Q1: The characteristic dimensionless groups for heat transfer to a fluid flowing through a pipe in laminar flow are

ANS:D - Nu, Gz

The combination of Nusselt number (Nu) and Grashof number (Gr), often denoted as Nu·Gr, represents a dimensionless group that characterizes natural convection heat transfer. Here's an explanation of Nu·Gr:

1. Nusselt Number (Nu):
   • The Nusselt number (Nu) represents the ratio of convective heat transfer to conductive heat transfer across a fluid boundary layer.
   • It is defined as the ratio of convective heat transfer coefficient to conductive heat transfer coefficient.
   • In natural convection, Nu characterizes the enhancement of heat transfer due to fluid motion induced by density variations (buoyancy forces).
2. Grashof Number (Gr):
   • The Grashof number (Gr) represents the ratio of buoyancy forces to viscous forces in a fluid flow.
   • It quantifies the relative importance of buoyancy-driven natural convection to viscous effects.
   • Gr is defined as the product of the density difference, gravitational acceleration, characteristic length scale, and squared velocity scale, divided by the kinematic viscosity.
3. Nu·Gr:
   • Nu·Gr represents the combined effect of Nusselt number and Grashof number in natural convection heat transfer.
   • It characterizes the heat transfer enhancement due to buoyancy-driven flow phenomena compared to conductive heat transfer.
   • The product Nu·Gr indicates how the convective heat transfer coefficient varies with changes in buoyancy forces, which in turn depend on the temperature difference, fluid properties, and geometry of the system.
   • A high value of Nu·Gr indicates strong convective heat transfer due to significant buoyancy-driven flow, while a low value indicates weaker natural convection effects.

In summary, Nu·Gr is a dimensionless group that captures the combined influence of convective heat transfer (Nu) and buoyancy-driven flow (Gr) in natural convection processes. It provides insights into the heat transfer characteristics and flow behavior in systems where natural convection plays a significant role, such as in heated fluids or around heated surfaces.