Nusselt Number For Hydrodynamic Length Fully Developed And Thermal Length Still Developing Calculator

Nusselt Number Formula:

\[ Nu = 3.66 + \frac{0.0668 \cdot \frac{D}{L} \cdot Re_D \cdot Pr}{1 + 0.04 \cdot \left( \frac{D}{L} \cdot Re_D \cdot Pr \right)^{0.67}} \]

Nusselt Number (Nu):

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1. What is the Nusselt Number?

The Nusselt Number is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection and diffusion. It is a dimensionless number used in heat transfer calculations.

2. How Does the Calculator Work?

The calculator uses the Nusselt Number formula for hydrodynamic length fully developed and thermal length still developing:

\[ Nu = 3.66 + \frac{0.0668 \cdot \frac{D}{L} \cdot Re_D \cdot Pr}{1 + 0.04 \cdot \left( \frac{D}{L} \cdot Re_D \cdot Pr \right)^{0.67}} \]

Where:

\( D \) — Diameter (m)
\( L \) — Length (m)
\( Re_D \) — Reynolds Number Dia
\( Pr \) — Prandtl Number

Explanation: This formula calculates the Nusselt number for cases where the hydrodynamic boundary layer is fully developed while the thermal boundary layer is still developing.

3. Importance of Nusselt Number Calculation

Details: The Nusselt number is crucial for determining the convective heat transfer coefficient in fluid flow systems. It helps engineers design efficient heat exchangers, cooling systems, and other thermal management applications.

4. Using the Calculator

Tips: Enter diameter and length in meters, Reynolds number and Prandtl number as dimensionless quantities. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does this specific Nusselt number formula represent?
A: This formula is used for cases where the hydrodynamic boundary layer is fully developed while the thermal boundary layer is still developing in circular tubes.

Q2: What are typical values for Nusselt number?
A: For laminar flow in circular tubes, Nusselt number typically ranges from 3.66 (fully developed flow) to higher values for developing flow.

Q3: When is this formula applicable?
A: This formula is specifically designed for laminar flow in circular tubes where the hydrodynamic profile is fully developed but the thermal boundary layer is still developing.

Q4: What are the limitations of this formula?
A: This formula is specifically for circular tubes and may not be accurate for other geometries or turbulent flow conditions.

Q5: How does this differ from other Nusselt number correlations?
A: This correlation specifically addresses the transitional case where hydrodynamic length is fully developed while thermal length is still developing, making it more accurate for certain flow conditions.