Library / Heat Transfer / HTR-01
Heat Transfer
Heat flow through a composite wall
Steady heat rate through a wall with a fluid film on each side.
- Ref
- HTR-01
- Rev
- v1
- Field
- Heat Transfer
- Result
- Q̇ [W]
Series layers carry the same heat rate under steady one-dimensional conduction without generation. Include both fluid films when the specified temperatures are bulk fluid temperatures. The calculator has one wall layer and two films.
Heat flows through the wall and its two surface films like current through resistors in series; the total resistance sets the flow.
Calculator
- Total resistance ΣR0.4 K/W
- Overall U-value2.5 W/(m²·K)
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- For a 0.10 m wall with k = 0.5 W/(m K) and h = 10 on both sides the total resistance is 0.40 K/W, so a 30 K difference drives 75 W.
- The biggest resistance dominates: improving a low-resistance layer barely helps.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (W) | Local step | Change in result |
|---|---|---|---|---|---|---|
| A Wall area | 0.1 to 100 m² | 7.5 | 7,500 | 7,493 | +10% | +10 % |
| T∞,h Hot fluid temperature | 0 to 200 °C | −25 | 475 | 500 | +10% | +13.3 % |
| T∞,c Cold fluid temperature | −50 to 100 °C | −150 | 225 | 375 | +10% | −3.33 % |
| k Thermal conductivity | 0.02 to 400 W/(m·K) | 5.769 | 149.8 | 144 | +10% | +4.76 % |
| L Wall thickness | 0.005 to 1 m | 13.64 | 142.9 | 129.2 | +10% | −4.76 % |
| h₁ Hot-side coefficient | 2 to 1,000 W/(m²·K) | 37.5 | 99.67 | 62.17 | +10% | +2.33 % |
| h₂ Cold-side coefficient | 2 to 1,000 W/(m²·K) | 37.5 | 99.67 | 62.17 | +10% | +2.33 % |
Sweep of Wall thickness
| Wall thickness (m) | Heat rate (W) |
|---|---|
| 0.005 | 142.9 |
| 0.009696 | 136.7 |
| 0.0188 | 126.3 |
| 0.03646 | 109.9 |
| 0.07071 | 87.87 |
| 0.1371 | 63.26 |
| 0.2659 | 40.99 |
| 0.5157 | 24.36 |
| 1 | 13.64 |
Sweep one variable
Variables and how each one contributes
Heat rate
What the equation gives you. Everything else feeds it.
Hot fluid temperature
Bulk temperature of the hot fluid. Raises the heat rate.
Cold fluid temperature
Bulk temperature of the cold fluid. Lowers the heat rate.
Wall area
Area normal to heat flow. Directly proportional.
Wall thickness
Thickness of the wall layer. Raises the wall resistance.
Thermal conductivity
Conductivity of the wall. Lowers the wall resistance.
Hot-side coefficient
Convection coefficient on the hot side. Lowers the film resistance.
Cold-side coefficient
Convection coefficient on the cold side. Lowers the film resistance.
Worked example with the values above
- Films: 1/(h₁A) = 0.1 and 1/(h₂A) = 0.1 K/W; wall: L/(kA) = 0.2 K/W.
- Total resistance ΣR = 0.4 K/W.
- Q = (40 − 10) / 0.4 = 75 W.
Assumptions and limits
- Steady one-dimensional conduction with no generation.
- Constant properties.
Common mistakes
- Forgetting the film resistances.
- Using the wrong area for each layer.
Statistics and uncertainty
Convection coefficients are uncertain by ±20–30%, which dominates the result when the films carry most of the resistance.
Where it is used
- Insulation and building-envelope heat loss.
- Enclosure and equipment thermal design.
Maths you need
- Conduction: q = −kA dT/dx
- Series resistances: add like electrical resistors