Natural Convection in a Square Cavity

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Model Data

Type: multiphysics heat transfer fluid dynamics

Physics Modes: heat transfer navier stokes equations

Keywords: natural convection validation

This multiphysics model illustrates natural convection effects in a unit square domain using the Boussinesq approximation. The model involves a Navier-Stokes equations physics mode, representing the fluid flow with solid wall or no-slip boundary conditions everywhere. In addition a heat transfer physics mode is added to model the temperature field . The top and bottom boundaries are perfectly insulated while the left boundary is prescribed a unit temperature and the right zero.

The physics modes are two way coupled through the vertical source term in the Navier-Stokes equations, Pr·Ra·T, and the velocities transporting the temperature coming directly from the fluid flow. First, the Prandtl and Rayleigh numbers are set to Pr = 0.71 and Ra = 103, respectively, after which the Ra number will be increased to 104. The references contain benchmark reference and comparison results for a number of quantities such as maximum velocities and the Nusselt number [1,2].

This model is available as an automated tutorial by selecting Model Examples and Tutorials… > Multiphysics > Natural Convection in a Square Cavity from the File menu. Or alternatively, follow the linked step-by-step instructions.


FEATool Multiphysics Tutorial - Natural Convection in a Square Cavity


References

[1] D. de Vahl Davis, Natural Convection of Air in a Square Cavity - A Benchmark Solution, Int. J. Numer. Meth. Fluids, vol. 3, pp. 249-264, 1983.

[2] D. de Vahl Davis and I. P. Jones, Natural Convection of Air in a Square Cavity - A Comparison Exercise, Int. J. Numer. Meth. Fluids, vol. 3, pp. 227-248, 1983.