R and U Values
In calculating the conduction through a pane of glass, or system of glass panes, one must consider the effect of the inner and outer air films, which, as air is a good insulator, contribute a substantial amount to the Thermal Resistance (R value) of the window pane. Diagram 1 below shows the inner and outer air film and their effects on the R value of a window (Note that the equivalent thermal Resistance can be found by simply summing the R values of each material within the thermodynamic system). However, it is first important to understand what an R value actually is.
The R value is the thermal resistance to heat transfer of a given thickness of a given material. To find the R value of a material, one divides the thickness of the material in question [x], by the coefficient of thermal conductivity [k]. Note: Attention must be given to the dimensional homogeneity of the equation.
This R value is useful in calculating the heat loss through a window pane via conduction. The specific heat loss q can be calculated as follows.
As a comparison, some Common R values of common building materials can be found at the bottom of this page.
Specifically regarding windows, a simple R value is often insufficient for reasons of rapid comparison and is fairly complicated requiring above average thermodynamic engineering to translate into meaningful values for the average consumer. To solve this dilemma, the Overall Heat Transfer Coefficient, U, was created. The U value is simply the inverse of the sum of the R values (including that of the inside and outside air films for a window.)
Noting this, the specific heat loss q can be obtained by multiplying the U value by the change in temperature. As shown in the equation below:
This value of specific heat loss can then be multiplied by the area through which the heat is flowing (Q=qA=AUdT) to determine the net flow of heat through a given area for a given interval of time.
Example: The U value of the above equation can be found as follows:
Example: Using the U value to find the heat loss Q for a 2ft x 3ft window pane given in Diagram 1 can be found as follows:
This is a huge number (nearly 25 times larger) compared to the heat loss through a similar size section of fiberglass insulated wall (5/8 inch gypsum board, 2x6 construction, R-19 fiberglass batt-type insulation) and 1/2 inch plywood exterior).
This is why windows are considered one of the most inefficient aspects of any arctic or sub-arctic home or other building, and precisely the reason that a great deal of research has been performed on creating glass with better thermal resistances.
Background Photo by Daniel Oliva