Question

Which one of the following options is correct?

In a convective heat transfer for laminar flow over a flat plate, Nusselt number is a function of Reynolds number and Prandtl number. Similarly, in a convective mass transfer for laminar flow over a flat plate, Sherwood number is a function of:

• A. Schmidt number and Reynolds number
• B. Weber number and Reynolds number
• C. Schmidt number and Weber number
• D. Weber number and Prandtl number

Hint:

Swap the Nusselt number for the Sherwood number and the Prandtl number for its mass transfer counterpart, the Schmidt number.

Answer 1

The Correct Option is A

Step 1: Recall the heat and mass transfer analogy.
For laminar flow over a flat plate, the heat transfer solution gives the Nusselt number as a function of the Reynolds number and the Prandtl number,
\[ Nu = f(Re, Pr) \]
Heat and mass transfer are governed by very similar boundary layer equations, since both are diffusion processes carried along by the same flowing fluid. Because of this, the mass transfer result can be written by simply swapping the matching mass transfer quantities into the heat transfer result.

Step 2: Match each number to its physical meaning.
The Reynolds number,
\[ Re = \frac{\rho V L}{\mu} \]
compares inertia forces to viscous forces and fixes the flow field and the boundary layer thickness. It stays exactly the same quantity whether the problem is about heat transfer or mass transfer, because it only describes the flow.
The Prandtl number,
\[ Pr = \frac{\nu}{\alpha} \]
compares momentum diffusivity to thermal diffusivity, and it is what makes the Nusselt number depend on how heat spreads relative to how momentum spreads.
The direct mass transfer counterpart of the Prandtl number is the Schmidt number,
\[ Sc = \frac{\nu}{D_{AB}} \]
which compares momentum diffusivity to mass diffusivity in exactly the same way that Pr compares momentum diffusivity to thermal diffusivity.

Step 3: Write the mass transfer analogue.
Replacing the Nusselt number with the Sherwood number and the Prandtl number with the Schmidt number gives
\[ Sh = f(Re, Sc) \]
So the Sherwood number is a function of the Reynolds number and the Schmidt number, which is option (A).

Step 4: Rule out the Weber number options.
The Weber number compares inertia forces to surface tension forces and matters only when a free surface, droplets or bubbles are involved, such as in atomization or two-phase flow. A simple laminar boundary layer flowing over a solid flat plate has no free surface or interface where surface tension plays a role, so the Weber number has no place in this correlation. This removes options (B), (C) and (D), since each one drags in the Weber number.

Step 5: Final Answer.
The Sherwood number for laminar flow over a flat plate depends on the Reynolds number and the Schmidt number.
\[ \boxed{\text{Schmidt number and Reynolds number}} \]