Insulation Thermal Properties

Analogies between heat transfer and electricity are standard in many engineering courses. Heat energy “flows” through materials much like electricity flows through materials, and as such, many correlations and terms share similar meanings when

discussing heat transfer and electricity. For example, “conductivity” is a term that shares similar meaning between the two disciplines. The thermal conductivity (k) of a material is the “time rate of heat flow through a unit area of homogenous material in a direction perpendicular to isothermal planes, induced by a temperature gradient.” Basically, just like in terms of electricity, highly heat conductive materials transfer heat more readily than materials which are less conductive (insulators) [24].

As described previously, the primary function of thermal insulation is to resist the flow of heat energy by conduction, convection, and/or radiative heat transfer modes. Thermal resistance is a measure of the effectiveness at which a material retards (resists) heat flow. A material with a high thermal resistance is an effective insulator; however, if a material has a low thermal resistance (high thermal conductance) then the material will readily transfer heat and is a poor candidate for insulating purposes. The thermal

resistance of a material is known as the “R-value.” The academic definition of the R- value is “under steady state conditions (not varying with time), the mean temperature difference between two defined surfaces of material or construction that induces unit heat flow through a unit area.” Thermal resistance (R-value) has units of m^2*K/W or

hr*ft2*˚F / Btu [25]. R-values for a wide range of building materials are published in various academic, research resources, and design handbooks/manuals.

Thermal resistance and electrical resistance are dealt with in the same manor when it comes to evaluating structures of composite (multiple) materials such as the

insulating systems found in walls, ceilings, and floors. If materials are “stacked” one of top of the other (a single row) they are said to be in “series.” Just like series resistors in electrical component design, the effective thermal resistance (REff) of a series of

insulators is the numerical sum of each individual material thermal resistance represented by:

REff = R1 + R2 + R3 + … + Rn

In many installations, insulating materials are arranged so that heat flows in parallel paths of different conductances. If no heat flows between lateral paths (called thermal bridging) then the materials are said to be in “parallel.” The effective thermal resistance (REff) of insulators in parallel is given by:

REff = [(1 / R1) + (1 / R2) + (1 / R3) + … + (1 / Rn)] -1

Thermal resistance can be resistance to heat flow due to one of the three modes of heat transfer (conduction, convection, or radiation). Therefore, equations for evaluating resistance will change accordingly. For heat transfer due to conduction (materials physically touching one another) thermal resistance is represented by:

Rconduction = L / k*A

In this equation L is the length of the material in the direction of heat transfer (seen as the material thickness in most cases), k is the thermal conductivity of the material, and A is the cross sectional area of the material perpendicular to the direction of heat transfer.

For heat transfer due to convection (heat transfer by fluid) thermal resistance is represented by:

Rconvection = 1 / h*A

In this equation h is a parameter called the convection heat transfer coefficient and A is the area of the material which is contacted by the fluid.

Lastly, for heat transfer due to radiation (energy emitted by a material) thermal resistance is represented by:

Rradiation = 1 / hr*A

In this equation hr is the linearized radiation heat transfer coefficient and is a function of the material surface temperature and a nearby surrounding temperature.

The thermal transmittance (U-factor) of a material is the “time rate of heat flow per unit area under steady conditions from the fluid on the warm side of a barrier to the fluid on the cold side, per unit temperature difference between the two fluids.” The U- factor has units of W/ (m2*K) or Btu/ (hr*ft2*˚F) and is merely the reciprocal of the R- value of a material (U = 1/R). The U-factor is sometimes called the overall coefficient of heat transfer. In building practice, the heat transfer “fluid” described in the formal definition of the U-factor is simply air [25].

Calculating the U-factor for a composite wall, such as a home exterior wall, roof, or floor is an important task for this section of energy calculations. The easiest way to determine the overall coefficient of heat transfer for a wood-framed wall with cavity insulation (typical wall construction) is to sum all the thermal resistances in each heat transfer “parallel path” (through the studs or through the cavity) and weight each path by the percentage of area found in the wall construction. For a typical residential wall with studs constructed with their centers separated by 16 inches (common building term 16” O.C.) it is estimated that the stud heat transfer path represent 15% of the total wall area (area in which heat transfer is occurring from outside to inside or vice versa), and that 85% of the total wall area is the cavity section of the wall [28]. Therefore, the overall coefficient of heat transfer for a 16” O.C. residential wall is given by:

Uwall = 0.15*Ustuds + 0.85*Ucavity

The overall coefficients of heat transfer for the studs and cavity (Ustuds and Ucavity respectively) can be determined by applying the appropriate thermal resistance

combinations (series and parallel paths) described above. A detailed explanation of this process will be described later in this chapter.

Once the thermal resistance or the overall coefficient of heat transfer for a

material (or a composite of materials) are known the heat that will be transferred through that medium per rate of time is given by the equation:

q = U*A*ΔT

In this equation ΔT is the overall temperature difference, U is the overall heat transfer coefficient of the materials, and A is the cross sectional area of the material perpendicular to the direction of heat transfer. The rate of heat transfer through the medium (q) has units of Btu/hr or Watts. This equation can be used to determine the rate of heat transfer that will be transferred to or from the conditioned space of a building (through the walls, roof, floor, etc) given the composition of the insulating system and the inside/outside temperature conditions.