Thermal Resistance Formula
Calculate thermal resistance using R = L/(kA) or R = ΔT/Q.
Learn how to analyze heat flow through materials with worked examples.
The Formula
Thermal resistance measures how much a material resists the flow of heat. It is the thermal equivalent of electrical resistance — just as electrical resistance opposes current, thermal resistance opposes heat flow.
Materials with high thermal resistance are good insulators (like fiberglass or foam). Materials with low thermal resistance are good conductors (like copper or aluminum).
This concept is fundamental to building insulation design, electronics cooling, and industrial heat exchangers. The R-value you see on insulation products at the hardware store is directly related to this formula.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| R_th | Thermal resistance | K/W (kelvin per watt) or °C/W |
| L | Thickness of the material | m |
| k | Thermal conductivity of the material | W/(m·K) |
| A | Cross-sectional area perpendicular to heat flow | m² |
Alternative Form
Where ΔT is the temperature difference across the material and Q is the rate of heat flow in watts. This form is useful when you know the temperatures and heat flow rate directly.
Series and Parallel
Like electrical resistors, thermal resistances combine:
- Series (layers): R_total = R₁ + R₂ + R₃ + ...
- Parallel (side by side): 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
Example 1
A brick wall is 0.2 m thick with k = 0.7 W/(m·K) and an area of 10 m². What is its thermal resistance?
Identify values: L = 0.2 m, k = 0.7 W/(m·K), A = 10 m²
R_th = L / (k × A) = 0.2 / (0.7 × 10)
R_th = 0.2 / 7
R_th ≈ 0.0286 K/W
Example 2
A wall has three layers in series: brick (R = 0.03 K/W), fiberglass insulation (R = 0.85 K/W), and drywall (R = 0.08 K/W). The inside is 22°C and outside is −5°C. What is the heat loss?
Total resistance: R_total = 0.03 + 0.85 + 0.08 = 0.96 K/W
Temperature difference: ΔT = 22 − (−5) = 27 K
Heat flow: Q = ΔT / R_total = 27 / 0.96
Q ≈ 28.1 W — the insulation layer provides most of the resistance
When to Use It
- Building insulation design and energy efficiency calculations
- Electronics thermal management — heatsink sizing
- HVAC system design and heat loss estimation
- Industrial heat exchanger analysis
- Comparing insulation materials for cost-effectiveness