Nusselt Number Correlations to Know for Heat and Mass Transport

Nusselt number correlations are essential for understanding heat transfer in various flow conditions. These correlations help estimate heat transfer rates in pipes, plates, and cylinders, linking fluid dynamics to thermal performance in engineering applications.

1. Dittus-Boelter correlation for turbulent flow in smooth pipes

   • Applicable for Reynolds numbers greater than 10,000.
   • Used to estimate the Nusselt number for turbulent flow in circular pipes.
   • Assumes constant heat flux or constant wall temperature conditions.
   • Correlation: Nu = 0.023 Re^0.8 Pr^n, where n = 0.3 for heating and n = 0.3 for cooling.

2. Sieder-Tate correlation for viscous heating effects

   • Designed for laminar and turbulent flow in pipes with significant viscous heating.
   • Accounts for the effect of temperature-dependent viscosity on heat transfer.
   • Correlation: Nu = (0.3 + (0.62 Re^0.5 Pr^0.33) / (1 + (0.4/Pr)^0.67))^2.
   • Useful for fluids with high viscosity or large temperature differences.

3. Gnielinski correlation for transitional and turbulent flow in pipes

   • Valid for Reynolds numbers from 1,000 to 100,000.
   • Combines features of both laminar and turbulent flow for better accuracy.
   • Correlation: Nu = (f/8)(Re - 1000)Pr / (1 + 12.7(f/8)^(0.5)(Pr^(2/3) - 1)).
   • Suitable for a wide range of flow conditions.

4. Churchill-Chu correlation for natural convection on vertical plates

   • Applicable for both laminar and turbulent natural convection.
   • Covers a wide range of Rayleigh numbers (10^4 to 10^12).
   • Correlation: Nu = (0.68 + (0.67 Ra^(1/4)) / (1 + (0.492/Pr)^(9/16)))^4/3.
   • Useful for vertical surfaces in various thermal environments.

5. McAdams correlation for natural convection on horizontal plates

   • Focuses on laminar flow conditions for horizontal surfaces.
   • Correlation: Nu = 0.332 Ra^(1/4) for laminar flow (Ra < 10^9).
   • Provides a simple method for estimating heat transfer in natural convection scenarios.
   • Applicable for low to moderate temperature differences.

6. Zhukauskas correlation for external flow over cylinder banks

   • Designed for flow over multiple cylinders in a staggered arrangement.
   • Accounts for the effects of cylinder spacing and arrangement on heat transfer.
   • Correlation: Nu = 0.3 + 0.6 Re^0.5 Pr^0.33.
   • Useful in applications like heat exchangers and cooling systems.

7. Hilpert correlation for external flow over a single cylinder

   • Applicable for both laminar and turbulent flow around a single cylinder.
   • Correlation: Nu = 0.3 + 0.62 Re^0.5 Pr^0.33 for Re < 10^5.
   • Provides a straightforward approach to estimate heat transfer in cylindrical geometries.
   • Useful in various engineering applications involving cylindrical objects.

8. Nusselt correlation for laminar flow over a flat plate

   • Valid for laminar flow conditions with low Reynolds numbers.
   • Correlation: Nu = 0.332 Re^(1/2) Pr^(1/3).
   • Useful for calculating heat transfer in boundary layer flows.
   • Applicable in scenarios like heat exchangers and surface cooling.

9. Colburn analogy for heat and momentum transfer

   • Relates heat transfer to momentum transfer using a dimensionless approach.
   • Provides a method to estimate Nusselt number based on friction factor.
   • Useful for simplifying complex heat transfer calculations.
   • Applicable in both laminar and turbulent flow regimes.

10. Petukhov correlation for turbulent flow in smooth tubes

    • Designed for turbulent flow in smooth pipes with Reynolds numbers from 1,000 to 100,000.
    • Accounts for the effects of friction factor on heat transfer.
    • Correlation: Nu = (f/8)(Re - 1000)Pr / (1 + 12.7(f/8)^(0.5)(Pr^(2/3) - 1)).
    • Provides a reliable method for estimating heat transfer in turbulent flow conditions.