Heat-transfer rate Q̇
Calculated steady heat-transfer rate through the wall.
Thermal engineering · Heat transfer · conduction
Overall heat-transfer coefficient through a wall
Calculate hot-fluid → wall → cold-fluid heat transfer by combining both convection resistances with conduction through one plane wall.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
UResults
Heat flux q″
W/m²
Heat-transfer rate per unit area.
Overall conductance U
W/(m²·K)
Overall area conductance including both convection films and the wall.
Total area resistance R″tot
m²·K/W
Sum 1/hₕ + e/k + 1/h𝒸.
Total thermal resistance Rtot
K/W
Overall thermal resistance for the entered area.
R″h = — · R″wall = — · R″c = —Steady-state, one-dimensional heat transfer through a plane wall. The convection coefficients hₕ and h𝒸 are prescribed and uniform over the area.
01Formulas and symbols
Formulas used
R″h
1 / hₕHot-side convective resistanceR″wall
e / kWall conductive resistanceR″c
1 / h𝒸Cold-side convective resistanceU
1 / (1/hₕ + e/k + 1/h𝒸)Overall heat-transfer coefficientQ̇
U · A · ΔT∞Total heat-transfer rate| R″h | R″wall | R″c | ΔTₕ | ΔTwall | ΔT𝒸 |
|---|
02Assumptions and limits
Scope of validity
- Steady-state, one-dimensional heat transfer through a plane wall.
- The convection coefficients hₕ and h𝒸 are prescribed and uniform over the area.
- The wall is homogeneous with constant thermal conductivity k and no internal heat generation.
- T∞,h and T∞,c are bulk-fluid temperatures, not wall-surface temperatures.
- Radiation, contact resistance, thermal bridges, fouling and lateral conduction are excluded.
- The calculated U applies only to the entered model and is not a regulatory building or heat-exchanger rating.
03Validation example
Reference numerical case
- Reference case: hₕ = 10, h𝒸 = 25 W/(m²·K), k = 0.5 W/(m·K), e = 0.10 m, A = 10 m² and ΔT∞ = 20 K.
- R″h = 0.10; R″wall = 0.20; R″c = 0.04 m²·K/W, so R″tot = 0.34 m²·K/W.
- U = 2.941176 W/(m²·K) and q″ = 58.823529 W/m².
- Q̇ = 588.235294 W and Rtot = 0.034 K/W.
04References
Technical references
- Incropera et al. — Fundamentals of Heat and Mass Transfer: convection and plane-wall thermal-resistance circuits.
- NIST Special Publication 811 — SI units and temperature intervals.