When Prandtl number is increased for two cases tested over same Rayleigh number, the peak vertical-velocity decreases as Prandtl is increased. This is questionable to the fact that in general terms when Prandtl in increased the velocity boundary layer thickness increases due to increase in momentum diffusivity (\nu)
I'm actually uncertain about the fact that I should treat velocity Boundary layer thickness and peak velocity obtained as two different things.
Also, the current observation is done from the Numerically solved Rayleigh Benard Convection problem in OpenFOAM, with Pr and \nu (kinematic viscosity) as input parameters. For both cases (high and low Pr), \nu value is kept constant and indirectly the input is \kappa (thermal diffusivity) when Pr is changed. (can be a factor to get such behavior for velocity peaks)
The Prandtl number (Pr) is a dimensionless quantity that represents the ratio of viscous diffusion to thermal diffusion in a fluid. It plays a crucial role in natural convection, where heat transfer occurs due to buoyancy-driven flow.
Here are the descriptions of how Pr affects velocity:
Generally, as Pr increases, the fluid velocity in natural convection decreases. This can be explained through the following points:
Important Points:
- While higher Pr generally leads to decreased velocity, it also increases heat transfer rate due to the thinner conductive layer within the thermal boundary layer.
- In practical applications, optimizing Pr is crucial to balance competing demands for high heat transfer and low pumping power (fluid velocity).
To me your results make perfect sense. Firstly, the thickness of the velocity boundary layer is dictated by the thermal boundary layer (buoyancy depends on density differences caused by the varying temperature). Increasing Pr, e.g. by decreasing the thermal diffusivity will lead to a thinner thermal boundary layer, hence also a thinner velocity boundary layer. Given that the buoyancy forces are the same (temp.difference is constant), the thinner velocity boundary layer yields higher shear stresses and as a consequence a lower maximum velocity. Increasing Pr by increasing viscosity would also reduce the max fluid velocity simply because of the increased viscosity.
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