Heat-transfer rate Q̇
Steady heat-transfer rate through all active layers in series.
Thermal engineering · Heat transfer · conduction
Multilayer wall calculator — thermal resistance
Calculate steady conduction through 2 to 4 plane layers in series and see each layer's resistance and temperature drop.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
ΣR″Results
Heat flux q″
W/m²
Heat-transfer rate per unit wall area through the series layers.
Total area resistance R″tot
m²·K/W
Sum of the active layers' conductive resistances eᵢ/kᵢ.
Total thermal resistance Rtot
K/W
Total conductive resistance of the wall for the entered area.
Area conductance U
W/(m²·K)
Inverse of the total conductive area resistance, excluding surface films.
R″tot = —Steady-state, one-dimensional conduction through plane layers in series. Each layer is homogeneous, has constant area and constant thermal conductivity.
01Formulas and symbols
Formulas used
R″ᵢ
eᵢ / kᵢArea thermal resistance of layer iR″tot
Σ(eᵢ / kᵢ)Sum of the layer resistances in seriesU
1 / R″totConductive area conductance of the wallq″
ΔT / R″totHeat flux through all layersQ̇
A · q″Total heat-transfer rateeᵢe₁ … eₙmkᵢk₁ … kₙW/(m·K)AArea Am²ΔTTemperature difference ΔTKR″ᵢArea thermal resistance of layer im²·K/Wq″Heat flux q″W/m²Q̇Heat-transfer rate Q̇WUArea conductance UW/(m²·K)| # | e | k | R″ᵢ | ΔTᵢ |
|---|
02Assumptions and limits
Scope of validity
- Steady-state, one-dimensional conduction through plane layers in series.
- Each layer is homogeneous, has constant area and constant thermal conductivity.
- Select 2 to 4 layers; every selected layer must have strictly positive thickness.
- No contact resistance, surface convection or radiation is included.
- Thermal bridges, parallel paths, moisture and cylindrical geometries are outside this model.
- The displayed U value represents conduction through the entered layers only and is not a regulatory whole-assembly U-value.
03Validation example
Reference numerical case
- Reference case: A = 10 m² and ΔT = 20 K with three active layers.
- e₁/k₁ = 0.10/0.04 = 2.50; e₂/k₂ = 0.05/0.50 = 0.10; e₃/k₃ = 0.10/1.00 = 0.10 m²·K/W.
- R″tot = 2.70 m²·K/W; U = 0.37037 W/(m²·K).
- q″ = 7.4074 W/m² and Q̇ = 74.074 W for A = 10 m².
04References
Technical references
- MIT OpenCourseWare — Thermal Resistance Circuits: composite slab with resistances in series.
- NIST Special Publication 811 — SI units and temperature intervals.