Thermal boundary layer and hydrodynamic boundary layer

The thermal boundary layer and hydrodynamic boundary layer are two important concepts in fluid mechanics.

The thermal boundary layer refers to the region near a solid surface where the temperature changes occur due to the flow of a fluid over the surface. It is characterized by a temperature gradient, with the temperature at the surface being different from the temperature of the fluid far away from the surface.

The hydrodynamic boundary layer, on the other hand, refers to the region near a solid surface where the velocity of a fluid changes due to the flow over the surface. It is characterized by a velocity gradient, with the velocity at the surface being different from the velocity of the fluid far away from the surface.

Ratio of thickness

The ratio of the thickness of the thermal boundary layer (Δt) to the thickness of the hydrodynamic boundary layer (Δh) is given by (Prandtl number)n, where n is a constant.

The Prandtl number (Pr) is a dimensionless number that represents the ratio of momentum diffusivity to thermal diffusivity in a fluid. It is defined as the ratio of the kinematic viscosity (v) to the thermal diffusivity (α):

Pr = v/α

Explanation of the answer

The ratio of the thickness of the thermal boundary layer to the thickness of the hydrodynamic boundary layer is given by (Prandtl number)n.

Since the Prandtl number is defined as the ratio of the kinematic viscosity to the thermal diffusivity, it represents the relative importance of momentum diffusion to thermal diffusion in a fluid.

When the Prandtl number is less than 1, it means that the thermal diffusivity is greater than the kinematic viscosity, indicating that thermal diffusion is more important than momentum diffusion. In this case, the thermal boundary layer is thicker compared to the hydrodynamic boundary layer.

Conversely, when the Prandtl number is greater than 1, it means that the kinematic viscosity is greater than the thermal diffusivity, indicating that momentum diffusion is more important than thermal diffusion. In this case, the hydrodynamic boundary layer is thicker compared to the thermal boundary layer.

Therefore, the ratio of the thickness of the thermal boundary layer to the thickness of the hydrodynamic boundary layer is equal to (Prandtl number)n, where n is a constant. Since the Prandtl number is less than 1 for most fluids, the correct answer is option A, 1/3.