Heat flow can be a transient or a steady process. In the transient state, temperature and/or heat flow vary with time. Steady-state heat flow occurs when the temperature and heat flow reach a stable equilibrium condition that does not vary with time. Depending on the particular problem, the assumption of steady-state conditions may provide sufficiently accurate predictions of actual heat flow and temperature conditions. However, for some problems the assumption of steady flow can result in significant errors. 

Heat flow can occur in one, two, or three dimensions. In almost all real situations, heat flow occurs in three dimensions but, from a practical point of view, it is often acceptable to simplify considerations to only one-dimensional, or series, heat flow.

Heat transfer occurs by three primary mechanisms, acting alone or in some combination:

·         conduction,

·         convection, and

·         radiation.

Changes in moisture state, although not strictly an energy transfer mechanism, must also be considered since these state changes absorb and release heat energy, i.e., latent heat. 

Figure 1: Conduction of heat through a solid.

Conduction is the flow of heat through a material by direct molecular contact. This contact occurs within a material or through two materials in contact. It is the most important heat transport mode for solids; it is sometimes important for liquids, and it is occasionally important for gases.

Convection is the transfer of heat by the movement or flow of molecules (liquid or gas) with a change in their heat content. This is an important heat transfer mode between fluids and solids, or within fluids.

Radiation is the transfer of heat by electromagnetic waves through a gas or vacuum. Heat transfer by this mode therefore requires a line of sight connection between the surfaces involved.  All objects above absolute zero radiate heat energy; it is the net radiative heat transfer that is the heat transfer of interest. Radiation is mostly of importance for heat transfer between solids and within highly porous solids, but radiation between high-temperature gases is occasionally of practical importance. 

State change, sometimes called phase change, occurs at a constant temperature but still entails the movement of energy. For example, evaporation absorbs energy and condensation releases energy. This  energy is sometimes called latent heat.

The mode of heat transfer often changes during the process of heat flow through and within building systems. For example, the sun transmits heat by radiation to the earth, where it can be absorbed, for example, by a brick wall. The heat is then transferred by conduction through the brick and transferred to the indoor air by convection and to the indoor surfaces by radiation.

Figure 2: Convection and radiation

Insulation

All materials and layers in a building assembly have some resistance to heat flow. However, some materials with a k-value lower than about 0.05 to 0.07 W / m ∙ K are deliberately used in building assemblies for their ability to retard the flow of heat. These building products are called thermal insulations. Insulations are usually solid materials (so-called body insulation), but radiant barriers that control only radiation heat transfer across air spaces are also available. 

Since conduction is a major mode of heat transfer and still air is a low-cost insulator, insulation products tend to be low-density materials (i.e., porous materials with a large proportion of voids filled with air) and / or made of low-conductivity elements. For example, glass of 2500 kg/m3 density and 1.0 W/ m ∙ K thermal conductivity is spun into fibers and formed into a batt of about 16 kg/m3 density and 0.043 W/ m ∙ K thermal conductivity. Fiberglass batt insulation is widely used as insulation despite the high conductivity of glass because of the very high percentage of pores filled with air. This type of thermal insulation is approximately 99.4% air.

Foam plastic insulations have a lower percentage of air voids than glass fiber batts, but are made of lower conductivity plastic material. Soft wood of 500 kg / m3 density and 0.11 W/ m ∙ K thermal conductivity is produced to produce cellulose insulation of 60 kg / m3 density and 0.042 W/ m ∙ K thermal conductivity.

Most materials with high strength have relatively high density, and the strength of most building materials (e.g., concrete, wood, plastic) drops along with drops in their density. Hence, the need for low density (or more accurately, high porosity) reduces the structural capacity of most insulation. Accordingly, low-density insulation layers—such as glass fiber batt, and foamed plastics—are used to control heat flow in most modern building enclosures, while high-density, high-strength, high-conductivity materials such as steel studs, and concrete are used to support structural loads. In the past, building materials such as adobe, log, and low-density brick were used in a manner that combined both moderate insulating and acceptable load-bearing functions. Buildings constructed of these materials had thick walls, both to provide a reasonable level of resistance to heat flow and to provide sufficient strength.

Within porous insulations like fibers and foams, all three modes of heat transfer actually occur simultaneously. At low densities, the effective conductivity is high since convection and radiation can move heat through the relatively open space. At high densities, convection and radiation are suppressed, but conduction through the increasing proportion of solid material becomes important.  Therefore, an optimum density can be chosen: one that varies with the type of material. For glass fiber A (a very fine glass fiber), the optimum density is about 2 pounds per cubic foot (30 kg/m3).  However, since the cost increases as more material is used, the density of glass fiber batt is more commonly less than 1 pcf (15 kg/m3). If higher strength is required (as it is for low slope roof, curtainwall, and exterior basement applications), higher density fibrous products of 3 to 8 pcf (50 to 125 kg/m3 density) are available. Foam plastic insulations provide better R-value if higher strengths are needed. For example, extruded polystyrene with a density of only 2 pounds per cubic foot can easily resist pressures of 10 psi (or 1440 psf).

The wide range of values for thermal conductivity, and the inverse relationship of strength to thermal resistance, may be appreciated from the thickness required to achieve a certain level of thermal resistance. Figure 3 is a plot of the thickness of various building materials required to achieve a thermal resistance of RSI3.5 (R-20).

Rockwool fiber is thicker than glass (since the spun rock contains more impurities than glass), and hence conduction plays a larger role at lower densities. Rockwool products therefore tend to use higher densities to achieve the same thermal performance as spun glass. This extra density provides these products with greater strength and more resistance to convection and radiation effects. Even though more material is used for the same thermal resistance, rockwool products compete in applications that require these properties.

Figure 3: Comparison of the thickness of various materials required to achieve R20 (RSI3.5).