User:JDavidWright/sandbox

Heat flux method
The R-value of a building element can be determined by using a heat flux sensor in combination with two temperature sensors. By measuring the heat that is flowing through a building element and combining this with the inside and outside temperature, it is possible to define the R-value precisely. A measurement that lasts at least 72 hours with a temperature difference of at least 5 °C is required for a reliable result according to ISO 9869 norms, but shorter measurement durations give a reliable indication of the R-value as well. The progress of the measurement can be viewed on the laptop via corresponding software and obtained data can be used for further calculations. Measuring devices for such heat flux measurements are offered by companies like FluxTeq, Ahlborn, greenTEG and Hukseflux.

Placing the heat flux sensor on either the inside or outside surface of the building element allows one to determine the heat flux through the heat flux sensor as a representative value for the heat flux through the building element. The heat flux through the heat flux sensor is the rate of heat flow through the heat flux sensor divided by the surface area of the heat flux sensor. Placing the temperature sensors on the inside and outside surfaces of the building element allows one to determine the inside surface temperature, outside surface temperature, and the temperature difference between them. In some cases the heat flux sensor itself can serve as one of the temperature sensors. The R-value for the building element is the temperature difference between the two temperature sensors divided by the heat flux through the heat flux sensor. The mathematical formula is:

$$R_{val}=\frac{\Delta T}{\phi_q}=\frac{T_o-T_i}{q/A}$$

where:


 * $$R_{val}$$ is the R-value (K⋅W-1⋅m2),
 * $$\phi_q$$ is the heat flux (W⋅m-2),
 * $$A$$ is the surface area of the heat flux sensor (m2),
 * $$q$$ is the rate of heat flow (W),
 * $$T_i$$ is the inside surface temperature (K),
 * $$T_o$$ is the outside surface temperature (K), and
 * $$\Delta T$$ is the the temperature difference (K) between the inside and outside surfaces.

The U-value can be calculated as well by taking the reciprocal of the R-value. That is,

$$U_{val}=\frac{1}{R_{val}}.$$

where: The derived R-value and U-value may be accurate to the extent that the heat flux through the heat flux sensor equals the heat flux through the building element. Recording all of the available data allows one to study the dependence of the R-value and U-value on the inside or outside temperature.
 * $$U_{val}$$ is the U-value (W⋅m-2⋅K-1)

R-value (insulation) excerpt
In building and construction, the R-value is a measure of how well a two-dimensional barrier, such as a layer of insulation, a window or a complete wall or ceiling, resists conductive flow of heat. The R-value per unit of a barrier's exposed area measures the thermal resistance of the barrier.

$$\frac{R_{val}}{A}=R$$

where:


 * $$R_{val}$$ is the R-value (K⋅W-1⋅m2)
 * $$A$$ is the area of a barrier's exposed area m2)
 * $$R$$ is the thermal resistance (K⋅W-1)

The equation above summarizes the previous sentence but the units show that the previous sentence is clearly in error. The greater the R-value, the greater the resistance, and so the better the thermal insulating properties of the barrier. R-values are used in describing effectiveness of insulating material and in analysis of heat flow across assemblies (such as walls, roofs, and windows) under steady-state conditions. Heat flow through a barrier is driven by temperature difference between two sides of the barrier, and the R-value quantifies how effectively the object resists this drive: The temperature difference divided by the R-value and then multiplied by the surface area of the barrier gives the total rate of heat flow through the barrier, as measured in watts or in BTUs per hour.

R-value (insulation) excerpt 2
The more a material is intrinsically able to conduct heat, as given by its thermal conductivity, the lower its R-value. On the other hand, the thicker the material, the higher its R-value. Sometimes heat transfer processes other than conduction (namely, convection and radiation) significantly contribute to heat transfer within the material. In such cases, it is useful to introduce an "apparent thermal conductivity", which captures the effects of all three kinds of processes, and to define the R-value in general as the thickness of a sample divided by its apparent thermal conductivity. That is:


 * $$ R_{val} = \frac{\Delta x}{k^\prime} = \Delta x \times r^\prime$$

where:
 * $$R_{val}$$ is the R-value (K/W) across the thickness of the sample
 * $$\Delta x$$ is the thickness (m) of the sample (measured on a path parallel to the heat flow)
 * $$k^\prime$$ is the apparent thermal conductivity of the material (W/(K·m))
 * $$r^\prime = {k^\prime}^{-1} $$ is the apparent thermal resistivity of the material (K·m/W)

However, this generalization comes at a price because R-values that include non-conductive processes may no longer be additive and may have significant temperature dependence.

Derived from Fourier's Law for heat conduction
From Fourier's Law for heat conduction, the following equation can be derived, and is valid as long as all of the parameters (x and k) are constant throughout the sample.


 * $$ R_{\theta} = \frac{\Delta x}{A \times k}$$

where:
 * $$R_{\theta}$$ is the absolute thermal resistance (K/W) across the thickness of the sample
 * $$\Delta x$$ is the thickness (m) of the sample (measured on a path parallel to the heat flow)
 * $$k$$ is the thermal conductivity (W/(K·m)) of the sample
 * $$A$$ is the cross-sectional area (m2) perpendicular to the path of heat flow.

In terms of the temperature gradient across the sample and heat flux through the sample, the relationship is:


 * $$ R_{\theta} = \frac{\Delta x}{A \times \phi_q}\frac{\Delta T}{\Delta x} = \frac{\Delta T}{q}$$

where:
 * $$R_{\theta}$$ is the absolute thermal resistance (K/W) across the thickness of the sample,
 * $$\Delta x$$ is the thickness (m) of the sample (measured on a path parallel to the heat flow),
 * $$\phi_q$$ is the heat flux through the sample (W·m−2),
 * $$\frac{\Delta T}{\Delta x}$$ is the temperature gradient (K·m−1) across the sample,
 * $$A$$ is the cross-sectional area (m2) perpendicular to the path of heat flow through the sample,
 * $$\Delta T$$ is the temperature difference (K) across the sample,
 * $$q$$ is the rate of heat flow (W) through the sample.