# ASTM C680-14

Designation C680 − 14Standard Practice forEstimate of the Heat Gain or Loss and the SurfaceTemperatures of Insulated Flat, Cylindrical, and SphericalSystems by Use of Computer Programs1This standard is issued under the fixed designation C680; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon ´ indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice provides the algorithms and calculationologies for predicting the heat loss or gain and surfacetemperatures of certain thermal insulation systems that canattain one dimensional, steady- or quasi-steady-state heattransfer conditions in field operations.1.2 This practice is based on the assumption that the thermalinsulation systems can be well defined in rectangular, cylindri-cal or spherical coordinate systems and that the insulationsystems are composed of homogeneous, unily dimen-sioned materials that reduce heat flow between two differenttemperature conditions.1.3 Qualified personnel familiar with insulation-systemsdesign and analysis should resolve the applicability of theologies to real systems. The range and quality of thephysical and thermal property data of the materials comprisingthe thermal insulation system limit the calculation accuracy.Persons using this practice must have a knowledge of thepractical application of heat transfer theory relating to thermalinsulation materials and systems.1.4 The computer program that can be generated from thealgorithms and computational ologies defined in thispractice is described in Section 7 of this practice.The computerprogram is intended for flat slab, pipe and hollow sphereinsulation systems.1.5 The values stated in inch-pound units are to be regardedas standard. The values given in parentheses are mathematicalconversions to SI units that are provided for ination onlyand are not considered standard.1.6 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards2C168 Terminology Relating to Thermal InsulationC177 Test for Steady-State Heat Flux Measure-ments and Thermal Transmission Properties by Means ofthe Guarded-Hot-Plate ApparatusC335 Test for Steady-State Heat Transfer Propertiesof Pipe InsulationC518 Test for Steady-State Thermal TransmissionProperties by Means of the Heat Flow Meter ApparatusC585 Practice for Inner and Outer Diameters of ThermalInsulation for Nominal Sizes of Pipe and TubingC1055 Guide for Heated System Surface Conditions thatProduce Contact Burn InjuriesC1057 Practice for Determination of Skin Contact Tempera-ture from Heated Surfaces Using a Mathematical Modeland Thermesthesiometer2.2 Other DocumentNBS Circular 564 Tables of Thermodynamic and TransportProperties of Air, U.S. Dept of Commerce3. Terminology3.1 Definitions3.1.1 For definitions of terms used in this practice, refer toTerminology C168.3.1.2 thermal insulation systemfor this practice, a thermalinsulation system is a system comprised of a single layer orlayers of homogeneous, unily dimensioned materialsintended for reduction of heat transfer between two differenttemperature conditions. Heat transfer in the system is steady-state. Heat flow for a flat system is normal to the flat surface,and heat flow for cylindrical and spherical systems is radial.3.2 Symbols1This practice is under the jurisdiction of ASTM Committee C16 on ThermalInsulation and is the direct responsibility of Subcommittee C16.30 on ThermalMeasurement.Current edition approved Sept. 1, 2014. Published December 2014. Originallyapproved in 1971. Last previous edition approved in 2010 as C680 - 10. DOI10.1520/C0680-14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume ination, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.1 The following symbols are used in the development ofthe equations for this practice. Other symbols will be intro-duced and defined in the detailed description of the develop-ment.whereh surface transfer conductance, Btu/h·ft2·°F W/m2·K hiat inside surface; hoat outside surfacek apparent thermal conductivity, Btu·in./h·ft2·°F W/m·Kke effective thermal conductivity over a prescribed tem-perature range, Btu·in./h·ft2·°F W/m·Kq heat flux, Btu/h·ft2W/m2qp time rate of heat flow per unit length of pipe, Btu/h·ftW/mR thermal resistance, °F·h·ft2/Btu K·m2/Wr radius, in. m; rm1− rm thicknesst local temperature, °F Kti inner surface temperature of the insulation, °F Kt1 inner surface temperature of the systemto temperature of ambient fluid and surroundings, °F Kx distance, in. m; xm1− xm thicknessε effective surface emittance between outside surfaceand the ambient surroundings, dimensionlessσ Stefan-Boltzmann constant, 0.1714 10-8Btu/h·ft2·°R4 5.6697 10-8W/m2·K4Ts absolute