Rayleigh number is the equivalent of [[Reynolds number]] for free convection. It can be used to tell if the flow is laminar or turbulent $Ra_L=\frac{g\beta (T_s-T_{\infty})L^3}{\alpha \nu}$ or $Ra_L=\frac{g\beta (T_s-T_{\infty})L^3}{\nu^2}Pr$ $g$ is gravitational constant 9.8 $m/s^2$ or 32.1741 $ft/s^2$ $\beta$ is volumetric thermal expansion coefficient (volume expansivity in [[REFPROP]]) i.e. fractional change in density to a change in temperature at constant pressure $\beta = -\frac{1}{\rho}\left(\frac{\partial \rho }{\partial T}\right)_p$ for ideal gas $\rho=p/RT$ and the above equation reduces to $\beta=\frac{1}{T}$ $\alpha$ is [[Thermal Diffusivity]] Rayleigh Number is [[Grashof number]] $\times$ [[Prandtl number]] ## 1 Transition to turbulent flow In free convection, the flow is considered to be turbulent if $Ra_L > 10^9$