Library / Heat transfer and thermal systems / HTS-26
Heat transfer and thermal systems
Average heat-transfer coefficient on a laminar flat plate
Mean convection coefficient over an isothermal flat plate in parallel laminar flow from the leading edge, with fluid properties at the film temperature.
- Ref
- HTS-26
- Rev
- v1
- Field
- Heat transfer and thermal systems
- Result
- h̄ [W/(m² K)]
For laminar flow over an isothermal flat plate from the leading edge, the local Nusselt number is Nux = 0.332 Rex^½ Pr^⅓, and the average over length L is twice that: h̄ = (k/L) 0.664 ReL^½ Pr^⅓. Use properties at the film temperature, Pr ≥ 0.6 and ReL typically below about 5×10⁵, where laminar flow ends.
Mean convection coefficient over an isothermal flat plate in parallel laminar flow from the leading edge, with fluid properties at the film temperature. Use for Pr ≥ 0.6 and ReL below about 5×10⁵.
Calculator
- Mean Nusselt number, 0.664 Re^½ Pr^⅓194.9
- Local coefficient at the trailing edge, h̄/25.848 W/(m² K)
- Heat flux for a 10 K difference, 10 h̄117 W/m²
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 plate has an average coefficient of 11.7 W/(m² K), so a 10 K difference moves 117 W/m².
- The coefficient is highest at the leading edge and falls along the plate as the boundary layer thickens, reaching half the average value at the trailing edge, 5.848 W/(m² K).
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (W/(m² K)) | Local step | Change in result |
|---|---|---|---|---|---|---|
| L Heated plate length | 0.01 to 5 m | 1.17 | 584.8 | 583.6 | +10% | −9.09 % |
| k Fluid conductivity | 0.01 to 0.7 W/(m K) | 3.898 | 272.9 | 269 | +10% | +10 % |
| Pr Prandtl number | 0.6 to 100 | 10.63 | 58.48 | 47.85 | +10% | +3.23 % |
| ReL Reynolds number based on L | 100 to 500,000 | 0.3698 | 26.15 | 25.78 | +10% | +4.88 % |
Sweep of Reynolds number based on L
| Reynolds number based on L | Mean heat-transfer coefficient (W/(m² K)) |
|---|---|
| 100 | 0.3698 |
| 290 | 0.6298 |
| 840.9 | 1.072 |
| 2,438 | 1.826 |
| 7,071 | 3.11 |
| 20,500 | 5.296 |
| 59,460 | 9.018 |
| 172,400 | 15.36 |
| 500,000 | 26.15 |
Sweep one variable
Variables and how each one contributes
Mean heat-transfer coefficient
What the equation gives you. Everything else feeds it.
Fluid conductivity
The fluid conductivity, in W/(m K). Raises the coefficient in direct proportion. Raising it by 10 % (to 0.033) moves the result by +10 %, from 11.7 to 12.86 W/(m² K).
Heated plate length
The heated plate length, in m. A longer plate has a lower average coefficient at fixed Re, in inverse proportion. Raising it by 10 % (to 0.55) moves the result by −9.09 %, from 11.7 to 10.63 W/(m² K).
Reynolds number based on L
The Reynolds number based on L. Raises the coefficient as the square root. Raising it by 10 % (to 110,000) moves the result by +4.88 %, from 11.7 to 12.27 W/(m² K).
Prandtl number
The Prandtl number. Raises the coefficient as the cube root. Raising it by 10 % (to 0.88) moves the result by +3.23 %, from 11.7 to 12.07 W/(m² K).
Worked example with the values above
- Nusselt number: 0.664 × √100,000 × 0.8^⅓ = 194.92.
- Scale: k/L = 0.03 / 0.5 = 0.06 W/(m² K).
- h̄ = 0.06 × 194.92 = 11.695 W/(m² K).
Assumptions and limits
- Fluid properties are evaluated at the film or bulk temperature as stated, and are otherwise constant.
- The geometry and flow regime match the correlation range, such as smooth tubes, single cylinders or isothermal plates.
Common mistakes
- Using a correlation outside its Reynolds, Prandtl or Rayleigh range.
- Using the wrong characteristic length, for example plate length instead of tube diameter.
- Taking the properties at the wall or free-stream temperature when the film temperature is intended.
Statistics and uncertainty
Published correlations typically scatter by 10 % to 25 % against experiment, and the property evaluation temperature adds to the error. Use the result as an estimate to be confirmed by test for critical designs.
Where it is used
- Estimating coefficients for heat sinks, ducts, tubes and walls.
- Screening calculations before a detailed model or test.
Maths you need
- Reynolds number: Re = ρUL/μ
- Prandtl number: Pr = μcp/k
- Nusselt number: Nu = hL/k