Question

What is the physical significance of the Schmidt number? How is it defined? To what dimensionless number does it correspond in heat transfer? What does a Schmidt number of 1 indicate?

Short answer

In summary, the Schmidt number is a dimensionless number used in fluid dynamics to describe the ratio of momentum diffusivity (kinematic viscosity) to mass diffusivity. It acts as a representative of the rate at which a fluid diffuses momentum compared to mass. Its corresponding dimensionless number in heat transfer is the Prandtl number, which is related to thermal diffusivity. A Schmidt number of 1 indicates that momentum diffusion and mass diffusion are equal within the fluid.

Step-by-step solution

Definition of Schmidt number

The Schmidt number (Sc) is a dimensionless number used in fluid dynamics to describe the ratio of momentum diffusivity (kinematic viscosity) to mass diffusivity. It is defined as Sc = ν/D, where ν is the kinematic viscosity and D is the mass diffusivity.

Physical significance

The Schmidt number is used to compare the rate at which a substance is diffused through a fluid due to its concentration gradient (mass diffusion) and the rate at which momentum is transferred within the fluid (momentum diffusion). In other words, it represents how easily a fluid can transport momentum compared to the transport of mass.

Corresponding dimensionless number in heat transfer

In heat transfer, the corresponding dimensionless number is the Prandtl number (Pr), which is the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It is defined as Pr = ν/α, where α is the thermal diffusivity.

Schmidt number of 1

A Schmidt number of 1 implies that the rate of momentum diffusion and mass diffusion are equal within the fluid. In other words, the fluid diffuses momentum and mass at the same rate. This could be the case for certain gases like air, where both processes are relatively equal in magnitude.