Do you Know what is the of the Prandtl number value since you can say that thermal diffusive process is minor compared with viscous diffusive process, in a cylindrical tube.
Re: critical Prandtl
The Prandtl number is just nu/kappa, the ratio of the viscous coefficient and the thermal diffusivity one. So when it is much larger than one the viscosity affects the flow, while when it is much smaller the diffusion does. But the picture is not that simple since other numbers enter the picture. For example for a flow that is subject to gravity and temperature difference, convection might take place. When the rayleigh number (Ra) is higher than about 1,700 (or about 700 depending on the exact boundary conditions) the flow is unstable to convection. Now, whether the instability will lead to convective motion organized (circulation - involving only a few unstable modes) or will lead to turbulence depends on the Prandtl number (Pr). At small Pr (Pr much smaller than 1) the flow will be turbulent, while for large Pr number (much larger than 1), the flow will have an organized convective motion at Ra higher than 1,700 but it will be turbulent at Ra or the order of 10,000-100,000 (while for Pr small it is turbulent immediately for Ra of the order of 2,000, without passing through an organized convective motion - circulation). Patrick
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