Average Nusselt Number For Constant Wall Temperature Calculator

Average Nusselt Number Formula:

\[ Nu_{avg} = 0.68 + \frac{0.67 \times (Gr \times Pr)^{0.25}}{(1 + (0.492/Pr)^{0.5625})^{0.444}} \]

Average Nusselt Number (Nu_avg):

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1. What is the Average Nusselt Number?

The Average Nusselt number is a dimensionless number that represents the ratio of convective to conductive heat transfer across a boundary. For constant wall temperature conditions, it provides an average measure of the heat transfer coefficient over the entire surface.

2. How Does the Calculator Work?

The calculator uses the formula for average Nusselt number:

\[ Nu_{avg} = 0.68 + \frac{0.67 \times (Gr \times Pr)^{0.25}}{(1 + (0.492/Pr)^{0.5625})^{0.444}} \]

Where:

\( Nu_{avg} \) — Average Nusselt number
\( Gr \) — Grashof number (dimensionless)
\( Pr \) — Prandtl number (dimensionless)

Explanation: This formula calculates the average Nusselt number for natural convection over a vertical plate with constant wall temperature, considering both Grashof and Prandtl numbers.

3. Importance of Nusselt Number Calculation

Details: The Nusselt number is crucial for heat transfer analysis as it quantifies the enhancement of heat transfer through convection compared to conduction alone. It helps in designing heat exchangers, cooling systems, and various thermal management applications.

4. Using the Calculator

Tips: Enter Grashof number and Prandtl number as positive dimensionless values. Both values must be greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of Nusselt number?
A: The Nusselt number represents the ratio of convective to conductive heat transfer at a boundary. A higher Nusselt number indicates more efficient convective heat transfer.

Q2: How does Grashof number affect the Nusselt number?
A: Grashof number represents the ratio of buoyancy to viscous forces. Higher Grashof numbers (indicating stronger natural convection) generally lead to higher Nusselt numbers.

Q3: What is the typical range of Prandtl numbers?
A: Prandtl numbers vary widely: ~0.7 for gases, 5-50 for water, 50-100 for oils, and up to 1000+ for very viscous fluids.

Q4: When is this formula applicable?
A: This formula is specifically for natural convection over a vertical flat plate with constant wall temperature boundary condition.

Q5: Are there limitations to this equation?
A: This correlation is valid for laminar natural convection. For turbulent flow or other geometries, different correlations should be used.