n
0.9<\/td>\n<\/tr>\n
\n
Silicon impregnated fiberglass fabric<\/td>\n
0.9<\/td>\n<\/tr>\n
\n
Stainless steel, new, cleaned<\/td>\n
0.2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\u00a9American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.<\/p>\n
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<\/sub>) may be estimated for a number of simple geometries using 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 \"Fundamentals of Heat and Mass Transfer.\" These correlations are also summarized in the\u00a0ASTM Standard Practice C680<\/a>,<\/u>\u00a0and in the\u00a0ASHRAE Handbook\u2014Fundamentals<\/a><\/em>.<\/p>\n
X = (k\/h)\u00b7[(Thot<\/sub>\u2013Tsurf<\/sub>)\/(Tsurf<\/sub>\u2013Tamb<\/sub>)]<\/p>\n<\/td>\n
\n
(9)<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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.<\/p>\n
In the example above, assume the surface coefficient can be estimated as 1.0 Btu\/h ft2<\/sup> \u00a0\u00b0F, and the conductivity of the insulation to be used is 0.25 Btu-in\/h ft2<\/sup>\u00a0\u00b0F. The required thickness can then be estimated as:<\/p>\n
X = (0.25\/1.0) [(450-140)\/(140-80) = 1.29 in.<\/p>\n
This estimated thickness would be rounded up to the next available size, probably 1\u2011\u00bd\".<\/p>\n
For radial heat flow, the thickness calculated would represent the equivalent thickness; the actual thickness (r2<\/sub>-r1<\/sub>) would be less\u2014see Equation (8).<\/p>\n
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.<\/p>\n
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 .<\/p>\n
For mechanical insulation systems, it is also important to realize that the thermal conductivity (k) of most insulation products varies significantly with temperature. Manufacturers\u2019 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 versus temperature curve, or (as an approximation) utilizing the conductivity evaluated at the mean temperature across the insulation layer. ASTM C680 provides the algorithms and calculation methodologies for incorporating these equations in computer programs.<\/p>\n
These complications are readily handled for a variety of boundary conditions using available software, such as NAIMA\u2019s 3E Plus\u00ae (www.pipeinsulation.org<\/em><\/a>).<\/p>\n