Corresponding to Prandtl number in heat transfer, the dimensionless group in mass transfer is the __________ number.

ANS:A - Schmidt

The Schmidt number (Sc) is a dimensionless group used in fluid mechanics and heat transfer to characterize the relative importance of momentum diffusivity to mass diffusivity in a fluid. It is defined as the ratio of momentum diffusivity (kinematic viscosity) to mass diffusivity. Mathematically, the Schmidt number (Sc) is defined as: Sc=Kinematic viscosityMass diffusivity=𝜈𝐷Sc=Mass diffusivityKinematic viscosity​=Dν​ Where:

• 𝜈ν is the kinematic viscosity of the fluid.
• 𝐷D is the mass diffusivity of the substance being transported within the fluid.

The Schmidt number provides insight into how quickly momentum is transferred relative to how quickly mass is transferred in a fluid flow. Key points about the Schmidt number:

1. Interpretation: A high Schmidt number indicates that momentum diffuses more rapidly than mass does, while a low Schmidt number indicates that mass diffuses more rapidly than momentum does.
2. Applications: The Schmidt number is particularly relevant in problems involving mass transfer, such as diffusion of chemical species in fluids, pollutant dispersion in air or water, and biological processes like nutrient uptake in organisms.
3. Analogous to Other Dimensionless Numbers: In some contexts, the Schmidt number is analogous to the Prandtl number in heat transfer and the Reynolds number in fluid dynamics. Just as the Prandtl number relates the rates of momentum and thermal diffusivity, and the Reynolds number relates inertial forces to viscous forces, the Schmidt number relates momentum diffusivity to mass diffusivity.
4. Influence on Mass Transfer Rates: In mass transfer processes, the Schmidt number plays a crucial role in determining the rate of mass transfer. For instance, in the context of mass transfer from a solid surface into a flowing fluid, a higher Schmidt number typically results in slower mass transfer rates due to the relatively slower diffusion of the solute in the fluid.

In summary, the Schmidt number is an important dimensionless parameter used in the analysis of mass transfer processes, providing insight into the relative rates of momentum and mass diffusion within a fluid.