ANS:C - Rayleigh

The parameter used in place of the Grashof number in free convection heat transfer is the Rayleigh number. The Rayleigh number (Ra) is a dimensionless number that represents the ratio of buoyancy to viscosity forces within a fluid undergoing free convection. It is defined as the product of the Grashof number (Gr) and the Prandtl number (Pr). Mathematically, the Rayleigh number is expressed as: Ra=Gr×Pr where:

• Grashof number (Gr) is the ratio of buoyancy to viscous forces and is defined as the product of the length scale cubed, gravitational acceleration, temperature difference, and kinematic viscosity.
• Prandtl number (Pr) is the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity in a fluid.

The Rayleigh number is particularly useful in determining the onset of fluid motion due to thermal buoyancy forces in free convection flows. It helps characterize the flow regime and predict the transition from laminar to turbulent flow. Therefore, the correct answer is: Rayleigh