Answer:

The Prandtl number (Pr) is a dimensionless number that relates the momentum diffusivity (kinematic viscosity) to the thermal diffusivity. 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.

In the case of a fluid flowing over a flat plate with a Prandtl number greater than unity (Pr > 1), the thermal boundary layer for laminar forced convection is thinner than the hydrodynamic boundary layer. This can be explained based on the properties of the fluid and the respective boundary layers.

Hydrodynamic Boundary Layer:
The hydrodynamic boundary layer is the region near the surface of the flat plate where the velocity of the fluid increases from zero at the surface to its free-stream value. In this region, viscous forces dominate and the flow is described by the Navier-Stokes equations. The thickness of the hydrodynamic boundary layer, known as the boundary layer thickness (δ), increases with distance from the leading edge of the plate.

Thermal Boundary Layer:
The thermal boundary layer is the region near the surface of the flat plate where the temperature of the fluid increases from the surface temperature to the free-stream temperature. In this region, thermal diffusion dominates and the flow is described by the energy equation. The thickness of the thermal boundary layer, known as the thermal boundary layer thickness (δt), also increases with distance from the leading edge of the plate.

Explanation:
When the Prandtl number is greater than unity (Pr > 1), it means that the thermal diffusivity of the fluid is smaller compared to its kinematic viscosity. This implies that heat is conducted through the fluid more slowly compared to the momentum transfer. As a result, the thermal boundary layer develops more slowly compared to the hydrodynamic boundary layer.

Since the thermal boundary layer develops more slowly, it is thinner than the hydrodynamic boundary layer. This means that the temperature of the fluid reaches its free-stream value at a smaller distance from the leading edge of the plate compared to the velocity reaching its free-stream value. Hence, option 'A' is the correct answer.

It is important to note that this relationship holds true for laminar forced convection over a flat plate with a Prandtl number greater than unity. In the case of turbulent flow or other geometries, the relationship between the thickness of the hydrodynamic and thermal boundary layers may be different.