4.6. RADIATION HEAT TRANSFER Radiation, which may be considered to be energy streaming through space at the speedof light, may originate in various ways. Some types of material will emit radiation when they are treated by external agencies.All substances at temperatures above absolute zero emit radiation that is independent of external agencies.Radiation that is the result of temperature only is called thermal radiation.Fundamental facts concerning radiationRadiation moves through space in straightlines, or beams, and only substances in sightof a radiating body can intercept radiation from that body.Radiation as such is not heat, and when transformed into heat on absorption, it is no longer radiation.lThe fraction that is absorbed is called absorptivity .lThe fraction that is transmitted is called transmissivity .lThe fraction of the radiation falling on a body that is reflected is called reflectivity . The maximum possible absorptivity is unity. A body which absorbs all incident radiation is called a black body.The sum of these fractions must be unity, or+ + =14.6-1Emission of radiationThe radiation emitted by any given mass of substance is independent of other material in sight of , or in contact with, the mass. The net energy gained or lost by a body is the difference between the energy emitted by the body and that absorbed by it from the radiation reaching it from other bodies. When bodies at different temperatures are placed in sight of one another inside an enclosure, the hotter bodies loss energy by emission of radiation faster than they receive energy by absorption of radiation from the cooler bodies. Temperatures of hotter bodies decrease.Wavelength of radiation Known electromagnetic radiations cover an enormous range of wavelengths, from the short cosmic rays to long wave broadcasting wave. Although radiation of any wavelength is, in principle, convertible into heat on absorption by matter, the portion of the electromagnetic spectrum that is of importance in heat flow lies in the wavelength range between 0.5 and 50 m. Visible light covers a wavelength range of about 0.38 to 0.78 mAt temperature above about 5000C ，heat radiation in the visible spectrum become significant. The higher the temperature of the radiating body, the shorter the predominant wavelength of the thermal radiation emitted by it.Emissive power The monochromatic energy emitted by a radiating surface depends on the temperature of the surface and on the wavelength of the radiation. At constant surface temperature, a curve can be plotted showing the rate of energy emission as a function of the wavelength. The monochromatic radiation emitted in this manner from unit area in unit time, divided by the wavelength, is called the monochromatic radiating power W. For the entire spectrum of the radiation from a surface, the total radiating power W is the sum of all the monochromatic radiations from the surface, or , mathematically,4.6-2 Blackbody radiation A blackbody has the maximum attainable emissive power at any given temperature. The ratio of the total emissive power W of a body to that of a blackbody WB is by definition the emissivity of the body, thus4.6-3 Emissivities of solidsEmissivity usually increases with temperature.Emissivities of polished metals are low, in therange 0.03 to 0.08. Emissivities of most oxidized metals range from 0.6 to 0.85, those of nonmetals from 0.65 to 0.95.Practical source of blackbody radiation No actual substance is a blackbody, although some materials, such as certain grades of carbon black, do approach blackness.The distribution of energy in the spectrum of a blackbody is known accurately. It is given by Plancks law4.6-6 Laws of blackbody radiationPlancks law can be shown to be consistent with the Stefan-Boltzmann law by substituting Wb, from Eq 4.6-6 into Eq 4.6-2 and integrating. A basic relationship for blackbody radiation is the Stefan-Boltzmann law, which states that the total emissive power of a blackbody is proportional to the fourth power of the absolute temperature, or Where is a universal constant4.6-5 WB=T4Absorption of radiation by opaque solids Kirchhoffs law states, at temperature equilibrium, the ratio of the total radiating power of any body to the absorptivity of that body depends only upon the temperature of the body. Thus, consider any two bodies in temperature equilibrium with common surroundings. Kirchhoffs law states that4.6-9 Thus By definition, the emissivity of the second body 2 isIf the first body is blackbody, 1=1, and4.6-11 4.6-10 Thus, when any body is at temperature equilibrium with its surroundings, its emissivity and absorptivity are equal. Kirchholff law applies whether or not the two surfaces are at same temperature.Radiation between surfaces The total radiation from a unit area of an opaque body of area A1, emissivity1, and absolute temperature T1 is4.6-13Qualitatively, the interception of radiation from an area element of a surface by another surface of finite size can be visualized in terms of the angle of vision. The factor F is called the view factor or angle factor; it depends upon the geometry of the two surface4.6-14The equation for two bodies radiating each other can be written in the formIf surface A1 is chosen for A, Eq(4.6-14) canbe written4.6-154.6-16If surface A2 is chosen In general, for gray surfaces, Eq(4.6-15)and Eq(4.6-16) can be written(4.6-26)F12 and F21 are the overall interchange factor and are functions of 1 and 2.Two large parallel planes4.6-274.6-28One gray surface completely surrounded by anotherproblem A chamber for heat-curing large aluminum sheets, lacquered black on both sides, operates by passing the sheets vertically between two steel plates 150 mm apart. One of the plates is at 300C, and the other, exposed to the atmosphere, is at 25C.(a) What is the temperature of the lacquered sheet? (b) What is the heat transferred between the walls when equilibrium has been reached? Neglect convection effects. Emissivity of steel is 0.56; emissivity of lacquered sheets is 1.0.Solution(a) Let subscript 1 refer to hot plate, 2 to lacquered sheets, and 3 to cold plate:1, 3 = 0.56 2 = 1.0T1 = 573K T3 = 298KFrom Eq. (4.6-27)Since A1 = A2 ,T2 = 490.4K = 217.4C(b) From Eq. (4.6-26) the heat flux is= 5.672 0.56(5.734 4.9044) = 1587W/m2Check:= 5.672 0.56(4.9044 2.984) = 1587W/m2Note: If the lacquered sheet is removed, q13 = 3174 W/m2 Problem A shell-and-tube heat exchanger consists of 120 tubes of internal diameter 22 mm and length 2.5m. It is operated as a single-pass condenser with benzene condensing at a temperature of 350 K on the outside of the tubes and water of inlet temperature 290 K passing through the tubes. Initially there is no scale on the walls, and a rate condensation of 4 kg/s is obtained with a water velocity of 0.7 m/s through the tubes. After prolonged operation, a scale of resistance 0.20 m2 K/kW is formed on the inner surface of the tubes. What is the outlet temperature of water? And what is the rate of benzene condensing?Assumption that the coefficient for the condensing vapor is 2.25kW/m2K, based on the inside area. The latent heat of benzene is 400kJ/kg.