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A mathematical model has been developed for the transfer of heat through fibrous insulating materials. Model development was an outgrowth of a study of heat transfer mechanisms and insulating material efficiencies.
This paper describes the mathematical derivation of the model based upon fundamental concepts of heat transfer and certain simplifying assumptions. It is shown that the efficiency of a fibrous insulation may be characterized by three model constants. One constant is calculated from fiber emissivity data and the other two may be determined from measurement of the “apparent” thermal comductivity at two different temperatures by the ASTM Test for Steady-State Thermal Transmission Properties by Means of the Guarded Hot Plate, (C 177-76). Actual test data are included to indicate the model's validity throughout the temperature ranges of practical interest for the materials investigated.
In one form, the model may be used to estimate the “apparent” thermal conductivity of a material for various combinations of hot-face and cold-face temperatures. The model may also be used to calculate heat losses and corresponding temperature profiles through insulated systems under known or assumed boundary conditions without relying upon the concept of “mean” temperature.
mathematical model, heat transfer, insulation, thermal conductivity, calculation, (material) characterization, physical properties, (temperature) profile
Research engineer, Eagle Picher Industries, Inc., Joplin, Mo.