Estimating R-values for enclosed reflective air spaces

Thermal resistance calculation
The equations for estimating the thermal resistance of an enclosed rectangular air space are taken from ISO 6946, but have been converted for use with IP units. The heat-flow consists of two parts, each represented by a heat transfer coefficient (h). Heat-flow by radiation is represented by hrad, while heat-flow by conduction-convection is represented by hcc. The thermal resistance, R#, of the air space is calculated from the two heat-transfer coefficients using Equation 1:

The radiation term depends on the average temperature of the air space, T (in degrees Fahrenheit), as shown by Equation 2:

The conduction-convection term is taken to be the greater of h1 and h2, quantities that are calculated from the following equations. Equation 3 differs from ISO 6946 due to the introduction of the variation of the thermal conductivity of air with temperature:

                                

Depending on the direction of the heat-flow, Equation 4 can differ in three ways. When there is upward heat-flow, one should use Equation 4a:

When there is horizontal heat-flow, one should use Equation 4b:

When there is downward heat-flow, one should use Equation 4c:

The R# estimate based on Equations 1 to 4 proceeds as follows:
Step A: Determine the emittances of the two surfaces and calculate E.
Step B: Choose T and calculate hrad.
Step C: Choose d (i.e. distance across air space in inches) and calculate h1.
Step D: Select the heat-flow direction and calculate h2.
Step E: Identify hcc, which is the larger of the two numbers: h1, h2.
Step F: Calculate R# using Equation 1.
Step G: Thermal resistance for the RIS equals R# + Rmaterial.

A practical example
To illustrate how this works, a practical example is in order. A 1 ¼-in. air space of interest is anticipated to be at 75 F, with a temperature difference across the air space of 6 F. One side of the air space has emittance 0.9, while the second side of the air space has emittance 0.03. The heat-flow direction is downward.

  1. From Equation 2: E = 0.0299 and hrad = 0.0313
  2. From Equation 3: h1 = 0.1438
  3. From Equation 4c: h2 = 0.0964
  4. From Step E: hcc = 0.1438
  5. From Equation 1: R# = 5.71 sf·h·F/Btu
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