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

Pr = ν/α

where ν is the kinematic viscosity and α is the thermal diffusivity.

The Prandtl number provides information about the relative thicknesses of the hydrodynamic boundary layer and the thermal boundary layer in a flowing fluid. The boundary layer is a thin layer of fluid that forms near a solid surface due to the viscous effects of the fluid. It plays a crucial role in determining the heat and mass transfer characteristics of the fluid.

Based on the given options, we are asked to determine the relationship between the Prandtl number and the thickness of the hydrodynamic boundary layer (δ_h) and the thermal boundary layer (δ_t).

Let's analyze each option:

a) Greater than thermal boundary layer thickness:
If the Prandtl number is greater than unity (Pr > 1), it indicates that the kinematic viscosity is larger compared to the thermal diffusivity. This implies that the momentum diffusivity is dominant over the thermal diffusivity.

In such cases, the hydrodynamic boundary layer thickness (δ_h) will be greater than the thermal boundary layer thickness (δ_t). This is because the fluid has a higher resistance to momentum transfer (due to higher viscosity) compared to heat transfer (due to lower thermal diffusivity). As a result, the fluid forms a thicker boundary layer in the momentum direction compared to the thermal direction.

Therefore, option 'a' is the correct answer.

b) Equal to thermal boundary layer thickness:
If the Prandtl number is equal to unity (Pr = 1), it means that the kinematic viscosity is equal to the thermal diffusivity. In this case, the fluid has similar resistance to momentum and heat transfer.

c) Greater than hydrodynamic boundary layer thickness:
This option is incorrect because if the Prandtl number is greater than unity, it implies that the fluid has a higher resistance to momentum transfer, resulting in a thicker hydrodynamic boundary layer.

d) Independent of thermal boundary layer thickness:
This option is also incorrect because the Prandtl number is directly related to the thermal diffusivity, and therefore, it provides information about the thickness of the thermal boundary layer.

In conclusion, when the Prandtl number of a flowing fluid is greater than unity (Pr > 1), the hydrodynamic boundary layer thickness is greater than the thermal boundary layer thickness.