Forced Convection Free Convection

External Flow

Internal Flow

We focus on free convection problems in which the density gradient is due to a temperature gradient and the body force is gravitational. However, the presence of a fluid density gradient in a gravitational field does not ensure the existence of free convection currents.

Buoyancy is due to the combined presence of a fluid density gradient and a body force that is proportional to density.

A plate at uniform temperature Twall immersed in a stagnant fluid at Tfluid.

Tfluid > Twall

Two assumptions are kept for the following analysis:

1) The boundary layer is thin enough to accommodate the simplifications made in forced convection.

2) The Prandtl number is approximately 1.

Recall that the Reynolds number provides a measure of the ratio of the inertial to viscous forces acting on a fluid element. In contrast, the Grashof number is a measure of the ratio of the buoyancy forces to the viscous forces acting on the fluid.

In this correlation, the thermal properties should all be evaluated at the film temperature, Tf = (Tfluid + Twall)/2, except for �, which is to be evaluated at Tfluid if the fluid is a gas.

SPHERE

Uniform heat flux

Combined Forced and Free convection

Combined Forced and Free convection