# Natural Convection in a Square Cavity

## 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 = 10 ^{3}*, respectively, after which the

*Ra*number will be increased to

*10*. The references contain benchmark reference and comparison results for a number of quantities such as maximum velocities and the Nusselt number [1,2].

^{4}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.

## 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.