Analysis of heat transfer in building thermal insulation

The measurement of the apparent thermal properties (i.e., conductivity, resistivity, and resistance) of insulation by the guarded hot-plate technique is mathematically simulated on a computer by assuming that coupled conductive and radiative heat transfer occurs in an absorbing and emitting single-phase gray medium. Calculations are performed for insulation extinction coefficients between 0.001 and 1000 ft-/sup 1/, thicknesses between 0.0208 and 1.0 ft, continuous-phase thermal conductivities between 0.1800 and 0.1980 Btu in./(h ft/sup 2/ /sup 0/F), hot-plate temperatures between 485 and 635/sup 0/R, and cold-plate temperatures between 435 and 585/sup 0/R. A three-region approximate solution to coupled conductive and radiative heat transfer in an infinite slab of absorbing and emitting gray material bounded by black surfaces is also developed and shown to agree to within +-0.5% of the numerical results for most cases. The approximate solution to the coupled problem and the exact solution to the uncoupled problem are used to establish the effect of test conditions (such as specimen thickness, plate emissivity, plate temperatures, and continuous-phase thermal conductivity) on the measured apparent thermal properties of an insulation specimen. Examples of the temperature profiles within the insulation and a table of representative thicknesses for guarded hot-plate test specimens (i.e., the minimummore » specimen thickness required for measurement of an apparent thermal resistivity that is within 2% of the value at infinite thickness) are also presented. A means to extrapolate thermal resistance data from thin to thick specimens is suggested by ths analysis. Predictions from the extrapolation are shown to be consistent with existing thermal resistance data on low-density mineral fiber building insulation batts.« less