Heat-transfer rate Q̇
Calculated steady heat-transfer rate through the wall.
Thermal engineering · Heat transfer · conduction
Heat conduction calculator — Fourier's law
Calculate steady heat conduction through a homogeneous plane wall, or solve for the required thickness or thermal conductivity.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
|ΔT|Results
Required thickness e
Calculated wall thickness for the specified heat-transfer rate.
Required conductivity k
W/(m·K)
Calculated thermal conductivity for the specified heat-transfer rate.
Heat flux q″
W/m²
Heat-transfer rate per unit area.
Thermal resistance R
K/W
Total conductive thermal resistance for the entered area.
Area-normalized resistance R″
m²·K/W
Area-normalized conductive thermal resistance.
Relation and numerical substitutionFourier · 1D
Q̇ = k · A · ΔT / eq″ = k · ΔT / eR = e / (k · A)R″ = e / kQ̇Heat-transfer rate Q̇W
q″Heat flux q″W/m²
kThermal conductivity kW/(m·K)
AArea Am²
eThickness em
ΔTTemperature difference ΔTK
Relation and numerical substitution
ΔT = 20 K
Q̇ = 0.04 × 10 × 20 / 0.2 = 40 WSteady-state, one-dimensional conduction. Homogeneous plane wall with constant area and constant thermal conductivity k.
01Formulas and symbols
Formulas used
Q̇
k · A · ΔT / eQ̇ = k·A·ΔT/eq″
k · ΔT / eq″ = k·ΔT/eR
e / (k · A)R = e/(k·A)R″
e / kR″ = e/ke / k
e = kAΔT/Q̇ ; k = Q̇e/(AΔT)e = kAΔT/Q̇ ; k = Q̇e/(AΔT)02Assumptions and limits
Scope of validity
- Steady-state, one-dimensional conduction.
- Homogeneous plane wall with constant area and constant thermal conductivity k.
- No internal heat generation and no contact resistance.
- Surface convection and radiation are not included.
- Multilayer walls, cylindrical geometries and thermal bridges are outside this model.
- This physical calculation is not a code-compliance check.
03Validation example
Reference numerical case
- Reference case: k = 0.04 W/(m·K), A = 10 m², e = 0.20 m and ΔT = 20 K.
- Q̇ = 40 W and q″ = 4 W/m².
- R = 0.5 K/W and R″ = 5 m²·K/W.
- Inverse calculations return e = 0.20 m and k = 0.04 W/(m·K).
04References
Technical references
- MIT OpenCourseWare — Heat Transfer: Fourier conduction through a plane wall.
- NIST Special Publication 811 — SI units and temperature intervals.