ANS:D - viscous sub-layer

At Prandtl number (Pr) greater than 1, conduction in an ordinary fluid flowing through a heated pipe is mainly limited to the viscous sub-layer. Here's why:

1. Prandtl Number (Pr): Prandtl number is a dimensionless number that relates the momentum diffusivity to the thermal diffusivity in a fluid. It's defined as the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. Mathematically, it's expressed as Pr = μCp/κ, where μ is the dynamic viscosity, Cp is the specific heat at constant pressure, and κ is the thermal conductivity.
2. Prandtl Number Effects: A Prandtl number greater than 1 indicates that the fluid has a higher momentum diffusivity compared to its thermal diffusivity. In such fluids, thermal diffusion occurs more slowly than momentum diffusion.
3. Viscous Sub-layer: In fluid dynamics, the viscous sub-layer refers to the thin layer of fluid adjacent to the solid boundary where viscous effects dominate. In this layer, the flow velocity gradients are significant, and molecular diffusion (conduction) plays a crucial role in heat transfer.

When the Prandtl number is greater than 1, thermal diffusivity is relatively low compared to momentum diffusivity. Consequently, thermal conduction (diffusion) is more pronounced in the viscous sub-layer, where molecular transport dominates. In contrast, in the turbulent core, where convective transport dominates, the influence of conduction is typically minimal compared to advection. Therefore, at Prandtl numbers greater than 1, conduction in an ordinary fluid flowing through a heated pipe is mainly limited to the viscous sub-layer.