At what value of Prandtl number, the hydrodynamic and thermal boundary layers of a fluid flowing over a heated plate will be identical ?

ANS:A - 1

The hydrodynamic and thermal boundary layers of a fluid flowing over a heated plate will be identical when the Prandtl number (Pr) is equal to 1. Explanation:

1. Prandtl Number (Pr): Prandtl number is the dimensionless ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity in a fluid. It is defined as =momentum diffusivitythermal diffusivity=Pr=thermal diffusivitymomentum diffusivity​=αν​, where ν is the kinematic viscosity and α is the thermal diffusivity.
2. Hydrodynamic and Thermal Boundary Layers: When a fluid flows over a heated surface, it forms boundary layers near the surface due to viscosity effects. These boundary layers include a hydrodynamic boundary layer, where momentum dominates, and a thermal boundary layer, where heat transfer dominates.
3. Identical Boundary Layers: The hydrodynamic and thermal boundary layers will have identical thicknesses when the rates of momentum and thermal diffusions are equal. This occurs when the Prandtl number is equal to 1, indicating that the fluid's momentum diffusivity is equal to its thermal diffusivity.
4. Significance of Prandtl Number: For Pr < 1, momentum diffusivity is higher compared to thermal diffusivity, resulting in a thicker hydrodynamic boundary layer compared to the thermal boundary layer. For Pr > 1, thermal diffusivity is higher, leading to a thicker thermal boundary layer compared to the hydrodynamic boundary layer. When Pr = 1, the two diffusivities are equal, and thus, the boundary layers are identical in thickness.