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**.

**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)- Σ
*R*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:

**R**_{total} = R_{siding} + R_{insulation} + R_{drywall} = 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.