How Inaccurate Is (Heat Transfer Estimate In) Your Energy Model? U-factor Calculation Methods for Building Envelope

By Ravi Srinivasan, CEM, LEED AP

Heat transfer methodologies can be largely classified based on the envelope material composition and heat transfer (spatial) dimensionality. In the material composition type, a mass wall and metal- or wood- framed wall may be categorized into separate groups. While a mass wall’s U-factor can be accurately computed using a “one-dimensional heat flow” method, the metal- or wood- framed wall require a “two-dimensional heat flow” method (ASHRAE 2009).

The metal- framed envelope’s U-factor can be computed using the “isothermal-planes method” as the conductivities moderately differ from those of the adjacent materials in particular. The U-factor of a wood-framed envelope can be analyzed using the “parallel-path method” as the thermal conductivity of the dissimilar materials in the layer is rather close in value (within the same order of magnitude). Moreover, if the envelope includes materials with a very high difference in conductivities (two orders of magnitude or more), a “zone method” or “modified zone method” is appropriate.

Experiments carried out to evaluate multi-dimensional heat transfer analysis show up to 44% errors in R-value calculations for metal-framed envelope, using a one-dimensional approach (Kosny and Kossecka, 2002). The framing configuration produced different R-values, figure 1 and table 1 below, when the total framing percentage within walls were maintained in relation to insulation.

This error is unacceptable for Net Zero Energy building design process as the design load calculated based on this flawed U-factor will be overly inaccurate and will result in system under- or over-sizing.

Case I: wall section divided into two zones, 20% framing & 80% insulating materials.

Case II: wall section divided into five zones, two 10% framing & three zones of insulating materials making up 80%.

Case III: wall section divided into nine zones, four 5% framing & five zones of insulating materials making up 80%.

Figure 1. Wall configurations with 20% framing materials. (Kosny and Kossecka, 2002).

Three different framing materials were assumed for thermal modeling.

Wood: 00.83 Btu in/(h sf degF)

Concrete: 10.00 Btu in/(h sf degF)

Steel: 47.60 Btu in/(h sf degF)

Table 1. R-value differences estimation (Kosny and Kossecka, 2002).

Heat flow phenomena occur in all three-dimensions concurrently and spatially. All of the heat transfer methods discussed above are, in spatial terms, “uni-directional.” In other words, these methods are simplifications of complex envelope assemblies in one-dimensional space, i.e. considering heat flows from the surface with higher temperature to a surface with lower temperature in one particular direction. In reality, heat flow is three-dimensional, and may not be simplified to one-dimensional investigation. Several studies confirm the inaccuracies in the one-dimensional approach over two- or three-dimensional analysis and actual testing of envelope assemblies (Kosny and Kossecka, 2000). Two-dimensional heat flow analysis solves issues related to thermal bridging in walls, windows and other envelope components unlike one-dimensional analysis. Needless to say, thermal bridges significantly affect energy performance of the building envelope, and thereby, overall building energy consumption, which is a critical factor for Net Zero Energy building design-approach. Currently, computing the heat flow for two- or three-dimensions spatially is achieved by using auxiliary programs.

One of the tools used for such two-dimensional analysis is THERM. THERM is a finite-element heat transfer analysis tool using a steady-state conduction algorithm, CONRAD (Curcija et al., 1995). THERM’s calculation routine evaluates conduction and radiation from first principles (Huizenga et al., 1999). Furthermore, three-dimensional heat transfer analysis using PDE-solvers can accurately address thermal bridge problems (Bloomberg, 1996; Posey and Dalgliesh, 2005).

Ravi  Srinivasan will be teaching four upcoming courses this spring on building envelope design for Net Zero Energy buildings:

• NZE 421: Building Envelope Concepts & Analysis- March 16, 8:30am-12:30pm. Discounted registration by March 9. Register now.
• NZE 422: High Performance Building Envelope Design Strategies & Emerging Technologies- April 1, 1:30-5:30pm. Discounted registration by March 25. Register now.
• NZE 521: Modeling Building Envelope & Internal Loads- April 14, 8:30am-5:30pm. Discounted registration by April 7. Register now.
• NZE 621: Building Envelope & Internal Loads Optimization- May 25-26, 8:30am-5:30pm. Discounted registration by May 18. Register now.

Write to me (Ravi) at ravi@greenroundtable.org.

References

ASHRAE, American Society for Heating, Refrigeration and Air Conditioning Engineers, Fundamentals, 2009.

Bloomberg, T. “Heat conduction in two- and three-dimensions, computer modeling of building physics applications.” Department of Building Physics, Lund University, Sweden, ISBN 91-88722-05-8.

Curcija, D., Power, J.P., and Goss, w.P. “CONRAD: A finite element method based computer program  module for analyzing 2-D conductive and radiative heat transfer in fenestration system.” Draft report, University of Massachusetts at Amherst, 1995.

Huizenga, C., Arasteh, D., Finalyson, E., Mitchell, R., Griffith, B., and Curcija, D. “Teaching student about two-dimensional heat transfer effects in buildings, building components, equipment, and appliances using THERM 2.0.” ASHRAE Transactions 105(1), 1999.

Kosny, J., and Kossecka. “Computer modeling of complex wall assemblies – some accuracy problems.” International Building Physics Conference, Eindhoven, The Netherlands. 2000.

Kosny, J., and Kossecka, E. “Multi-dimensional heat transfer through complex building envelope assemblies in hourly energy simulation programs.” In: Energy and Buildings, 34(2002) 445-454.

Posey, J.B., and Dalgliesh, w.A. “Thermal bridges – heat flow models with Heat2, Heat3, and a general purpose 3-D solver,” 2005.

Image Credits (from top): The Green Roundtable / NEXUS; Lawrence Berkeley National Laboratory