Document pBo7wkY6zZzawZeRkZVNO5q2a

52 CHAPTER 4 1965 Guide And: Data Boole Table 4------ Emhsivilie, and Absorptivity faf.ojFew.Swfacet (See Abo Chapter 69 and References 8 and 9) dots 1 2 3 5 6 7 8 10 11 Total Norand EaUdvrty* AS 50-100 F At 1000 F AbtorpthrOf for Solar SadiaHorn A small hole in a large box, sphere, furnace, or enclosure..!.. .v:...... Black noD-metallic surfaces such as asphalt, carbon, elate, paint, paper. Rad brick and tile, concrete and stone, rusty steel and iron, dark paints (red, brown, green, etc.)..................... ; ;............................................... _ Yellow and buff brick and stone, firebrick, fire clay................................. White or light-cream brick, tile, paint or paper, plaster, whitewash.... ^ 0.97 to 0.99 0.90 to 0.98 0.85 to 0.95 0.85 to 0.95 0.85 to 0.95J 0.97 ^0.99' 0.90 to 0.98 0.75 to 0.90 0.70 to 0.85 0.60 to 0.75 0.30 to 0.50 Bright aluminum paint; gilt or bronse naint................. Dull brass, copper, or aluminum- eahmniMl Polished hnun, copper, monel mete) pnltvtwvi hm Highly polished aluminum, tin plate, nickel; chromium......................... Selective Surfaces Stainless steel wire mesh.......................... ............................................. . 0.40 to 0.60 0.20 to 0.30 0.02 to 0.05 0:02 to 0.04 0.30 to 0.50~ 0.05 to 0.15 0.05 to 0.10 0.10 to 0.40 0.23 to 0.28 0.63 to 0.88 Copper treated with solution of NaClOt and NaOH .___ 0.13 Copper, nickel, and aluminum plate with CuO ^noting.......................... 0.09 to 0.21 0.08 to: 0.93 k Abat*i 4 ------------------------* where X b the wave length, and Ci and Cj are universal con- ' stanta having the vatues 3.7413 X 10-4 erg - cm1/sec 'and 1.4388 cm K, respectively. where ex is called the monochromatic hemispherical emissivity. The relationship between c and ex b given by: The symbol denotes the monochromatic emissive power or intensity, defined as the energy emitted per unit surface area at wave length X per unit wave length interval around X. That is, the rate of energy emission in the interval dX b equal to FP^dX. The Planck law of radiant energy distribution b connected to the Stefan-Boltsmann emissive power IP* by the following relation: 1 - flfad (5) Actual Radiation Different substances and surfaces show various,divergences from the Stefan-Boltsmann and Planck laws. IP* and IP*x are the maTnmnm emissive powers for any given surface tempera ture. Actual surfaces emit and absorb less readilylahd- are called nonblack. The emissive power of,a nonblack surfaoe, at temperature T, to the hemispherical region above it'b written as: ' _ !V.! W - IP* -**T*, \'V. V . 7(6) T> - fwuOk - fa ITdx (8) One type of monochromatic emissivity characteristic b of special importance because of the simplicity of the resulting ' relation between t and ex. Iix does not depend upon X, then `' from Equation 8, e - ex: Surfaces having this characteristic are called gray. In heat transfer calcubtioW* gT&y-siirface characteristics are often assumed because several important ebssesof'surfaces approximate'this condition;at least in' Borne ngiaib'of the spectrum/The resulting mmplinitytwVtegirghla', but care ` must be exercised, especially if the - temperatures involved are high: .The-assumption 'of grayness b -sometimes unavoidable, `because of the-absence of information- relating qfand'X.V'"'** - ' -o` U>> ms- fi * " Whea radiant ehergy falb oh a surface* itcan be'absoxbed, reflected or transmitted through' the'material'`Therefore, from the firstlaw of thermodynamics*.^-- ;- uAere b'called the hemispherical cmUswity.* in general,'the embsivity'b a function of the material, the.condition'of its surface, and also the temperature of the surface: Selected values are listed in Table 4. Extensive listings of such informa tion may be found in References 8 and 9. +r +p 1 ^(9) where,.... , . ' a-- fraction of incidentradiation absorbedor atoorptmly.ii - r." fraction of incident radiation transmitted or trmsmisswity. , p. --, fraction of incident radiation reflected or reJUatwity. The monochromatic emissive power of a nonblack surface b similarly written as: '' m"\- 1 JPk xfPi " Ok- C,X- (7) The term , arftan c*flcd Mtttooe. particularly when referring to pica, {OfMtcnal u rt^ctuaUy ensu. In th eaae, Ua tens ia -t*-A (or drjcriWnc tba property of tto bdk c "teriaL indepeadest cf (aotoeVr or -For'an opaque surface, r * O and a + p -- 1; for a black surface, a **'l,;by definition. However, no really bbcksui- faces exist. Platinum black and gold black, which are about as black as any found in nature, exhibit absorptivities of about 0.98.- - ................. / " - A useful relation between emissivity and absorptivity of any opaque surface, wrilftri Kvchhoffe law, may be developed directly from 'thermodynamic'considerations.' Thb' relation Heat Traibfer 53 states that for any surface ex - ax- If the surface b gray, or the incident radiation is from a-black surface at the same concave surface may see itself,'F-jf rf 0, and that'if n surfaces form an enclosure: I :. ; , temperature, then also e - a. However, many surfaces are cot Say as may be seen from the data in Table 4. For most Ef-1 : ` (10) surfaces listed, absorptivity for solar radbtion b different than emissivity for low temperature level radbtion. Thb b because the wave length distributions are different in the two - easea, and a varies with wave length. `' The foregone discussion relates to total hemispherical radi-- ation from surfaces. No regard b given to the way. in which the energy.is distributed over such a hemispherical region - Equations and'graphs for angle factors for. many surfaoe arrangements are available in References 10 and 11. One' such chart b reproduced in Pig. 1. A useful technique for visualising ' the angle factor b given by Eckert and Drake.