Heat transfer by radiation

1 Basic Definitions and Elementary Concepts of Thermal Radiation 

Radiative heat transfer or thermal radiation is a distinctly separate mechanisms from conduction and convection for the transport of heat. Thermal radiation is associated with the rate at which energy is emitted by the material as a result of its finite temperature. The mechanism of emission is related to energy released as a result of oscillations or transitions of the many electrons that constitute the material. These oscillations are, in turn, supported by the internal energy for this reason the temperature drops. The emission of thermal radiation is thus associated with thermally excited conditions within the matter. 

Radiation also possesses the standard wave properties of frequency u and wavelength A. For radiation propagating in a particular medium, the two properties are related by  

All states of matter (solids, liquids, and gases) emit thermal radiation. For gases and for semi-transparent solids, such as glass and salt crystals at elevated temperatures, emission is a volumetric phenomenon. That is, radiation emerging from a 

Consider a heated enclosure with surface A and volume V filled with radiating material. If qAdA is defined as the radiant surface energy flux arriving at dA from a surface element dAs, and the volumentric energy flux qvdV arrives at dA from a volume element t/y, then the radiative energy flux from the entire enclosure arriving at dA is  

The wavelengths of thermal radiation follow a probability distribution depending only on temperature, which is given for a black-body by Planck s law. The most likely wavelength of the emitted radiation is given by Wien s law [Wilhelm Wien (1864—1928), 2-r,iax in p.m= 2898/Tj. 

Radiation heat transfer must account for incoming and outgoing thermal radiation. Incoming radiation is either reflected, absorbed, or transmitted, and for the relative fractions we have  

Since most solid bodies are opaque to thermal radiation, transmission is negligible in most cases. To account for a body s outgoing radiation, we make a comparison with a perfect body that emits as much radiation as possible, known as a black-body. The ratio of the actual heat flow to the heat flow of a black-body is defined as the surface emissivity e, and ranges from about 0.05 for polished metal surfaces to more than about 0.7 for ice, cast iron, corroded iron, rubber, and brick. The surface emissivity equals the absorption fraction (Kirchhoffs law)  

The radiated power of a body is given by the Stefan-Boltzmann law Joseph Stefan, see box below, and Ludwig Boltzmann, see box in Section 3.1.4)  

Joseph Stel (1835-1893), a Slovene-Austrian physicist, is best known for originating the law that the radiation from a black-body is proportional to the fourth power of temperature. In 1884, this law was theoretically derived by his student Ludwig Boltzmann and is known as the Stefan-Boltzmann law. Stefan s electromagnetic equations are also important, as his work on the kinetic theory of heat. He was among the first physicists who understood Maxwell s electromagnetic theory. 

In this section a brief introduction to the fundamental concepts of thermal radiation modeling is given. The main purpose of this survey is to elucidate the basic assumptions involved deriving the conventional engineering model of thermal radiation fluxes. To this end the thermal radiation flux is determined in terms of a heat transfer coefficient. 

Explanations of radiation physics and more detailed descriptions of the concepts of thermal radiation can be found in the books by Long [91], Arpaci et al [5], Hagen [56], Incropera and DeWitt [60], Siegel and Howel [136], Eckert and Drake [39], among many others. 

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Simultaneous Loss by Radiation The heat transferred by radiation is often of significant magnitude in the loss of heat from surfaces to the surroundings because of the diathermanous nature of atmospheric gases (air). It is convenient to represent radiant-heat transfer, for this case, as a radiation film coefficient which is added to the film coefficient for convection, giving the combined coefficient for convection and radiation (h + hf In Fig. 5-7 values of the film coefficient for radiation are plotted against the two surface temperatures for emissivity = 1.0. 

Vacuum Insulation Heat transport across an evacuated space (1.3 X lO"" Pa or lower), is by radiation and by conduction through the residual gas. The heat transfer by radiation generally is predominant and can be approximated by... 

Heat-transfer coefficients in steam-tube dryers range from 30 to 85 J/(m s K). Coefficients will increasewith increasing steam temperature because of increased heat transfer by radiation. In units carrying saturated steam at 420 to 450 K, the heat flux UAT will range from 6300 J/(m s) for difficult-to-diy and organic solids and to 1890 to 3790 J/(m s) for finely divided inorganic materials. The effect of steam pressure on heat-transfer rates up to 8.6 X 10 Pa is illustrated in Fig. 12-71. 

The factors that must be controlled for efficient insulation are the amounts of heat transferred by radiation, by conduction through the solid structure, and by conduction through the residual gases. 

From equation 9.117, it is seen that the rate of heat transfer by radiation from a hot body at temperature Tt to a cooler one at temperature T is then given by ... 

Equation 9.127 may be extended in order to determine the net rate of radiation heat transfer from a surface in an enclosure. If the enclosure contains n black surfaces, then the net heat transfer by radiation to surface i is given by ... 

