R-value and U-value are two important concepts in HVAC. R-value is a measure of a material’s resistance to heat flow. The higher the R-value, the better the insulation. U-value is a measure of a material’s ability to transfer heat. The lower the U-value, the better the insulation.
Equations
R-value:
Thermal resistance is a measure of a material’s ability to resist the flow of heat. The higher the thermal resistance, the better the material is at insulating. Thermal resistance is measured in R-value, which is expressed in Imperial units as Hr. Sq. Ft. °F/Btu and in SI units as m².K/W.
$$R = \frac{1}{C} = \frac{1}{K} \times \text{Thickness}$$U-value:
U-value is a measure of the rate of heat transfer through a material. The lower the U-value, the better the material is at insulating. U-value is measured in Imperial units as Btu/Hr. Sq. Ft. °F and in SI units as W/m².K.
R-value and U-value are inversely proportional to each other. This means that the higher the R-value, the lower the U-value, and vice versa.
$$U = \frac{1}{\Sigma R}$$where:
- R is the R-value (hr-ft²·°F/Btu)
- U is the U-value (Btu/hr-ft²·°F)
- C is the conductance (Btu/hr-ft²·°F)
- K is the conductivity (Btu·in/hr-ft²·°F)
- ΣR is the sum of the individual R-values
Units
R-value and U-value can be expressed in both Imperial and SI units.
Imperial units:
- R-value: hr-ft²·°F/Btu
- U-value: Btu/hr-ft²·°F
SI units:
- R-value: m²·K/W
- U-value: W/m²·K
The following conversion factors can be used to convert between Imperial and SI units of thermal resistance and U-value:
Property | Imperial Unit | SI Unit | Conversion Factor |
|---|---|---|---|
Thermal resistance | Hr. Sq. Ft. °F/Btu | m².K/W | 0.1761 |
U-value | Btu/Hr. Sq. Ft. °F | W/m².K | 5.678 |
Example
A wall is made up of three layers: a layer of siding with an R-value of 0.5, a layer of insulation with an R-value of 10, and a layer of drywall with an R-value of 0.5. The total R-value of the wall is:
Rtotal = Rsiding + Rinsulation + Rdrywall = 0.5 + 10 + 0.5 = 11 hr-ft²·°F/Btu
The U-value of the wall is:
$$U = \frac{1}{\Sigma R} = \frac{1}{11} = 0.091 Btu/hr-ft²·°F$$Conclusion
R-value and U-value are important concepts in HVAC. By understanding these concepts, you can better design and operate HVAC systems to improve energy efficiency and comfort.