What causes an increase in boundary layer thickness in fluid flow?

[engnr_arsalan]

hi all,i have recently started studying a subject heat transfer,in which i learned that there are two types boundary layers.one is velocity boundary and other is temperature boundary layer..now my question is that..boundary layer thickness increases in flow direction,what is the physical phenomenon behind that..both in velocity and temperature boundary layer?
thanks in advance

 

[Chestermiller]

The easiest way to explain this is to consider the case of thermal boundary layer development for the idealized case of a flat velocity profile. Before doing that, however, let's first consider the case of an infinitely long solid cylinder that is initially at a temperature T₀, and suppose that, at time zero, the temperature at the surface is suddenly raised to T₁ and held there for all time. How will the temperature within the cylinder vary with time. Well, the temperature within the cylinder will not rise uniformly. The outside will begin heating up first and, as heat gets conducted toward the center of the cylinder, the temperature further in will begin to rise. Initially, all the temperature variation will be confined to a thin (thermal boundary layer) region near the outer radius, where the temperature will change rapidly from T₁ at the surface to essentially T₀ only a short distance below the surface. As time progresses, and heat gets conducted further inward, the thickness of this thermal boundary layer will increase with time, eventually penetrating all the way to the center of the cylinder.

Now consider the case where the cylinder is moving axially with velocity v. Its temperature is T₀ at x < 0, and its surface temperature is held at T₀ at x < 0. However, at all locations x >0, the surface temperature of the cylinder is set at T₁. As the cylinder progresses in the x direction, a thermal boundary layer begins developing near its surface in which the temperature varies rapidly from T₁ at the surface to T₀ a short distance below the surface. As the distance downstream increases, and heat gets conducted further inward, the thickness of this thermal boundary layer will increase with distance, eventually penetrating all the way to the center of the cylinder.

Do you recognize the similarity between the two situations I described. Suppose that, rather than watching the cylinder go by at velocity v, you travel downstream along with the cylinder at velocity v. From your perspective, the cylinder is stationary, and is experiencing unsteady state heat conduction starting at t = x/v = 0. To you it looks like the heat is penetrating into the cylinder as a function of time, and you see the same temperature profiles and boundary layer thicknesses developing as in the first case where the cylinder is not moving.

 

[engnr_arsalan]

sir,it would be more understanding if u give an example of flow over a plate..i understand that thermal and velocity boundary layer will grow thicker as "x" is increased..which is the distance that would be travel by fluid.kindly try to explain it from following diagram..what is actualy happening there..at molecular level..

 

[Chestermiller]

sir,it would be more understanding if u give an example of flow over a plate..i understand that thermal and velocity boundary layer will grow thicker as "x" is increased..which is the distance that would be travel by fluid.kindly try to explain it from following diagram..what is actualy happening there..at molecular level..

To understand it at the molecular level, you have to understand how viscosity works at the molecular level. See Transport Phenomena by Bird, Stewart, and Lightfoot.

 

[boneh3ad]

The boundary layer gets thicker due to the diffusive properties of a fluid flow. As you get farther downstream, both the momentum (velocity) and the energy (temperature) have more of a chance to diffuse throughout the boundary layer. For momentum, the low momentum fluid near the wall will be continually mixed with the higher momentum fluid higher in the boundary layer, and as you get toward the boundary layer edge, the retarded flow in the boundary layer will slowly mix with the edge flow, effectively slowing down the flow at the edge a bit and increasing the boundary layer thickness.

For the thermal boundary layer, it is the same process, only with heat conduction instead of momentum diffusion.

Once the boundary layer becomes turbulent, these processes are greatly sped up and the boundary layer gets even thicker.