Question

The hydrodynamic and thermal boundary layers will merge when

• A. Prandtl number is zero
• B. Schmidt number tends to infinity
• C. Nusselt number tends to infinity
• D. Prandtl number is one

Hint:

When \(Pr=1\), momentum diffusivity equals thermal diffusivity, so hydrodynamic and thermal boundary layers have similar thickness.

Answer 1

The Correct Option is D

The hydrodynamic boundary layer is related to momentum transfer. The thermal boundary layer is related to heat transfer. The relative thickness of these two boundary layers depends on Prandtl number. Prandtl number is: \[ Pr=\frac{\nu}{\alpha}. \] Here: \[ \nu=\text{momentum diffusivity} \] and: \[ \alpha=\text{thermal diffusivity}. \] If: \[ Pr=1, \] then momentum diffusivity and thermal diffusivity are equal. This means heat and momentum diffuse at the same rate. As a result, the hydrodynamic and thermal boundary layers have the same thickness and merge. Therefore, the boundary layers merge when: \[ Pr=1. \]