from the Reynolds number alone one could think that the flow is laminar.
This is, however, misleading whenever buoyancy (natural convection) is involved in addition to the forced convection. Thus, a mixed convection prevails.
The ratio between natural and forced convection is often correlated to the so-called Richardson numer Ri=Gr/Re^2. For very small numbers of Ri
I found Bastian Schmandt's very interesting, but how to find experimental data.
I have been working over 30 years with Ljungström Air Preheaters and experimental data were made with a heat transfer test rig. We usually always got a break point in the Colburn factor at approx 2000. Reynolds number was based on the hydraulic diameter for all types of elements.
Below Re=2000 the flow was laminar and over Re = 2000 the flow was turbulent.
The Ra number indicates transition to turbulence for an object in free space. In a confined space as a chimney the Reynolds number based on the flow velocity, the pipe diameter and the fluid viscosity is the relevant parameter. However the geometry is quite important. One can distinguish fully developed flows from flows at local discontinuities. In a fully developed flow for smooth walls turbulence will not be maintained for Re