Correlation For Local Nusselt Number For Laminar Flow On Isothermal Flat Plate Calculator

Formula Used:

\[ Nux = \frac{0.3387 \times Rel^{1/2} \times Pr^{1/3}}{(1 + (0.0468/Pr)^{2/3})^{1/4}} \]

Local Nusselt Number (Nux):

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1. What is the Local Nusselt Number Correlation?

The correlation for local Nusselt number for laminar flow on an isothermal flat plate is a fundamental equation in heat transfer that describes the relationship between convective and conductive heat transfer across a boundary. This specific correlation provides an accurate estimation of heat transfer characteristics in laminar flow conditions over flat surfaces.

2. How Does the Calculator Work?

The calculator uses the following correlation:

\[ Nux = \frac{0.3387 \times Rel^{1/2} \times Pr^{1/3}}{(1 + (0.0468/Pr)^{2/3})^{1/4}} \]

Where:

\( Nux \) — Local Nusselt number (dimensionless)
\( Rel \) — Local Reynolds Number (dimensionless)
\( Pr \) — Prandtl Number (dimensionless)

Explanation: This correlation accounts for the combined effects of fluid motion (through Reynolds number) and thermal properties (through Prandtl number) on local heat transfer characteristics in laminar flow over flat plates.

3. Importance of Local Nusselt Number Calculation

Details: Accurate calculation of local Nusselt number is crucial for designing heat transfer equipment, predicting thermal performance of systems, and optimizing thermal management in various engineering applications involving laminar flow over flat surfaces.

4. Using the Calculator

Tips: Enter Local Reynolds 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 range of validity for this correlation?
A: This correlation is valid for laminar flow conditions (typically Rel < 5×10⁵) over isothermal flat plates with constant properties.

Q2: How does Prandtl number affect the Nusselt number?
A: Higher Prandtl numbers generally lead to higher Nusselt numbers, as fluids with higher Prandtl numbers have thinner thermal boundary layers relative to momentum boundary layers.

Q3: What are typical values for Local Nusselt number?
A: Local Nusselt number values typically range from 0.1 to several hundred, depending on flow conditions and fluid properties.

Q4: When is this correlation most applicable?
A: This correlation is most applicable for engineering calculations involving laminar forced convection over flat plates with constant surface temperature.

Q5: How does this correlation compare to other Nusselt number correlations?
A: This specific correlation provides improved accuracy for a wider range of Prandtl numbers compared to simpler correlations that assume constant Prandtl number effects.