Question

Which among the following expression(s) is/are correct?

• A. Reynolds number = \(\frac{{\text{Density} \times \text{Velocity} \times \text{Characteristic dimension}}}{{\text{Viscosity}}} \)
• B. Nusselt number = \(\frac{{\text{Convective heat transfer coefficient} \times \text{Characteristic dimension}}}{{\text{Thermal conductivity of solid}}} \)
• C. Schmidt number = \(\frac{{\text{Kinematic viscosity of fluid}}}{{\text{Diffusivity}}} \)
• D. Biot number = \(\frac{{\text{Convective heat transfer coefficient} \times \text{Characteristic dimension}}}{{\text{Thermal conductivity of fluid}}} \)

Hint:

These dimensionless numbers are key to understanding fluid flow and heat transfer, each representing a different physical phenomenon like flow regime, heat conduction, and convection.

Answer 1

The Correct Option is A, C

Step 1: Understanding the expressions.
Each of these dimensionless numbers is used in fluid mechanics and heat transfer to characterize different physical phenomena.

Step 2: Analyzing the options.
- (A) Correct, the Reynolds number is used to predict flow patterns and is calculated as \(\frac{{\text{Density} \times \text{Velocity} \times \text{Characteristic dimension}}}{{\text{Viscosity}}}\).
- (B) Correct, the Nusselt number represents the ratio of convective to conductive heat transfer and is calculated as \(\frac{{\text{Convective heat transfer coefficient} \times \text{Characteristic dimension}}}{{\text{Thermal conductivity of solid}}}\).
- (C) Incorrect, the Schmidt number is given by the ratio of kinematic viscosity to diffusivity, not as stated.
- (D) Correct, the Biot number is a ratio that compares thermal resistance within a body to the thermal resistance at its surface and is calculated as \(\frac{{\text{Convective heat transfer coefficient} \times \text{Characteristic dimension}}}{{\text{Thermal conductivity of fluid}}}\).
Step 3: Conclusion.
The correct expressions are (A) Reynolds number, (B) Nusselt number, and (D) Biot number.