ANS:D - Grashoff number

The Grashof number (Gr) is a dimensionless number used in fluid dynamics and heat transfer to characterize the relative importance of buoyancy forces to viscous forces in a fluid flow. The formula for Grashof number is: 2Gr=ν2g⋅L3⋅β⋅ΔT​ Where:

• g is the acceleration due to gravity.
• L is a characteristic length (such as the height of a vertical plate).
• β is the coefficient of thermal expansion.
• ΔT is the temperature difference between the surface and the fluid.
• ν is the kinematic viscosity of the fluid.

The Grashof number is commonly used in natural convection problems, particularly for fluids near solid surfaces where buoyancy forces dominate. It helps determine the type of fluid flow that will occur, whether it's laminar or turbulent, as well as the magnitude of the convective heat transfer. For example, in a vertical plate heated from below, the Grashof number indicates whether the heat transfer will be dominated by buoyancy-induced natural convection (high Grashof number) or by conduction (low Grashof number). In summary, the Grashof number quantifies the ratio of buoyancy forces to viscous forces in a fluid flow, providing valuable information about the heat transfer characteristics of the system.