Question

The local convection coefficient on a plate decreases as the thickness of the boundary layer grows along the plate. After transition from laminar to turbulent flow, the local convection coefficient becomes much larger, even though the boundary layer is much thicker. Explain why this is so.

Explain with a paragraph in a clear and straightforward manner, please.

Answer 1

There could be two reasons:

1. As the term boundary layer indicates, it is a region in the fluid where the fluid has a relatively lower velocity than the mainstream. The reason for this is mainly due to the viscosity introduced by the wall separating the two regions. As the fluid has a lower velocity than the mainstream, it will be able to transfer heat (the process can be either advection or convection) efficiently, leading to a smaller heat transfer coefficient.
2. Mathematically speaking, as the fluid near the boundary is slow, it will have a lower temperature than the fluid in the mainstream. Let us call the two temperatures as Tw and Tm. Here, Tw indicates the temperature of the fluid near the wall, and Tm indicates the temperature of the fluid in the mainstream. Even though the temperature of the fluid can be assumed to be constant, but as the width of the boundary layer increases, the ratio of change in temperature (Tm- Tw) to the change in thickness of the boundary layer decreases. Now we need to revoke Fourier's law of heat conduction. It states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and the area. Hence if the ratio mentioned above decreases, the heat transfer coefficient should also decrease.