Convection

Convection occurs in a moving fluid, generally from the fluid to a solid surface or vice versa. Although heat transfer between single particles is by con­duction, it is the energy transfer with the matter that governs the heat transfer. The basic laws of heat and mass transfer have to be considered in order to de­scribe convection mathematically.

Natural convection is self-induced and is created by the density dif­ferences, which are temperature related; the boiling of water in a kettle is an example of free convection. Forced convection is caused by an exter­nal force being applied by mechanical means such as a fan or pump; the cooling of a warm bottle in cool flowing water is an example of forced convection.

Convection is influenced by the fluid flow adjacent to the solid surface. To appreciate the mechanics of this mode of heat transfer, the nature of the fluid flow in relation to the particular flow process must be known. Consideration of the flow structure created by the passage of a turbulent fluid over a smooth solid surface shows (see Fig. 4.24)

Laminar Turbulent

FIGURE 4.24 Laminar and turbulent boundary layers and temperature distribution inside the boundary layer.

3. In a turbulent boundary layer, flow takes place in the direction perpendicular to the surface over which the flow occurs.

A heat transfer factor (a) between the fluid and surface is defined as

? = a0 = | = fP", (4.156)

Where 0 is the temperature difference between the surface and the fluid at a long distance from the surface.

When heat transfer occurs by conduction through the boundary layer,

Where S is the thickness of the boundary layer, and the unit of a is W m [1] K “1. The heat transfer factor a thus decreases as the boundary layer thickness in­creases. The following discussion gives some indication of the range of the heat transfer values obtained due to the different modes of convective heat transfer.

Next we give some values of a to give an idea of the magnitude of the heat transfer:

A, W m-J K-‘

Free convection 3.5-50

Forced convection, air 10-500

Forced convection, liquid 100-5000

A liquid has a higher rate of conductivity than a gas.

In boiling convection, liquid motion is created by steam bubbles breaking loose from the surface.

If steam condenses on a surface, there is no boundary layer; the resis­tance to heat flow is due to scale, metal thickness, and the condensed liq­uid layer, resulting in a high heat transfer factor. A thin layer of air or other noncondensing gas forms at the surface through which the steam dif­fuses. The heat transfer factor diminishes rapidly but is considerably higher than in dry convection.

Heat radiation is electromagnetic radiation that all bodies emit due to their temperature. The wavelength of electromagnetic radiation is be­tween 0.3 and 50 |xm. This mode of heat transfer does not depend on an intermediate agent. When radiation falls on a body, part of the energy is absorbed, part is reflected, and the remainder is transmitted through the body. These components of the incoming radiation are the absorption ra­tio a, reflectance ratio p and transmission ratio t. When a body is in a state of equilibrium, the incoming and outgoing radiation are equal. Hence, a + p + r = L

A body having good electrical conductivity will absorb the incoming ra­diation on a distance of one wavelength. Now r = 0 and a + p = 1.

A planar polished surface reflects heat radiation in a similar manner with which it reflects light. Rough surfaces reflect energy in a diffuse manner; hence radiation is reflected in all directions. A blackbody absorbs all incoming radi­ation and therefore has no reflection. A perfect blackbody does not exist; a near perfect blackbody surface such as soot reflects 5% of the radiation, mak­ing it the standard for an ideal radiator.

The radiant emittance of a blackbody is

Mm = aT 4, (4.158)

Where <t is the Stefan-Boltzmann constant, 11.865 W m-2 (MJ/kmolr4,

The radiation emitted by a body due to its temperature is defined by the factor Ђ, the emissivity,

EMm = eoT4. (4.159)

This leads to Kirchhoff’s law,

E(T, — ft, v) = a(T, ■&, v), (4.160)

For a given temperature, angle, and frequency. For approximate calculations the emissivity can be assumed constant over the whole frequency spectrum. In this case the body is classified as a gray body.

The net heat transfer between two surfaces according to Eq. (4.159) is proportional to the first or second power of the temperature differ­ence; hence the radiation heat transfer dominates at a high temperature

Or for large temperature differences. When the temperature difference is small, a heat transfer factor is used similar to that used for convective heat transfer:

Q = asA’T. (4.161)

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