Module 4. Radiation heat transfer

Lesson 21

THERMAL RADIATION

21.1  General Conceptions and Definitions

Radiant energy is the result of complicated molecular and atomic disturbances and occurs at the expense of other kinds of energy, mostly thermal. In a heated body, therefore, part of the thermal energy inevitably transforms into radiant energy. Since the temperature of the body is the original cause of interatomic disturbances, the quantity of generated radiant energy is determined by and essentially depends on temperature only.

Radiant energy is propagated by electromagnetic waves of a length ranging from fractions of a micron to many kilometers. Such waves are called Roentgen, ultraviolet, visible-light, infrared rays and electromagnetic waves. The properties of these rays are different. We are interested most in rays which are absorbed by the substances and the energy of which turns into heat energy in the course of absorption. Visible light and infrared rays, i.e., rays of a wavelength ranging approximately from 0.4 to 40 microns, possess such properties in the greatest measure. These rays are known as heat rays and the process of their propagation as thermal radiation or radiation. (Fig. 21.1)

Since the nature of heat and visible- light-rays is one and the same, their physical properties are essentially similar too. The only difference is their wavelength: the wavelength of visible rays is 0.4-0.8 microns and that of heat rays ranges from 0.8 to 40 microns. The laws of propagation, reflection and refraction of visible rays also hold for heat rays. Therefore, in order to conceive better any complicated phenomena of thermal radiation, it is always justifiable to draw an analogy with visible-light radiation of which we know more and which is directly observable.

Radiation is the property of all substances, and each continuously emits energy. The incident energy is partly absorbed, partly reflected, and a fraction of it passes through the body. The fraction of the incident radiant energy absorbed by the body again transforms into thermal energy. The reflected energy impinges upon other (surrounding) bodies and is absorbed by the latter. This also happens to the incident radiant energy passing through the body. Thus, after a series of absorption, radiant energy is fully distributed among the surrounding bodies. Hence, each body not only emits radiant energy continuously but also absorbs it continuously.

The process of radiant heat exchange is the result of these phenomena, linked with the double reciprocal transformation of energy (thermal-radiant-thermal). The amount of heat lost or absorbed is determined by the difference between the thermal energy radiated and absorbed by the substance. This difference is not zero if the bodies participating in the interchange of radiant energy are at different temperatures.

At equal temperature, the entire system is in the so-called mobile thermal equilibrium. In this case, all the bodies in the system also emit and absorb, but the amount of the energy absorbed is equal to that emitted in each given case.

The unit of radiant energy is the amount equivalent to one large calorie. The amount of energy Q emitted by the body per unit time is expressed in Kcal/hr. The amount of energy emitted by unit area per unit time is called the radiant power of a body and is denoted by E, hence,

E = Q / F[kcal/m²-hr]

Assuming that of all the incident energy Q_o, the fraction Q_A is absorbed, Q_R reflected and Q_D passes through the body,

Q_A + Q_R + Q_D = Q_o                                                 ….…..(a)

Dividing both sides of equation (a) by Q_o, we have

  …..….(b)

The first term of the relationship (b) characterizes absorptivity A of the body, the second, reflectivity R and the third, trasmissivity D. Hence,

A + R + D = 1                                           ………(c)

These values are dimensionless and vary from 0 to 1.

If A = 1 then R = 0 and D = 0; this means that incident energy entirely absorbed by the body. Such body is defined as a black body.

If R = 1, A = 0 and D = 0; this means that all the incident radiant energy is reflected, and if the reflection is correct, the body is called specular, and an absolutely white body in case of diffused reflection.

If D = 1, A = 0 and R = 0; this means that the entire incident radiant energy passes through the body. Such bodies are called absolutely transparent or diathermanous.

There are no absolutely black, white and transparent bodies in nature, and these conceptions are conditional when applied to real bodies. The value A, R and D depend on the nature of the body, its temperature and radiation wavelength. Air, for example, is transparent to heat rays, but the presence of water vapour or carbon dioxide makes air semitransparent to heat rays.

Solids and liquids are practically nontransparent (athermanous) to heat rays, i.e. D = 0; in this case

A + R = 1                                      ………. (d)

From relationship (d) it follows that a body of good reflectivity possesses poor absorptivity, and vice versa.

There are bodies, however, which are diathermanous (transparent) only to waves of a certain length. For example, quartz is athermanous (semi transparent) to heat rays of a wavelength λ > 4 microns and diathermanous to visible-light and ultraviolet rays. Rock salt, on the contrary, is diathermanous to heat rays and athermanous to ultraviolet rays. Window glass is transparent to visible-light and almost nontransparent to ultraviolet and heat rays.

This goes for absorption and reflection too. A white surface is a good reflector only for visible light. This property is made wide use of in everyday life- white summer cloth, white-painted refrigerator cars, tanks and other facilities where insolation is undesirable. On the other hand, white cloth and paint absorb invisible heat rays just as well as black cloth and paint. The absorption and reflection of heat rays depend greatly on the state of the surface and not its colour. The reflectivity of smooth and polished surfaces is many times higher than that of rough surfaces, irrespective of their colour.

The absorptivity of bodies is increased by coating surfaces with a layer of dark, rough paint, with oil black usually employed for this purpose. But even oil black absorbs only 90-96 per cent; it is not an absolutely black body. There is no such thing in nature, but it can be created artificially.

A hole in the wall of a hollow body possesses the property of a black body. For such a hole    A =1 because it may be assumed that the ray penetrating that hole is absorbed entirely inside the hollow body. All values pertaining to an absolutely black body shall hereafter be denoted by (0).

If the radiant powder of a body is E₁, it means the body emits E₁ [kcal/m²-hr]; this is the emission of the body proper and it depends only on the temperature of the body and its physical properties. At the same time, the considered body is affected by radiation E₂ [kcal/sq m-hr] from the surroundings; this is defined as incident radiation. A fraction of incident radiation equal to A₁E₂ is absorbed by the body-it is absorbed radiation; the rest (1-A₁) E₂ is reflected- it is reflected radiation. Radiation of the body proper plus reflected radiation is known as the effective radiation of the body. E_eff = E₁ + (1-A₁) E₂. This effective radiation of the body we can perceive or measure with the aid of instruments; it exceeds the radiation of the body proper by (1-A₁) E₂.

The physical properties of proper and reflected radiation differ and their spectra differ too for incident radiation E₂ depends on temperature and the properties of surrounding bodies. This, however, is immaterial for practical calculations which consider only the energy- transport phenomena of the process.