Explain with the help of a diagram the concept of hydrodynamic and thermal boundary layer for a laminar flow over a thin flat plate. Also define

Question

critical Reynolds number and the physical significance of Prandtl number?

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Hydrodynamic and Thermal Boundary Layer:

When a fluid flows over a solid surface, it experiences friction due to the viscosity of the fluid. This causes the fluid molecules to stick to the surface, creating a thin layer of fluid called the boundary layer. The thickness of the boundary layer increases with the distance from the surface.

There are two types of boundary layers - hydrodynamic and thermal. The hydrodynamic boundary layer is formed due to the friction between the fluid and the surface, while the thermal boundary layer is formed due to the temperature difference between the fluid and the surface.

When the flow is laminar, the boundary layer is thin and the flow is smooth. In the case of a flat plate, the hydrodynamic boundary layer starts from the leading edge and grows in thickness towards the trailing edge.

The thermal boundary layer also starts from the leading edge and grows in thickness towards the trailing edge. However, its thickness is dependent on the temperature difference between the fluid and the surface.

Critical Reynolds Number:

The Reynolds number is a dimensionless number used to predict the type of fluid flow (laminar or turbulent) over a surface. The critical Reynolds number is the value of Reynolds number at which the flow transitions from laminar to turbulent. For a flat plate, the critical Reynolds number is approximately 5 x 10^5.

Physical Significance of Prandtl Number:

The Prandtl number is a dimensionless number used to predict the relative importance of momentum diffusivity to thermal diffusivity in a fluid. A high Prandtl number indicates that momentum diffuses slower than heat, while a low Prandtl number indicates that momentum diffuses faster than heat.

In fluid dynamics, the Prandtl number plays an important role in the prediction of heat transfer, particularly in cases involving laminar flow. A high Prandtl number means thermal energy is being transported more quickly than kinetic energy, while a low Prandtl number means the opposite.