# 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 calculationmethodologies 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, uniformly 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 themethodologies 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 methodologies 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 information 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 Standards:2C168 Terminology Relating to Thermal InsulationC177 Test Method for Steady-State Heat Flux Measure-ments and Thermal Transmission Properties by Means ofthe Guarded-Hot-Plate ApparatusC335 Test Method for Steady-State Heat Transfer Propertiesof Pipe InsulationC518 Test Method 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 Document:NBS Circular 564 Tables of Thermodynamic and TransportProperties of Air, U.S. Dept of Commerce3. Terminology3.1 Definitions:3.1.1 For definitions of terms used in this practice, refer toTerminology C168.3.1.2 thermal insulation system—for this practice, a thermalinsulation system is a system comprised of a single layer orlayers of homogeneous, uniformly dimensioned material(s)intended 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 Symbols:1This 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. DOI:10.1520/C0680-14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, 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.where:h = 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·K))ke= effective thermal conductivity over a prescribed tem-perature range, Btu·in./(h·ft2·°F) (W/(m·K))q = heat flux, Btu/(h·ft2)(W/m2)qp= time rate of heat flow per unit length of pipe, Btu/(h·ft)(W/m)R = thermal resistance, °F·h·ft2/Btu (K·m2/W)r = radius, in. (m); rm+1− rm= thicknesst = local temperature, °F (K)ti= inner surface temperature of the insulation, °F (K)t1= inner surface temperature of the systemto= temperature of ambient fluid and surroundings, °F (K)x = distance, in. (m); xm+1− 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·K4))Ts= absolute surface temperature, °R (K)To= absolute surroundings (ambient air if assumed thesame) temperature, °R (K)Tm=(Ts+ 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·K))hc= average convection conductance, Btu/(h·ft2·°F) (W/(m2·K))kf= thermal conductivity of ambient fluid, Btu/(h·ft·°F)(W/(m·K))V = free stream velocity of ambient fluid, ft/h (m/s)υ = kinematic viscosity of ambient fluid, ft2/h (m2/s)g = acceleration due to gravity, ft/h2(m⁄s2)β = volumetric thermal expansion coefficient of ambientfluid, °R-1(K-1)ρ = density of ambient fluid, lb/ft3(kg⁄m3)∆T = absolute value of temperature difference betweensurface and ambient fluid, °R (K)Nu = 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, Refs(1,2,3,4,5,6). Heat flux solutions are derived for temperaturedependent thermal conductivity in a material. Algorithms andcomputational methodologies 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 datainput, analysis and data output into an easy to use, interactivecomputer program. By making the program interactive, littletraining for operators is needed to perform accurate calcula-tions.4.2 The operation of the computer program follows theprocedure listed below:4.2.1 Data Input—The computer requests and the operatorinputs information that describes the system and operatingenvironment. The data includes:4.2.1.1 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 Description—Material and thickness foreach layer (define sequence from inside out).4.2.2 Analysis—Once input data is entered, the programcalculates the surface transfer conductances (if not entereddirectly) and layer thermal resistances. The program then usesthis information 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 Output—Once convergence of the tempera-tures is reached, the program prints a table that presents theinput 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 information on personnel protection or surface con-densation. However, additional information 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 information. 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 performance. However, it is important to note that theaccuracy of results is extremely dependent on the accuracy ofthe input 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 evaluation for heatedsurfaces. Infrared inspection, in-situ heat flux measurements,or both are often used in conjunction with Practice C680 toevaluate insulation system performance 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 performed in accordancewith this practice may be used as design data for specific jobconditions, or may be used in general form to represent theperformance of a particular product or system. When theresults will be used for comparison of performance of similarproducts, it is recommended that reference be made to thespecific constants used in the calculations. These referencesshould include:8.1.1 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 information, the sourceand limitations,8.1.6.2 If calculated or measured, the method 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 theformat 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 format-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 1—The 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 input data and the applicability of theassumptions used in the method 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 input 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 input thermal conductivity data.The accuracy of applicability of thes