ANS:C - that across the entire pipe

he Nusselt number is not defined as the ratio of the temperature gradient at the wall to that across the entire pipe. Let me clarify the concept: The Nusselt number (Nu) characterizes the convective heat transfer behavior in a fluid flow. It is defined as the ratio of the convective heat transfer coefficient (ℎh) times a characteristic length (L) to the thermal conductivity (k) of the fluid. Mathematically, it is expressed as: Nu=kh⋅L​ Here's what each term represents:

• ℎh: Convective heat transfer coefficient, which represents the ability of the fluid to transfer heat through convection.
• L: Characteristic length, which depends on the geometry of the flow. For example, in flow through a pipe, it could be the hydraulic diameter or the length of the pipe.
• k: Thermal conductivity of the fluid.

The Nusselt number is dimensionless and is used to characterize different flow regimes and heat transfer behaviors. It varies with flow conditions, geometry, fluid properties, and other factors. The Nusselt number is not directly related to the temperature gradient across the entire pipe. Instead, it represents the ratio of convective heat transfer to conductive heat transfer within the fluid boundary layer near the surface. Therefore, it characterizes the local heat transfer behavior at the surface, rather than the temperature gradient across the entire pipe. If you have any further questions or if there's anything else I can assist you with, please feel free to ask!