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

This question is really testing the heat and mass transfer analogy for flow over a flat plate. Instead of deriving anything from scratch, it helps to line up the two problems side by side and match each quantity to its partner.

1. Heat transfer side (given): For laminar boundary layer flow over a flat plate, the classic result (from the Blasius solution) is $Nu = 0.332\,Re^{0.5}Pr^{1/3}$, so $Nu = f(Re, Pr)$. Here $Re$ describes the flow itself and $Pr = \nu/\alpha$ compares how fast momentum spreads to how fast heat spreads.
2. Mass transfer side (to find): Mass transfer in a laminar boundary layer follows the same type of equation as heat transfer, only the diffusing quantity is a chemical species instead of heat. The matching result is $Sh = 0.332\,Re^{0.5}Sc^{1/3}$, so $Sh = f(Re, Sc)$, where $Sc = \nu/D_{AB}$ compares momentum spreading to species spreading, playing exactly the role $Pr$ played for heat.
3. Weber number: $We$ compares inertia to surface tension and only becomes relevant when there is a free surface, a droplet, or a bubble in the flow. A flat plate with a boundary layer growing over it has no such interface, so $We$ does not belong in this correlation at all.

Since the Reynolds number carries over unchanged (it only describes the flow field) and the Schmidt number is the direct mass transfer twin of the Prandtl number, the Sherwood number must be a function of the Schmidt number and the Reynolds number.

Let's summarize:

• $Re$ stays the same in both the heat and mass transfer versions because it only fixes the flow.
• $Pr \to Sc$ is the swap that turns the heat transfer correlation into the mass transfer correlation; $We$ never enters a plain boundary layer problem with no interface.

So the correct pairing is Schmidt number and Reynolds number.

\[ \boxed{Sh = f(Re, Sc)} \]