Nusselt number in case of free convection is the function of Grashoff number and Prandtl number. Let us understand why.

Free Convection:
When heat transfer takes place due to buoyancy forces, it is referred to as free convection. In free convection, the fluid moves due to the density differences caused by temperature differences.

Nusselt Number:
Nusselt number is a dimensionless number that represents the ratio of convective to conductive heat transfer across a boundary. It is defined as:

Nu = hL/k

Where h is the convective heat transfer coefficient, L is the characteristic length, and k is the thermal conductivity of the fluid.

Grashoff Number:
Grashoff number is a dimensionless number that represents the ratio of buoyancy to viscous forces in a fluid. It is defined as:

Gr = gβΔTL^3/ν^2

Where g is the acceleration due to gravity, β is the coefficient of thermal expansion, ΔT is the temperature difference, L is the characteristic length, and ν is the kinematic viscosity.

Prandtl Number:
Prandtl number is a dimensionless number that represents the ratio of momentum diffusivity to thermal diffusivity in a fluid. It is defined as:

Pr = ν/α

Where ν is the kinematic viscosity and α is the thermal diffusivity.

Relationship between Nusselt Number, Grashoff Number, and Prandtl Number:
The Nusselt number in case of free convection is dependent on the Grashoff number and Prandtl number. The relationship between these numbers is given by the following equation:

Nu = C(GrPr)^n

Where C and n are constants that depend on the geometry of the system. The above equation shows that the Nusselt number is directly proportional to the Grashoff number and Prandtl number raised to the power of n. Thus, the Nusselt number in case of free convection is the function of Grashoff number and Prandtl number.