ANS:C - both (a) & (b)

The Nusselt number (Nu) is a dimensionless number used in fluid mechanics and heat transfer to quantify the convection heat transfer coefficient. It represents the ratio of convective heat transfer to conductive heat transfer across a fluid boundary layer. The Nusselt number (Nu) is a function of two dimensionless parameters:

1. Reynolds number (Re): The Reynolds number is a dimensionless quantity that characterizes the flow regime of the fluid. It is defined as the ratio of inertial forces to viscous forces within the fluid flow. Mathematically, Re is expressed as: Re=μρ⋅V⋅L​ Where:
   • ρ is the fluid density,
   • V is the flow velocity,
   • L is a characteristic length (such as the diameter of a pipe),
   • μ is the dynamic viscosity of the fluid.
   The Reynolds number determines whether the flow is laminar or turbulent, which significantly influences the convective heat transfer characteristics.
2. Prandtl number (Pr): The Prandtl number is another dimensionless parameter that characterizes the relative thickness of the momentum boundary layer to the thermal boundary layer. It is defined as the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. Mathematically, Pr is expressed as: Pr=kμ⋅cp​​ Where:
   • cp​ is the fluid's specific heat at constant pressure,
   • k is the fluid's thermal conductivity.
   The Prandtl number indicates how well a fluid conducts heat relative to how well it conducts momentum. Fluids with low Prandtl numbers (like liquid metals) transfer heat quickly compared to their momentum transfer, while fluids with high Prandtl numbers (like oils and gases) transfer heat more slowly compared to momentum transfer.

The Nusselt number (Nu) is therefore dependent on both the Reynolds number (Re) and the Prandtl number (Pr), making it a function of both these parameters. The exact relationship between Nu, Re, and Pr varies depending on the specific flow conditions and geometries involved in the heat transfer process.