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5.2.2 Natural Convection and Buoyancy-Driven Flows Theory

When heat is added to a fluid and the fluid density varies with temperature, a flow can be induced due to the force of gravity acting on the density variations. Such buoyancy-driven flows are termed natural-convection (or mixed-convection ) flows and can be modeled by ANSYS FLUENT.

The importance of buoyancy forces in a mixed convection flow can be measured by the ratio of the Grashof and Reynolds numbers :

 \frac{{\rm Gr}}{{\rm Re}^2} = \frac{g \beta \Delta T L}{v^2} (5.2-13)

When this number approaches or exceeds unity, you should expect strong buoyancy contributions to the flow. Conversely, if it is very small, buoyancy forces may be ignored in your simulation. In pure natural convection, the strength of the buoyancy-induced flow is measured by the Rayleigh number :

 {\rm Ra} = \frac{g \beta \Delta T L^3 \rho}{\mu \alpha} (5.2-14)

where $\beta$ is the thermal expansion coefficient:

 \beta = -\frac{1}{\rho} \left(\frac{\partial \rho}{\partial T}\right)_p (5.2-15)

and $\alpha$ is the thermal diffusivity:

 \alpha = \frac{k}{\rho c_p} (5.2-16)

Rayleigh numbers less than 10 $^8$ indicate a buoyancy-induced laminar flow, with transition to turbulence occurring over the range of 10 $^8$  $<$ Ra  $<$ 10 $^{10}$.

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