Natural Convection

Lecture 31, March 22, 2004 Natural Convection Contd. What is it that resists this buoyancy force? Viscous forces The resulting flow will be governed by a balance of viscous and buoyant forces in constrast to a balance of inertial and viscous forces in the case of forced convection (which was governed by the Reynolds number). We need a new dimensionless parameter to describe free convection flows. Introduce the Grashof number

We can expect, in general then that free convection flows may be governed by Re, Pr as before, as well as this new parameter, Gr

In practice though, any significant Re will dominate over the natural convection and therefore, the

problem will be described by the Grashof number and the Prandtl number, the product of which is given another name,

This parameter characterizes both the ratio of buoyancy forces to viscous forces, and the relative scale of the thermal and viscous boundary layers. We can expect then that correlations for free convection will be functions of Ra.

The Raleigh number characterizes the flow regime in free convection exactly as did the Reynolds number in forced convection.

A note on convection correlations in general. Often (way too often) people express experimental results in terms of non-dimensional parameters and calculate the exponents such as ‘n’ above. They then use these ‘n’ values to declare for example that the flow is laminar or turbulent, or some other physical interpretation. This is very often wrong! The heat transfer process depends strongly on the nature of

the flow, and the physics is almost completely removed once we get to a correlation.