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This study evaluated different models for calculating the effective thermal conductivity of fibrous insulation by comparing predicted values with certified values of Standard Reference Material 1450c, Fibrous Glass Board. This comparison involved the coupled effects of radiation and conduction heat transfer. To support these comparisons, the fiber diameter distribution was measured using X-ray computed tomography, and this distribution was used in several heat transfer models considered in this paper. For the evaluation of the radiative heat transfer, the diffusion approximation, the Schuster-Schwarzschild approximation, and the Milne-Eddington approximation were considered. The conduction of the gas and the fibers was treated by the kinetic theory and a semi-empirical model, respectively. Two models were considered for the evaluation of the radiative properties: the large specular reflecting approach and the application of Mie theory for media composed of infinite cylinders.

A mathematical model is presented for a new-generation guarded-hot-plate apparatus to measure the thermal conductivity of insulation materials. This apparatus will be used to provide standard reference materials for greater ranges of temperature and pressure than have been previously available. The apparatus requires precise control of 16 interacting heated components to achieve the steady temperature and one-dimensional heat-transfer conditions specified in standardized test methods. Achieving these criteria requires deriving gain settings for the 16 proportional-integral-derivative (PID) controllers, comprising potentially 48 parameters. Traditional tuning procedures based on trial-and-error operation of the actual apparatus impose unacceptably lengthy test times and expense. A primary objective of the present investigation is to describe and confirm the incremental control algorithm for this application and determine satisfactory gain settings using a mathematical model that simulates in seconds test runs that would require days to complete using the apparatus. The first of two steps to achieve precise temperature control is to create and validate a model that accounts for heating rates in the various components and interactions with their surroundings. The next step is to simulate dynamic performance and control with the model and determine settings for the PID controllers. A key criterion in deriving the model is to account for effects that significantly impact thermal conductivity measurements while maintaining a tractable model that meets the simulation time constraint. The mathematical model presented here demonstrates how an intricate apparatus can be represented by many interconnected aggregatedcapacity masses to depict overall thermal response for control simulations. The major assemblies are the hot plate with four subcomponents, two cold plates with three subcomponents each, and two edge guards with three subcomponents each. Using symmetry about the hot