ANS:A - less

When water flows over a flat plate heated along its entire length, the thermal boundary layer thickness compared to the hydrodynamic boundary layer thickness is typically less. To understand why this is the case, let's delve into the concept of boundary layers and the Prandtl number.

1. Boundary Layers: When a fluid flows over a solid surface, the fluid velocity near the surface is zero due to the no-slip condition. As the fluid moves away from the surface, its velocity gradually increases until it reaches the free stream velocity. The region where the velocity increases from zero to the free stream velocity is known as the boundary layer.
2. Thermal Boundary Layer vs. Hydrodynamic Boundary Layer: Similarly, in addition to the velocity boundary layer, there exists a thermal boundary layer where the temperature of the fluid near the solid surface differs from the bulk temperature. This thermal boundary layer thickness is influenced by the rate of heat transfer from the surface to the fluid.
3. Prandtl Number (Pr): The Prandtl number is a dimensionless parameter that describes the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity in a fluid. It is given by the ratio of the kinematic viscosity to the thermal diffusivity: Pr=Thermal Diffusivity /Kinematic Viscosity​ A low Prandtl number indicates that thermal diffusion occurs more rapidly compared to momentum diffusion. Water typically has a relatively low Prandtl number, around 6, which means that its thermal diffusivity is much higher compared to its kinematic viscosity.
4. Effect on Boundary Layer Thickness: In fluids with a low Prandtl number like water, thermal energy dissipates quickly away from the surface due to the high thermal diffusivity. This rapid dissipation results in a thinner thermal boundary layer compared to the hydrodynamic boundary layer. As a result, the thermal boundary layer thickness is typically less than the hydrodynamic boundary layer thickness.

In summary, the thermal boundary layer thickness is less compared to the hydrodynamic boundary layer thickness in scenarios involving fluids with low Prandtl numbers like water flowing over heated surfaces. This is because thermal energy dissipates rapidly in such fluids, leading to a thinner thermal boundary layer.