I. What Nu Measures
Nu = h·L / λ
h is the heat transfer coefficient, L is the characteristic length, λ is the fluid thermal conductivity. Intuitive understanding: if the fluid is treated as a stationary film of thickness L for pure conduction, Nu=1; actual convection "tears" the heat open through flow, so Nu is far greater than 1. Therefore the larger the Nu, the stronger the convective heat transfer.
II. Why Correlations Are Needed
Strictly solving convection requires solving the Navier-Stokes + energy equations, extremely difficult. In engineering, extensive experiments summarize the empirical relationship between Nu and Re, Pr; the most classic is circular-pipe turbulence:
Nu = 0.023 · Re^0.8 · Pr^0.4 (heating fluid)
The exponent 0.4 (heating) or 0.3 (cooling) comes from the direction of property change after the fluid is heated. After calculating Nu, substitute back h = Nu·λ/L, which can be used in Q = h·A·ΔT.
III. Overview of Common Correlations
| Correlation | Applicable |
|---|---|
| Dittus-Boelter | Circular-pipe turbulence, Re 1e4~1e5, Pr 0.7~120, small temperature difference |
| Sieder-Tate | Considers viscosity change with wall temperature, more accurate |
| Gnielinski | Wider applicability, includes transition zone |
| Flat-plate convection | External flow over flat plate, laminar/turbulent |
IV. Usage Boundaries and Pitfalls
- Do not exceed the applicable range: Applying Dittus-Boelter to laminar flow differs by an order of magnitude;
- Property temperature: Use properties at the film temperature (mean of wall temperature and fluid average temperature);
- Entrance effect: The h at the short-pipe entrance section is higher; correction is needed for small length-to-diameter ratios;
- Roughness/disturbance: Plate corrugation and inner fins break the smooth-pipe correlation, requiring manufacturer correction factors.
Correlations are engineering estimation methods; ±20% error is normal. Key selections are backed by experiments or manufacturer data.