由于认识到绝缘材料热性能的测量值可能取决于设备和绝缘材料，一些研究人员采用了实际传热问题的极限情况解决方案，以确定测量条件对测量结果的影响。这些尝试通常基于吸收、发射和散射单相灰色介质中的非耦合（即非相互作用）传导和辐射传热，或仅基于散射的传导和辐射传热。Viskanta、Lii和Ozisik提出了吸收、发射和各向同性散射单相灰色材料的传导和辐射耦合传热问题的精确解，该材料由非黑色等温无限平行板约束。这些分析表明，线性温度分布仅在纯散射情况下存在，并且随着散射相对于吸收的重要性降低，温度分布的非线性增加。 最严重的极限情况，如最非线性的温度分布所示，会发生。用于黑色边界曲面，并且在材质内没有散射。在目前的工作中，通过保护热板技术测量绝缘的表观热特性（即导电性、电阻率和电阻）是使用数字计算机建模的，该计算机解决了平行黑色等温板之间包含的吸收和发射单相灰色介质的传导和辐射耦合传热问题。最差极限情况下的这些计算结果和之前确定的最佳极限情况下的结果用于支撑样品厚度对绝缘表观热性能的影响，并开发一个外推方程，显示表观热性能和测量条件之间的关系（e。 g、 ，热板和冷板发射率、温度和试样厚度）。关于传热模型及其解决方案的全面发展，请参阅之前的出版物引文:《ASHRAE学报》，第87卷，第2部分，俄亥俄州辛辛那提

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