surface temperature, °R KTo absolute surroundings ambient air if assumed thesame temperature, °R KTmTs To/2L characteristic dimension for horizontal and verticalflat surfaces, and vertical cylindersD characteristic dimension for horizontal cylinders andspherescp specific heat of ambient fluid, Btu/lb·°R J/kg·Khc average convection conductance, Btu/h·ft2·°F W/m2·Kkf thermal conductivity of ambient fluid, Btu/h·ft·°FW/m·KV free stream velocity of ambient fluid, ft/h m/sυ kinematic viscosity of ambient fluid, ft2/h m2/sg acceleration due to gravity, ft/h2m⁄s2β volumetric thermal expansion coefficient of ambientfluid, °R-1K-1ρ density of ambient fluid, lb/ft3kg⁄m3∆T absolute value of temperature difference betweensurface and ambient fluid, °R KNu Nusselt number, dimensionlessRa Rayleith number, dimensionlessRe Reynolds number, dimensionlessPr Prandtl number, dimensionless4. Summary of Practice4.1 The procedures used in this practice are based onstandard, steady-state, one dimensional, conduction heat trans-fer theory as outlined in textbooks and handbooks, Refs1,2,3,4,5,6. Heat flux solutions are derived for temperaturedependent thermal conductivity in a material. Algorithms andcomputational ologies for predicting heat loss or gain ofsingle or multi-layer thermal insulation systems are providedby this practice for implementation in a computer program. Inaddition, interested parties can develop computer programsfrom the computational procedures for specific applicationsand for one or more of the three coordinate systems consideredin Section 6.4.1.1 The computer program combines functions of data, analysis and data output into an easy to use, interactivecomputer program. By making the program interactive, littletraining for operators is needed to per accurate calcula-tions.4.2 The operation of the computer program follows theprocedure listed below4.2.1 Data The computer requests and the operators ination that describes the system and operatingenvironment. The data includes4.2.1.1 Analysis identification.4.2.1.2 Date.4.2.1.3 Ambient temperature.4.2.1.4 Surface transfer conductance or ambient windspeed, system surface emittance and system orientation.4.2.1.5 System DescriptionMaterial and thickness foreach layer define sequence from inside out.4.2.2 AnalysisOnce data is entered, the programcalculates the surface transfer conductances if not entereddirectly and layer thermal resistances. The program then usesthis ination to calculate the heat transfer and surfacetemperature. The program continues to repeat the analysisusing the previous temperature data to update the estimates oflayer thermal resistance until the temperatures at each surfacerepeat within 0.1°F between the previous and present tempera-tures at the various surface locations in the system.4.2.3 Program OutputOnce convergence of the tempera-tures is reached, the program prints a table that presents the data, calculated thermal resistance of the system, heatflux and the inner surface and external surface temperatures.5. Significance and Use5.1 Manufacturers of thermal insulation express the perfor-mance of their products in charts and tables showing heat gainor loss per unit surface area or unit length of pipe. This data ispresented for typical insulation thicknesses, operatingtemperatures, surface orientations facing up, down, horizontal,vertical, and in the case of pipes, different pipe sizes. Theexterior surface temperature of the insulation is often shown toprovide ination on personnel protection or surface con-densation. However, additional ination on effects of windvelocity, jacket emittance, ambient conditions and other influ-ential parameters may also be required to properly select aninsulation system. Due to the large number of combinations ofsize, temperature, humidity, thickness, jacket properties, sur-face emittance, orientation, and ambient conditions, it is notpractical to publish data for each possible case, Refs 7,8.5.2 Users of thermal insulation faced with the problem ofdesigning large thermal insulation systems encounter substan-tial engineering cost to obtain the required ination. Thiscost can be substantially reduced by the use of accurateengineering data tables, or available computer analysis tools, orboth. The use of this practice by both manufacturers and usersof thermal insulation will provide standardized engineeringC680 − 142data of sufficient accuracy for predicting thermal insulationsystem perance. However, it is important to note that theaccuracy of results is extremely dependent on the accuracy ofthe data. Certain applications may need specific data toproduce meaningful