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: Understanding the Nusselt Number
The Nusselt number (\( Nu \)) is a dimensionless parameter indicating the ratio of convective to conductive heat transfer. It is typically related to the Reynolds number (\( Re \)) in laminar and turbulent flows.Step 2: Nusselt Number Formulas In laminar flow, the Nusselt number is proportional to the Reynolds number by \( Nu \propto Re^{0.5} \). For turbulent flow, the relationship is \( Nu \propto Re^{0.8} \).Step 3: Summary Therefore, for laminar flow, \( Nu \propto R \times e^{0.5} \), and for turbulent flow, \( Nu \propto R \times e^{0.8} \). Final Answer: \[ \boxed{R \times e^{0.5} \, \text{and} \, R \times e^{0.8}}\]