Question

The Nusselt number is related to the Reynolds number in laminar and turbulent flows respectively as:

• A. \( R \times e^{-0.5} \) and \( R \times e^{0.8} \)
• B. \( R \times e^{0.5} \) and \( R \times e^{0.8} \)
• C. \( R \times e^{-0.5} \) and \( R \times e^{0} \)
• D. \( R \times e^{0.5} \) and \( R \times e^{-0.8} \)

Hint:

The Nusselt number increases with the Reynolds number, and the relationship is typically \( Nu \propto Re^{0.5} \) for laminar flow and \( Nu \propto Re^{0.8} \) for turbulent flow.

Answer 1

The Correct Option is B

Step 1: Understand the Nusselt number relation.
The Nusselt number (\( Nu \)) is a dimensionless number that relates convective heat transfer to conductive heat transfer. The Nusselt number is typically related to the Reynolds number (\( Re \)) in both laminar and turbulent flow regimes. Step 2: Formula for Nusselt number For laminar flow, the relationship is \( Nu \propto Re^{0.5} \), and for turbulent flow, \( Nu \propto Re^{0.8} \). Step 3: Conclusion Thus, the correct relationship is \( Nu \propto R \times e^{0.5} \) for laminar flow and \( Nu \propto R \times e^{0.8} \) for turbulent flow. Final Answer: \[ \boxed{R \times e^{0.5} \, \text{and} \, R \times e^{0.8}} \]