Nusselt Number For All Value Of GrPr And Constant Wall Temperature Calculator

Nusselt Number Formula:

\[ Nu = \left(0.825 + \frac{0.387 \times (Gr \times Pr)^{0.167}}{\left(1 + \left(\frac{0.492}{Pr}\right)^{0.5625}\right)^{0.296}}\right)^2 \]

Nusselt Number (Nu):

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1. What is the Nusselt Number?

The Nusselt Number is a dimensionless number that represents the ratio of convective to conductive heat transfer at a boundary in a fluid. It is used to characterize heat transfer in fluid dynamics and thermal engineering applications.

2. How Does the Calculator Work?

The calculator uses the Nusselt Number formula for all values of GrPr and constant wall temperature:

\[ Nu = \left(0.825 + \frac{0.387 \times (Gr \times Pr)^{0.167}}{\left(1 + \left(\frac{0.492}{Pr}\right)^{0.5625}\right)^{0.296}}\right)^2 \]

Where:

\( Nu \) — Nusselt Number
\( Gr \) — Grashof Number (ratio of buoyancy to viscous force)
\( Pr \) — Prandtl Number (ratio of momentum diffusivity to thermal diffusivity)

Explanation: This empirical correlation provides the Nusselt number for natural convection heat transfer with constant wall temperature conditions across all ranges of the Grashof-Prandtl product.

3. Importance of Nusselt Number Calculation

Details: Accurate Nusselt number calculation is crucial for designing heat exchangers, cooling systems, and various thermal engineering applications where natural convection plays a significant role in heat transfer.

4. Using the Calculator

Tips: Enter Grashof Number and Prandtl Number as positive 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 quantifies the enhancement of heat transfer through convection compared to conduction alone. A higher Nu indicates more efficient convective heat transfer.

Q2: When is this specific correlation applicable?
A: This correlation is used for natural convection heat transfer with constant wall temperature conditions across all ranges of Grashof-Prandtl product.

Q3: What are typical ranges for Grashof and Prandtl numbers?
A: Grashof numbers can range from 10^3 to 10^12 for natural convection, while Prandtl numbers range from 0.01 (liquid metals) to 1000 (oils).

Q4: Are there limitations to this equation?
A: This correlation assumes constant properties, constant wall temperature, and may have reduced accuracy for extreme fluid properties or complex geometries.

Q5: How does this differ from forced convection correlations?
A: Natural convection correlations (like this one) depend on Grashof number, while forced convection correlations typically depend on Reynolds number.