Nusselt Number When Property Variation Is Larger Due To Temperature Variation Calculator

Formula Used:

\[ Nu = 0.25 \times (Re^{0.6}) \times (Pr^{0.38}) \times \left(\frac{Pf}{Prw}\right)^{0.25} \]

Reynolds Number (Re):

Prandtl Number (Pr):

Prandtl Number at Film Temperature (Pf):

Prandtl Number at Wall Temperature (Prw):

Nusselt Number (Nu):

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1. What is the Nusselt Number Formula for Property Variation?

The Nusselt number formula accounts for property variations due to temperature changes in fluid flow. It estimates the convective heat transfer coefficient relative to conductive heat transfer at a boundary.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Nu = 0.25 \times (Re^{0.6}) \times (Pr^{0.38}) \times \left(\frac{Pf}{Prw}\right)^{0.25} \]

Where:

\( Nu \) — Nusselt Number
\( Re \) — Reynolds Number
\( Pr \) — Prandtl Number
\( Pf \) — Prandtl Number at Film Temperature
\( Prw \) — Prandtl Number at Wall Temperature

Explanation: This formula accounts for the effects of fluid property variations due to temperature differences between the film and wall temperatures.

3. Importance of Nusselt Number Calculation

Details: Accurate Nusselt number calculation is crucial for designing heat exchangers, predicting heat transfer rates, and optimizing thermal systems where property variations due to temperature are significant.

4. Using the Calculator

Tips: Enter Reynolds number, Prandtl number, Prandtl number at film temperature, and Prandtl number at wall temperature. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is this specific formula used for property variation?
A: This formula specifically accounts for the variation in fluid properties (particularly Prandtl number) due to temperature differences between the film and wall.

Q2: What are typical ranges for these dimensionless numbers?
A: Reynolds number can range from 10³ to 10⁶, Prandtl number typically ranges from 0.7 to 1000, depending on the fluid.

Q3: When should this formula be used instead of standard Nusselt correlations?
A: This formula should be used when there are significant temperature differences that cause substantial variations in fluid properties.

Q4: Are there limitations to this equation?
A: This correlation may have limitations for extreme temperature differences, non-Newtonian fluids, or complex flow geometries.

Q5: How accurate is this correlation compared to experimental data?
A: This correlation provides reasonable accuracy for many engineering applications but should be validated against experimental data for specific cases.