results.5.3 The use of analysis procedures described in this practicecan also apply to designed or existing systems. In the rectan-gular coordinate system, Practice C680 can be applied to heatflows normal to flat, horizontal or vertical surfaces for all typesof enclosures, such as boilers, furnaces, refrigerated chambersand building envelopes. In the cylindrical coordinate system,Practice C680 can be applied to radial heat flows for all typesof piping circuits. In the spherical coordinate system, PracticeC680 can be applied to radial heat flows to or from stored fluidssuch as liquefied natural gas LNG.5.4 Practice C680 is referenced for use with Guide C1055and Practice C1057 for burn hazard uation for heatedsurfaces. Infrared inspection, in-situ heat flux measurements,or both are often used in conjunction with Practice C680 touate insulation system perance and durability ofoperating systems. This type of analysis is often made prior tosystem upgrades or replacements.5.5 All porous and non-porous solids of natural or man-made origin have temperature dependent thermal conductivi-ties. The change in thermal conductivity with temperature isdifferent for different materials, and for operation at a relativelysmall temperature difference, an average thermal conductivitymay suffice. Thermal insulating materials k tUwhere a1, a2, a3, b1, b2, b3 are constants, andtLand tUare, respectively, the lower and upperinflection points of an S-shaped curveAdditional or different relationships may be used, but the mainprogram must be modified.8. Report8.1 The results of calculations pered in accordancewith this practice may be used as design data for specific jobconditions, or may be used in general to represent theperance of a particular product or system. When theresults will be used for comparison of perance of similarproducts, it is recommended that reference be made to thespecific constants used in the calculations. These referencesshould include8.1.1 Name and other identification of products orcomponents,8.1.2 Identification of the nominal pipe size or surfaceinsulated, and its geometric orientation,8.1.3 The surface temperature of the pipe or surface,8.1.4 The equations and constants selected for the thermalconductivity versus mean temperature relationship,8.1.5 The ambient temperature and humidity, if applicable,8.1.6 The surface transfer conductance and condition ofsurface heat transfer,8.1.6.1 If obtained from published ination, the sourceand limitations,8.1.6.2 If calculated or measured, the and signifi-cant parameters such as emittance, fluid velocity, etc.,FIG. 2 Thermal Conductivity vs. Mean TemperatureC680 − 1498.1.7 The resulting outer surface temperature, and8.1.8 The resulting heat loss or gain.8.2 Either tabular or graphical representation of the calcu-lated results may be used. No recommendation is made for theat in which results are presented.9. Accuracy and Resolution9.1 In many typical computers normally used, seven signifi-cant digits are resident in the computer for calculations.Adjustments to this level can be made through the use of“Double Precision;” however, for the intended purpose of thispractice, standard levels of precision are adequate. The at-ting of the output results, however, should be structured toprovide a resolution of 0.1 for the typical expected levels ofheat flux and a resolution of 1°F 0.55°C for surface tempera-tures.NOTE 1The term “double precision” should not be confused withASTM terminology on Precision and Bias.9.2 Many factors influence the accuracy of a calculativeprocedure used for predicting heat flux results. These factorsinclude accuracy of data and the applicability of theassumptions used in the for the system under study.The system of mathematical equations used in this analysis hasbeen accepted as applicable for most systems normally insu-lated with bulk type insulations. Applicability of this practiceto systems having irregular shapes, discontinuities and othervariations from the one-dimensional heat transfer assumptionsshould be handled on an individual basis by professionalengineers familiar with those systems.9.3 The computer resolution effect on accuracy is onlysignificant if the level of precision is less than that discussed in9.1. Computers in use today are accurate in that they willreproduce the calculated results to resolution required ifidentical data is used.FIG. 3 Mean Temperature vs. Thermal ConductivityFIG. 4 Thermal Conductivity vs. Mean TemperatureC680 − 14109.4 The most significant factor influencing the accuracy ofclaims is the accuracy of the thermal conductivity data.The accuracy of applicability of thes