1.6 Mechanisms of heat transfer  (Page 3/27)

where P is the power or rate of heat transfer in watts or in kilocalories per second, A and d are its surface area and thickness, as shown in [link] , $T_{\text{h}}-T_{\text{c}}$ is the temperature difference across the slab, and k is the thermal conductivity    of the material. [link] gives representative values of thermal conductivity.

More generally, we can write

where x is the coordinate in the direction of heat flow. Since in [link] , the power and area are constant, dT / dx is constant, and the temperature decreases linearly from $T_{\text{h}}$ to $T_{\text{c}}.$

In developing insulation , the smaller the conductivity k and the larger the thickness d , the better. Thus, the ratio d/k , called the R factor , is large for a good insulator. The rate of conductive heat transfer is inversely proportional to R . R factors are most commonly quoted for household insulation, refrigerators, and the like. Unfortunately, in the United States, R is still in non-metric units of ${\text{ft}}^2·\text{°F}·\text{h/Btu}$ , although the unit usually goes unstated [1 British thermal unit (Btu) is the amount of energy needed to change the temperature of 1.0 lb of water by $1.0\text{°}\text{F}$ , which is 1055.1 J]. A couple of representative values are an R factor of 11 for 3.5-inch-thick fiberglass batts (pieces) of insulation and an R factor of 19 for 6.5-inch-thick fiberglass batts ( [link] ). In the US, walls are usually insulated with 3.5-inch batts, whereas ceilings are usually insulated with 6.5-inch batts. In cold climates, thicker batts may be used.