Nusselt Number Agreements

Configuration

I consider three Prandtl numbers: \(Pr = 10^{-1}, 10^0, 10^1\). The other parameters are listed below.

Result

\(Nu\) calculated by four different formulae are considered:

  • reference: heat flux on the walls

  • red: energy injection

  • blue: kinetic energy dissipation

  • green: thermal energy dissipation

Their deviations from the reference value \(Nu_{wall}\) are plotted to highlight the difference. The reason why the lines are partly discontinuous is that the discrepancies are smaller than \(10^{-15}\).

2D, \(Pr = 10^{-1}\):

https://raw.githubusercontent.com/NaokiHori/SimpleNSSolver/artifacts/artifacts/nusselt-2d-1.e-1/nusselt.png

2D, \(Pr = 10^{ 0}\):

https://raw.githubusercontent.com/NaokiHori/SimpleNSSolver/artifacts/artifacts/nusselt-2d-1.e+0/nusselt.png

2D, \(Pr = 10^{ 1}\):

https://raw.githubusercontent.com/NaokiHori/SimpleNSSolver/artifacts/artifacts/nusselt-2d-1.e+1/nusselt.png

3D, \(Pr = 10^{-1}\):

https://raw.githubusercontent.com/NaokiHori/SimpleNSSolver/artifacts/artifacts/nusselt-3d-1.e-1/nusselt.png

3D, \(Pr = 10^{ 0}\):

https://raw.githubusercontent.com/NaokiHori/SimpleNSSolver/artifacts/artifacts/nusselt-3d-1.e+0/nusselt.png

3D, \(Pr = 10^{ 1}\):

https://raw.githubusercontent.com/NaokiHori/SimpleNSSolver/artifacts/artifacts/nusselt-3d-1.e+1/nusselt.png

The deviations should be small enough (around the rounding error).