A plate. 1 m in diameter at 750 K, is to be heated by placing it beneath a hemispherical dome of the same diameter at 1200 K the distance between the plate and the bottom of the dome being 0.5 m, as shown in Figure 9.42. If the surroundings are maintained at 290 K, the surfaces may be regarded as black bodies and heat transfer from the underside of the plate is negligible, what is the net rate of heat transfer by radiation to the plate ... 

The rate of heat transfer by radiation between two surfaces may be reduced by inserting a shield, so that radiation from surface 1 does not fall directly on surface 2, but instead is intercepted by the shield at a temperature Tsh (where 7, > T,h > T2) which then reradiates to surface 2. An important application of this principle is in a furnace where it is necessary to protect the walls from high-temperature radiation. 

With very high values of AT, the heat transfer coefficient rises again because of heat transfer by radiation. These very high values are rarely achieved in practice and usually the aim is to operate the plant at a temperature difference a little below the value giving lhe maximum heat transfer coefficient. 

Would it be feasible to use a magnesia insulation which will not stand temperatures above 615 K and has a thermal conductivity 0.09 W/m K for an additional layer thick enough to reduce the outer surface temperature to 370 K in surroundings at 280 K Take the surface coefficient of heat transfer by radiation and convection as 10 W/m- IC... 

A bare thermocouple is used to measure the temperature of a gas flowing through a hot pipe. The heat transfer coefficient bet ween the gas and the thermocouple is proportional to the 0.8 power of the gas velocity and the heat transfer by radiation from the walls to the thermocouple is proportional to the temperature difference. 

The thermal conductivity of materials has been examined in Chapter 2 and Chapter 3. As we shall see in this chapter, in many cases, at very low temperatures, the heat conduction is not limited by the bulk thermal resistivity of the material but by the contact thermal resistance appearing at the interface of two materials. This is a particularly severe problem, below IK, in the case of the heat transfer between liquid He and a solid (see Section 4.3). Heat transfer by radiation will be considered in Section 53.2.2. 

Fig, 1.57. Heat transfer by radiation only. The figure shows only the order of magnitude. 

In tests on the drying of sand, Wenzel and White 53 1 found that the use of steam rather than air did not alter the general characteristics of the drying process, and that the drying rate during the constant rate period was determined by the heat transfer rate. In these tests, the heat transferred by radiation from the steam and surrounding surfaces was 7.5-31... 

Soot emission from hydrocarbon flames is an important snbject since it plays an important role in relation to both heat transfer by radiation and air pollution (Sha-had and Mohanuned, 2000). The use of CNG in internal combnstion (1C) engines permits operation with decreased advances and decreases NO without increasing soot formation. 

In many process fires, heat transfer by radiation is the dominant form of heat transfer. The heat radiated from a flame is emitted by gases, in particular the products of combustion and by soot. Aflame in which the radiation is emitted solely from the gaseous products of combustion is termed nonluminous and a flame in which there is soot is termed luminous (i.e., yellow or visible). 

The above equations hold for Rep > 10. At temperatures above about 400 °C and for large particles (> 0.25 in), heat transfer by radiation maybe significant and should be taken into account. 

At temperatures above 400 °C and for large particles, heat transfer by radiation should be also taken into account. 

The reactions take place only in active catalytic layer, the rates Rj are considered individually for each type of the converter (DOC, SCR, NSRC, TWC). The development of suitable reaction schemes and the evaluation of kinetic parameters are discussed generally in Section IV. The details for DOC, NSRC and SCR of NOx by NH3 are given in Sections V, VI and VII, respectively. The important species deposited on the catalyst surface are balanced (e.g. HC adsorption in DOC, oxygen and NOx storage in NSRC, NH3 adsorption in SCR). Heat transfer by radiation and homogeneous reactions... 

In the firebox, heat transfer by radiation reigns supreme governed by Lambert s laws, as follows ... 

The heat transfer by radiation to the reformer tubes has the form... 

Heat transfer by radiation only. The figure shows only the order of magnitude. Density of heat flow (q) as a function of 7"str2 (ice or product surface temperature) at three temperatures 7"strl of the radiation surface (+100, +50, +30 °C) as parameter... 

Considerable interest centres on the Mantle constituting, as it does, more than half of the Earth by volume and by weight. Attention has been focussed on several problems, including the chemical composition, mineralogy, phase transitions and element partitioning in the Mantle, and the geophysical properties of seismicity, heat transfer by radiation, electrical conductivity and magnetism in the Earth. Many of these properties of the Earth s interior are influenced by the electronic structures of transition metal ions in Mantle minerals at elevated temperatures and pressures. Such effects are amenable to interpretation by crystal field theory based on optical spectral data for minerals measured at elevated temperatures and pressures. 

For two large parallel plates with grey surfaces, the heat transfer by radiation between them is given by putting Ai = A2 in equation 150 to give ... 

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