Radiant Heat Exchange

a process that takes place as a result of the processes of conversion of the internal energy of matter into radiant energy, the transfer of the radiant energy, and its absorption by matter. The course of processes of radiant heat exchange is controlled by the relative spatial position of the bodies exchanging the heat and the properties of the medium separating the bodies. The basic difference between radiant heat exchange and other types of heat transfer (thermal conductivity and convective heat exchange) is that it can occur when no material medium separates the heat-exchange surfaces, since it occurs through the propagation of electromagnetic radiation.

The radiant energy incident on the surface of an opaque body in radiant heat exchange is characterized by the magnitude of the flux of the incident radiation Q_Inc, which is partially absorbed by the body and partially reflected from its surface (see Figure 1). The flux of absorbed radiation Q_abs is found from the relation

Q_abs = AQ_inc

where A is the absorptivity of the body. Since for an opaque body

Q_inc = Q_abs + Q_ref

where Q_ref is the flux of radiation reflected from the surface of the body, the latter quantity is

Q_ref = (1 — A)Q_inc

where 1 — A = R is the reflectivity of the body. If the absorptivity of a body is equal to 1 and, as a result, its reflectivity is equal to 0 (that is, the body absorbs all the incident energy), it is called an ideal blackbody.

Figure 1. Diagram of fluxes of radiation in radiant heat exchange

Any body at a temperature other than absolute zero emits energy because of the heat of the body. This radiation is called the self-radiation of the body and is characterized by a flux of self-radiation Q_self. The self-radiation divided by the surface area of the body is called the flux density of the self-radiation, or the emissivity of the body. According to the Stefan-Boltzmann law of radiation, the latter is proportional to the fourth degree of the body’s temperature. The ratio of the emissivity of any body to the emissivity of an ideal blackbody at the same temperature is known as the degree of blackness. For all bodies the degree of blackness is less than 1; if it is independent of the wavelength of the radiation for a body, then the body is called gray. The nature of the energy distribution of the radiation of a gray body with respect to wavelength is the same as for an ideal blackbody—that is, it is described by Planck’s radiation law. The degree of blackness of a gray body is equal to its absorptivity.

The surface of any body that is part of a system of radiant heat exchange emits fluxes of reflected radiation Q_ref and self-radiation Q_Self; the total quantity of energy coming from the surface of the body is called the effective radiation flux Q_eff and is found from the relation

Q_eff = Q_ref + Q_self

Part of the energy absorbed by a body is returned to the system in the form of self-radiation; therefore, the result of radiant heat exchange may be represented as the difference between the fluxes of the self-radiation and the absorbed radiation. The quantity Q_res = Q_self — Q_abs is called the resultant radiation flux and indicates the quantity of energy received or lost per unit time in radiant heat exchange. The resultant radiation flux can also be expressed in the form Q_res = Q_eff — Q_inc, that is, as the difference between the total emission and absorption of radiant energy at the body’s surface. Hence, by taking into account the fact that Q_inc = (Q_self — Q_res)/A, we obtain an expression that is widely used in calculations of radiant heat exchange:

Q_eff = Q_res (1 - 1/A) + (Q_self/A)

As a rule, the problem in calculating radiant heat exchange is to find the resultant radiation fluxes on all surfaces in a given system if the temperatures and optical characteristics of the surfaces are known. In solving this problem it is necessary to have, in addition to the last relation, the relations between the flux Q_inc on the given surface and the fluxes Q_eff on all the surfaces in the system of radiant heat exchange. The concept of the mean angular coefficient of radiation, which shows what portion of the hemispherical radiation (that is, the radiation emitted in all directions in a hemisphere) of any surface in the system is incident on the given surface, is used to determine these relations. Thus, the flux Q_inc on any surface in the system is given as the sum of the products of Q_eff of all the surfaces (including the given surface, if it is concave) and the corresponding angular coefficients of radiation.

Radiant heat exchange plays an important role in heat transfer processes that take place at temperatures of about 1000°C and higher. It is commonplace in various fields of technology, such as metallurgy, heat and power engineering, nuclear power engineering, rocket technology, chemical engineering, drying technology, and solar radiation engineering.