Consider laminar flow of air across a hot circular cylinder. At what point on the cylinder will the heat transfer be highest? What would your answer be if the flow were turbulent?

Laminar flow refers to the smooth and orderly movement of a fluid, where its layers slide over one another without much mixing. On the other hand, turbulent flow is characterized by chaotic and irregular fluid motion, leading to a higher degree of mixing. In general, heat transfer is affected by the flow regime, with turbulent flow typically leading to higher heat transfer rates compared to laminar flow.

The heat transfer between the hot surface of the cylinder and the airflow depends on the temperature difference between the surface and the fluid, the surface area of the object, the flow regime, and the thermal properties of the fluid. Highest heat transfer occurs at points where the temperature difference is the greatest, and the flow regime promotes heat exchange. For a hot circular cylinder, the temperature difference between the fluid and the surface is greatest at the stagnation point where the air temperature is the lowest.

In the case of laminar flow, the fluid layers slide over each other without significant mixing. The highest heat transfer occurs at the stagnation point on the cylinder, where the flow initially meets the cylinder and begins to move around its surface. This results in a larger temperature difference at this point, promoting heat transfer. So, the highest heat transfer will occur at the stagnation point for laminar flow.

When the flow becomes turbulent, there is increased mixing of fluid layers resulting in higher heat transfer rates overall. However, the highest heat transfer will still occur at the stagnation point on the cylinder due to the greater temperature difference and the effect of turbulence increasing heat transfer. Therefore, even with a turbulent flow, the highest heat transfer point remains at the stagnation point. In conclusion, the highest heat transfer in both laminar and turbulent flow occurs at the stagnation point on the hot circular cylinder, where the airflow first comes into contact with the cylinder surface. The temperature difference between the cylinder surface and the airflow is greatest at this point, promoting heat transfer.