Realizing that measured values for the thermal properties of insulation may depend on the apparatus as well as the insulation, several investigators have employed limiting-case solutions to the actual heat transfer problem to define the effect of measurement conditions on the measured result. These attempts have generally been based either on uncoupled (i.e., non-interacting) conductive and radiative heat transfer in an absorbing, emitting, and scattering single-phase gray medium or on conductive plus radiative heat transfer with only scattering.

Exact solutions to the coupled conductive and radiative heat transfer problem for absorbing, emitting, and isotropically scattering single-phase gray materials bounded by nonblack isothermal infinite parallel plates have been developed by Viskanta and by Lii and Ozisik. These analyses show that a linear temperature profile exists only for the pure scattering case and that as the importance of scattering relative to absorption decreases, the nonlinearity of the temperature profile increases. The worst limiting case, as indicated by the most nonlinear temperature profile, occurs.for black bounding surfaces and no scattering within the material.

In the current work, the measurement of the apparent thermal properties (i.e., conductivity, resistivity, and resistance) of insulation by the guarded hot-plate technique is modeled using a digital computer that solves the coupled conductive and radiative heat transfer problem for an absorbing and emitting single-phase gray medium contained between parallel black isothermal plates. The results of these calculations for the worst limiting case and the previously determined results for the best limiting case are used to bracket the effect of sample thickness on the apparent thermal properties of insulation and to develop an extrapolation equation that shows the relationship between the apparent thermal properties and the measurement conditions (e.g., hot- and cold-plate emissivities and temperatures and specimen thickness). A thorough development of the heat transfer models and their solution is given in an earlier publication