Nusselt Number For Hypersonic Vehicle Calculator

Nusselt Number Formula:

\[ Nu = \frac{q_w \times x_d}{k \times (T_{wall} - T_w)} \]

Local Heat Transfer Rate (q_w):

W/m²

Distance from Nose Tip (x_d):

Thermal Conductivity (k):

W/m·K

Adiabatic Wall Temperature (T_wall):

Wall Temperature (T_w):

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 for hypersonic vehicles.

2. How Does the Calculator Work?

The calculator uses the Nusselt Number formula:

\[ Nu = \frac{q_w \times x_d}{k \times (T_{wall} - T_w)} \]

Where:

\( q_w \) — Local Heat Transfer Rate (W/m²)
\( x_d \) — Distance from Nose Tip to Required Base Diameter (m)
\( k \) — Thermal Conductivity (W/m·K)
\( T_{wall} \) — Adiabatic Wall Temperature (K)
\( T_w \) — Wall Temperature (K)

Explanation: The formula calculates the dimensionless Nusselt number which characterizes the convective heat transfer relative to conductive heat transfer at a boundary.

3. Importance of Nusselt Number Calculation

Details: Accurate Nusselt number calculation is crucial for thermal analysis of hypersonic vehicles, heat exchanger design, and predicting heat transfer rates in various engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure temperature difference is not zero. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does a high Nusselt number indicate?
A: A high Nusselt number indicates efficient convective heat transfer compared to conductive heat transfer.

Q2: What are typical Nusselt number values?
A: Nusselt number values vary widely depending on flow conditions. For laminar flow, Nu ≈ 3-5; for turbulent flow, Nu can be 100+.

Q3: How is this formula used in hypersonic vehicle design?
A: It helps predict heat transfer rates at different points on the vehicle surface, which is critical for thermal protection system design.

Q4: What are the limitations of this formula?
A: This is a simplified local Nusselt number calculation and may not account for complex flow phenomena, boundary layer effects, or variable properties.

Q5: Can this be used for other applications besides hypersonic vehicles?
A: Yes, the Nusselt number concept applies to various heat transfer problems involving forced convection in different engineering fields.