Natural convection

Remarks

Example: still air around a hot vertical plate. The air near the plate is warmer and so lighter than the air far away, so it rises along the plate and carries heat away, with no outside forcing.

Non-example: the same plate in the air stream of a fan. The flow is imposed from outside, so this is forced convection. A fluid layer heated from above also shows no natural convection: the warm light fluid is already on top, the layering is stable, and heat moves by conduction only.

In models one often uses the Boussinesq approximation $\rho = \rho_0 \big(1 - \beta (T - T_0)\big)$ in the buoyancy term only, where $\beta$ is the thermal expansion coefficient. The strength of the buoyant flow is measured by the Grashof number $\mathrm{Gr} = g \beta \Delta T L^3 / \nu^2$ and the Rayleigh number $\mathrm{Ra} = \mathrm{Gr} \Pr$. Here $\Delta T$ is a temperature difference, $L$ a length and $\nu$ the kinematic viscosity.