scope:

INTRODUCTION

During the late 1990's, the American Society of Heating, Refrigeration and Air-Conditioning Engineers (ASHRAE) Standing Standard Project Committee (SSPC) 90.1 Envelope Subcommittee incorporated specific maximum allowable Ufactors (the overall heat transfer coefficients) for metal building roofs and walls into ANSI/ASHRAE/IESNA Standard 90.1-1999. Recently ASHRAE and other industry organizations have recognized that Standard 90.1 should be revised and updated to account for a more accurate understanding of the installation of insulation in metal building roof and wall assemblies. A comprehensive mathematical modeling based study of heat transfer in metal building roof insulation assemblies containing fiberglass insulation was undertaken to facilitate the revision of U-factors in the Standard 90.1. The first part of the study, summarized in a previous paper (Choudhary et al. 2010), involved the development and validation of a three-dimensional mathematical model for heat transfer (and air flow where applicable) in metal building roof insulation assemblies.

In the second part of the study, reported here, the validated model was used to calculate the U-factors for several standing seam roof (SSR) and through-fastened roof (TFR) insulation assemblies. In these modeling studies, the shape of the fiberglass insulation drape between two consecutive purlins was assumed to be parabolic. The assumption of the parabolic shape was based on measurements of the drape in prototypes of several metal building roof insulation assemblies (Christianson 2010). For the SSR, 30 assemblies were modeled; 15 each for a 1.375 in. (0.0349 m) tall clip and a 1.75 in. (0.0445 m) tall clip. The 15 cases corresponded to five different insulation types (R-10, R-11, R-13, R-16, and R-19), each at three levels of maximum drape. For a TFR, 8 different assemblies were modeled; four for R-19 and 1 each for R-16, R-13, R-11, and R-10. The U-factors for the 38 cases are summarized in this paper.

One may use the three-dimensional numerical heat transfer model described (Choudhary et al. 2010) to calculate U-factors for each of the cases included in the Standard 90.1. This, however, will be time consuming. Also, modeling tools and capabilities may not be readily available to many people and organizations with interest in understanding and specifying thermal performance of the metal building insulation assemblies. Therefore, and at the request of ASHRAE's 90.1 Envelope Subcommittee, an approach was developed to calculate the U-factor from an overall or system thermal resistance parameter, R_insul-sys, that combined thermal resistance of the insulation drapes between the purlins with the thermal resistance of the insulation above the purlin. The paper presents a derivation for an analytical expression for the thermal resistance (the R-value) of the parabolic insulation drape, a key part of R_insul-sys.

The model calculated 38 U-factors for the various roof insulation assemblies mentioned earlier were found to correlate highly (R2 = 0.998) with the overall or system thermal resistance parameter, R_insul-sys. Subsequently, four more assemblies were modeled to correspond to R_insul-sys values considerably outside the range of the earlier 38 cases. The correlation equation was found to work very well in predicting the U-factor with the worst discrepancy between the values from the model and the correlation equation being 15%.

The U-factor estimation approach outlined here is quite simple and greatly expands our ability to predict U-factors for metal building roof assemblies. The correlation derived here is for cases where several design parameters (e.g., spacing between the purlins and the dimensions of the purlins) were kept invariant. It would be relatively straightforward to extend the present approach to include other design parameters of interest.

In the following, we will first derive an expression for the overall or system thermal resistance parameter, R_insul-sys, then summarize the modeling results on U-factors for several roof insulation assemblies, and finally correlate the U-values calculated by the numerical model to R_insul-sys. The correlation based approach described below has been adopted by the 90.1 Envelope Subcommittee for calculating the U-factors for the single layer fiberglass insulation assemblies. We have followed the recommendation from the 90.1 Envelope Subcommittee (McBride and Waite 2009) to include the important steps in the derivation of expressions for various thermal resistances present in the metal building insulation assemblies.