Question

a heat transfer experiment consist of a stream of air blowing over a heated horizontal plate. what causes the formation of both velocity and thermal boundary layers? what causes a difference in thickness between them?

Answer 1

A thin layer of Air flowing over a plate will stick over it due to no-slip condition. This condition states that the velocity of the fluid at the solid surface equals the velocity of that surface. The result of this condition is that a velocity boundary layer is formed in which the relative velocity varies from zero at the wall to the value of the relative velocity(0.99%) at some distance from the wall.

Velocity Boundary layer thickness is denoted by ?. Velocity boundary layer thickness is taken as the point where the velocity is 99% of its free-flowing value.

Now talking about Temperature boundary layer: The thermal boundary layer, ?_t, is defined in a similar way to the velocity boundary layer, but with use of temperature instead of velocity.

At the plate surface, fluid layer sticks and hence at that point heat transfer takes place by conduction only, as we move up convection starts. As the plate is hotter than air flowing over it. And the immediate layer of air(no-slip condition) which is in contact with the plate will have almost same temperature as of plate. But as we move away from the surface the temperature decreases hence after a particular thickness the temperature will be same as freestream temperature. Thus the layer up to which temperature gradient exists significantly is called thermal boundary layer.

In a nutshell, it can be concluded that NO SLIP CONDITION IS BASICALLY RESPONSIBLE FOR BOUNDARY LAYER FORMATION(both).

Velocity and temperature boundary layer has the different thickness depending on heat transfer coefficient and dynamic viscosity. Basically, they are dependent on the balance of heat transfer (convection specifically) and inertial forces in the fluid.

Alternatively, it can be understood in the way that velocity boundary layer thickness is the height at which velocity becomes 0.99% of flow velocity. this factor is governed by shear stress which is influenced by viscosity. While on other hands thermal boundary layer is the height at which temperature difference becomes equal to 0.99% of the temperature difference between plate and free stream of air. This factor is governed by heat transfer coefficient(h). Hence two boundary layer thickness are different as they are governed by different properties of the fluid.

However, it must be noted that with a suitable choice of heat transfer coefficient and viscosity value both layer thickness can be made equal under special condition.