For laminar free convection flow over a vertical flat plate, the Nusselt number (Nu) can be correlated with the Rayleigh number (Ra) as:
Nu = 0.68 + 0.5 Ra^(1/4) / [1 + (0.492 / Pr)^(9/16)]^(4/9)
where:
Pr = Prandtl number of the fluid
The Rayleigh number is given by:
Ra = gβΔT L^3 / να
where:
g = acceleration due to gravity
β = coefficient of thermal expansion of the fluid
ΔT = temperature difference between the plate and the surrounding fluid
L = characteristic length of the plate (in this case, its height)
ν = kinematic viscosity of the fluid
α = thermal diffusivity of the fluid
By using the above equations and the known values of the parameters for a specific problem, the Nusselt number can be calculated and used to determine the rate of heat transfer through the fluid.