Question

Dimensionless numbers play an important role in correlating transfer coefficients during forced convection. In relation to the dimensionless numbers, the correct statement(s) is/are:

• A. Prandtl number in heat transfer is analogous to Schmidt number in mass transfer
• B. Small value of Prandtl number signifies lower thermal diffusion as compared to momentum diffusion
• C. Prandtl number is the ratio of momentum diffusivity to the thermal diffusivity of the fluid
• D. Lewis number is the product of Schmidt number and Prandtl number

Hint:

Remember: \(Pr\) links momentum and thermal diffusivities, \(Sc\) links momentum and mass diffusivities, and \(Le = Sc/Pr\). Always check definitions carefully before evaluating statements.

Answer 1

The Correct Option is A, B, C

Step 1: Recall definitions of dimensionless numbers. - Prandtl number (Pr): \[ Pr = \frac{\nu}{\alpha} = \frac{\text{momentum diffusivity}}{\text{thermal diffusivity}} \] - Schmidt number (Sc): \[ Sc = \frac{\nu}{D} = \frac{\text{momentum diffusivity}}{\text{mass diffusivity}} \] - Lewis number (Le): \[ Le = \frac{Sc}{Pr} = \frac{\alpha}{D} \]

Step 2: Verify statements. (A) Prandtl number in heat transfer is analogous to Schmidt number in mass transfer. This is True, because both compare momentum diffusivity with another type of diffusivity (thermal in Pr, mass in Sc). (B) Small value of Prandtl number signifies lower thermal diffusion as compared to momentum diffusion. This is True, since \(Pr = \nu/\alpha\). Small Pr means thermal diffusivity is higher than momentum diffusivity. (C) Prandtl number is the ratio of momentum diffusivity to the thermal diffusivity of the fluid. This is True, directly from the definition. (D) Lewis number is the product of Schmidt number and Prandtl number. This is False, because \[ Le = \frac{Sc}{Pr}, \text{not } Sc \cdot Pr \] \[ \boxed{\text{Correct statements: (A), (B), (C)}} \]