ANS:A - gD³.β.Δtρ²/μ²

The Grashof number (𝐺𝑟Gr) is a dimensionless number used in fluid mechanics and heat transfer to determine the significance of natural convection compared to forced convection. It is defined as the ratio of buoyancy forces to viscous forces in a fluid flow. The correct expression for the Grashof number is: 𝐺𝑟=𝑔⋅𝐷3⋅𝛽⋅Δ𝑇⋅𝜌2𝜇2Gr=μ2g⋅D3⋅β⋅ΔT⋅ρ2​ Where:

• 𝑔g is the acceleration due to gravity,
• 𝐷D is a characteristic length scale,
• 𝛽β is the coefficient of thermal expansion,
• Δ𝑇ΔT is the temperature difference,
• 𝜌ρ is the fluid density, and
• 𝜇μ is the dynamic viscosity of the fluid.