Question

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

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

Hint:

The Reynolds number, Schmidt number, and Biot number are all dimensionless numbers used in fluid mechanics and heat transfer. Ensure that the proper definitions and quantities are used when applying these numbers.

Answer 1

The Correct Option is A, C

Let's analyze each expression: - (A) Reynolds number: This number is given by the formula: \[ \text{Re} = \frac{\rho V L}{\mu} \] where $\rho$ is the density, $V$ is the velocity, $L$ is the characteristic dimension, and $\mu$ is the viscosity. This matches the given expression, so (A) is correct. - (B) Nusselt number: The Nusselt number is defined as: \[ \text{Nu} = \frac{hL}{k} \] where $h$ is the convective heat transfer coefficient, $L$ is the characteristic dimension, and $k$ is the thermal conductivity of the fluid (not the solid). Thus, the expression given is incorrect. (B) is incorrect. - (C) Schmidt number: The Schmidt number is defined as: \[ \text{Sc} = \frac{\nu}{D} \] where $\nu$ is the kinematic viscosity of the fluid and $D$ is the diffusivity. This matches the given expression, so (C) is correct. - (D) Biot number: The Biot number is defined as: \[ \text{Bi} = \frac{hL}{k_f} \] where $h$ is the convective heat transfer coefficient, $L$ is the characteristic dimension, and $k_f$ is the thermal conductivity of the fluid (not the solid). Thus, the given expression is incorrect. (D) is incorrect. Thus, the correct answers are (A) and (C).