Library / Mechanical / MEC-08
Mechanical
Convective heat transfer
Heat flow between a surface and a moving fluid.
- Ref
- MEC-08
- Rev
- v1
- Field
- Mechanical
- Result
- Q̇ [W]
Q̇ in watts, h film coefficient in W/(m²·K), A surface area, Ts surface temperature and T_∞ the bulk fluid temperature.
A surface loses heat to the air or water flowing past it in proportion to its area, the temperature difference, and a film coefficient that describes how effectively the flow carries heat away.
Calculator
- Heat flux1,000 W/m²
- Thermal resistance 1/(hA)0.02 K/W
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.
- The film coefficient is the hard part. It depends on the flow speed, fluid and geometry, and can only be estimated from correlations or tests.
- Doubling the air speed does not double h; for turbulent flow it rises roughly as speed to the 0.8 power.
- Surface and air temperature difference sets the rate; a hot component in cool moving air loses heat quickly.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (W) | Local step | Change in result |
|---|---|---|---|---|---|---|
| h Film coefficient | 5 to 1,000 W/(m²·K) | 400 | 80,000 | 79,600 | +10% | +10 % |
| A Surface area | 0.01 to 50 m² | 10 | 50,000 | 49,990 | +10% | +10 % |
| Ts Surface temperature | 30 to 120 °C | 500 | 5,000 | 4,500 | +10% | +15 % |
| T∞ Fluid temperature | −10 to 30 °C | 1,500 | 3,500 | 2,000 | +10% | −5 % |
Sweep of Film coefficient
| Film coefficient (W/(m²·K)) | Heat flow (W) |
|---|---|
| 5 | 400 |
| 9.696 | 775.7 |
| 18.8 | 1,504 |
| 36.46 | 2,917 |
| 70.71 | 5,657 |
| 137.1 | 10,970 |
| 265.9 | 21,270 |
| 515.7 | 41,250 |
| 1,000 | 80,000 |
Sweep one variable
Variables and how each one contributes
Heat flow
What the equation gives you. Everything else feeds it.
Film coefficient
Still air about 5–10, forced air 25–250, water 500–10 000. Directly proportional; the most uncertain input.
Surface area
Area in contact with the fluid. Directly proportional; fins increase it.
Surface temperature
Temperature of the solid surface. Linear through ΔT.
Fluid temperature
Bulk temperature of the passing fluid. Linear, opposing Ts.
Worked example with the values above
- Temperature difference: 60 − 20 = 40 K.
- Q = hAΔT = 25 × 2 × 40.
- Q = 2,000 W.
Assumptions and limits
- Steady state.
- Uniform surface temperature and a constant h.
- Radiation is neglected.
Common mistakes
- Using the wrong h for the flow regime.
- Forgetting that radiation can add 20–50% at high surface temperatures.
- Using the fluid’s temperature near the wall rather than the bulk.
Statistics and uncertainty
The film coefficient from correlations is typically uncertain by ±20–25%, which dominates any measurement error in the temperatures. Treat the result as an estimate, and add margin in cooling designs.
Where it is used
- Cooling of electronics and engines.
- Heat loss from pipes and hulls.
- Heat soak in sensor housings.
Maths you need
- Temperature difference: driving force
- Fluid flow: moving fluid carries heat away