Combined forced and natural convection

Combined forced convection and natural convection, or mixed convection, occurs when natural convection and forced convection mechanisms act together to transfer heat. This is also defined as situations where both pressure forces and buoyant forces interact.^[1] How much each form of convection contributes to the heat transfer is largely determined by the flow, temperature, geometry, and orientation. The nature of the fluid is also influential, since the Grashof constant increases in a fluid as temperature increases, but is maximized at some point for a gas.^[2]

Cases

Because of the wide range of variables, hundreds of papers have been published for experiments involving various types of fluids and geometries. This variety makes a comprehensive correlation difficult to obtain, and when it is, it is usually for very limited cases.^[2] Combined forced and natural convection, however, can be generally described in one of three ways.

First case

The first case is when natural convection aids forced convection. This is seen when the buoyant motion is in the same direction as the forced motion, thus enhancing the heat transfer.^[3] An example of this would be a fan blowing upward on a hot plate. Since heat naturally rises, the air being forced upward over the plate adds to the heat transfer.

Second case

The second case is when natural convection acts in the opposite way of the forced convection. Consider a fan forcing air upward over a cold plate.^[3] In this case, the buoyancy force of the cold air naturally causes it to fall, but the air being forced upward opposes this natural motion, keeping the cool air hovering around the cold plate. This, in turn, diminishes the amount of heat transfer.

Third case

The third case is referred to as transverse flow. This occurs when the buoyant motion acts perpendicular to the forced motion. This enhances fluid mixing, and enhances the heat transfer.^[3] An example of this is air flowing horizontally over a hot or cold pipe. This can encourage phase changes, which often creates a very high heat transfer coefficient. For example, steam leaving a boiler can pass through a pipe that has a fan blowing over it, cooling the steam back to a saturated liquidthat all

Calculation of total heat transfer

While it may seem like it is possible to simply add or subtract the heat transfer values to or from each other, this will yield inaccurate results. In order to determine the total heat transfer, experimental data has suggested that Nu_combined=(Nu_forcedⁿ ± Nu_naturalⁿ)^(1/n) where the plus sign is for cases where heat transfer is assisted (i.e. case one and three) and the minus sign is for when it is hindered (i.e. case two). The value of n ranges between 3 and 4 as the geometry aligns from vertically to horizontally respectively.

Applications

Combined forced and natural convection is often seen in very-high-power-output devices where the forced convection is not enough to dissipate all of the heat necessary. At this point, combining natural convection with forced convection will often deliver the desired results. Examples of these processes are nuclear reactor technology and some aspects of electronic cooling.^[2]

References