Question

Will a thermal boundary layer develop in flow over a surface even if both the fluid and the surface are at the same temperature?

Short answer

Answer: No, it is highly unlikely that a thermal boundary layer will develop when both the fluid and the surface are at the same temperature, as there is no temperature difference necessary for heat transfer to take place and lead to changes in fluid properties that would result in the formation of a thermal boundary layer.

Step-by-step solution

Understand the Thermal Boundary Layer Concept

A thermal boundary layer is a thin layer of fluid adjacent to a solid surface, where significant temperature variations occur due to the fluid motion and the heat transfer between the fluid and the surface. It plays a crucial role in determining the heat transfer rate between the fluid and the surface.

Identify the Key Factors for Thermal Boundary Layer Development

The development of a thermal boundary layer mainly depends on the temperature difference between the fluid and the surface. When there is a temperature difference, heat transfer takes place from the hotter object to the colder one. This phenomenon, in turn, causes changes in fluid properties like viscosity and density, leading to the development of a thermal boundary layer.

Analyzing the Given Conditions

In this exercise, it is given that both the fluid and the surface are at the same temperature. Since there is no temperature difference between them, the heat transfer between the fluid and the surface should be minimal. As the temperature difference is the driving factor for thermal boundary layer formation, it is less likely that a thermal boundary layer will develop in this case.

Conclusion

Under the given conditions where both the fluid and the surface are at the same temperature, it is highly unlikely that a thermal boundary layer will develop. The primary reason for this is the absence of a temperature difference which is necessary for heat transfer to take place, leading to changes in fluid properties and the formation of a thermal boundary layer.