** In addition, several'mathematical methods have been-introduced for the calculation .ofvalues not given in charts.11:? above the surface. However, the nature of the distribution of energy in the region above an emitting surface has an impor- : 'Calculation of Radiant Exchange' tant effect upon the rates of-heat transfer in various geometric / The information of principal interest to the engineer in a arrangements. -radiant energy exchange calculation b the net' rate of radiant Very early in the study of radbtion phenomena the quest. energy loss from a surface. Thb quantity will be denoted by q, tkm of the spatial distribution of the emitted energy was ; or by for. Af. it b the rate of emission of the surface minus investigated. One result of these investigations was the fonnu-J - the total rate of radiant energy absorption at the surface due latioc of a -law of radiant energy distribution subsequently to all radiant effects in its surroundings, including perhaps the fpim lan&trf* law. Lambert's bw states that the intensity - return of some of its own emission. Tbst.b, q b the rate at of radiant energy over a hemispherical surface above the - which .energy .must be supplied to the surface material by emitting surface varies as the cosine of the angle between the ~ mother exchange processes if its temperature' b to remain normal to the radiating surface and the line joining the radi constant. Therefore, in order that q be defined, the 'total ating surface to the point of the hemispherical surface. Such - . radiant surroundings must be specified. These total surround radbtion b called defuse radbtion. It can be seen that the i ings constitute in effect an enclosure and,- from thb point of Ibmbert intensity .variation b equivalent to the assumption : view, all problems are enclosure, problems. that the radbtion from a surface in a direction other than nor-., - Consider- a simple enclosure, made up of three black sur mal occurs as if it came from an equivalent area having the - - faces, Ai, At, and Ay There being no reflections, the rate same emissive power (per unit area) as the original surface/: Thb equivalent area b obtained by projecting the original .' area upon a plane normal to the direction of.radbtion. of radiant energy- loss from A\ is: "9WtA, - PtiWtAx - FnWtAt - FaWA (11) Black surfaces obey the Lambert bw exactly. The bw ` Many more complicated enclosure. problems have been holds approximately- for many actual radbtion and reflection solved.For ah enclosure made up of two gray surfaces processes, especially those involving rough surfaces and non- one of which, At, does not see itself, the result b: metallic materials. However, it has many exceptions.- ' , The subsequent dismission deals with techniques usedfor the estimation of heat transfer rates between surfaces of-. different geometries, radbtion characteristics, and orienta-_n_ turns. The following assumptions are made: (1) all surfaces rA,(7y.^- TV)' - 7 + zW ! (12) are either gray or black; (2) radbtion and reflection processes . Equation 12 b strictly valid only if A\ and At uniformly are diffuse; (3) properties are uniform over the extent of the irradiate each other. Special applications of thb equation are surfaces; (4) absorptivity b equal .to emissivity-and inde-_... . for infinite parallel plates, AJAt = l,.and for a small object pendent of the temperature of the source of incident radi placed in a large enclosure, A-JA 0. ation; (5) the material occupying the space between the Most engineering problems require the calculation of radi radiating surfaces neither emits nor absorbs radbtion. ant-energy loss-rates from surfaces whose effective radiant These assumptions are not strictly valid in many problems surroundings are made up of many surfaces, some of which of practical importance. They are usually used because of the may be reflecting. Since simple solutions do not exist for these considerable simplification they provide, although the results more complicated cases, a number .of methods have been in such circumstances must be considered approximate. In developed for treating them.'*14-11 A technique u-n for calcu many cases the development of new techniques not requiring lating 9/ directly for an tveurface effective enclosure b pre these assumptions would involve computations so'lengthyand sented here. Thb' method b simple and direct, and b con- complex as to be impractical. - venlent for machine calculation. TTie Angle Factor . Consider the jth-surface, which emits at a raterW7A>, in an n-surface enclosure. The other enclosure surfaces, A,, emit at a - The distribution of radbtion leaving a surface, among th surfaces it irradiates, b indicated by a quantity variously called an interception, view, configuration, or angle factor. rate FT,-A,-. Some of thb emission may be absorbed at A) due to direct irradiation or after reflections and re-reflections from the n surfaces. An absorption factor b defined as the frac In terms of two surfaces, * and j, the anglefactor from surface * to surface j, Fa, b defined as the fraction of radiant energy tion of the emission of A,- absorbed at Aj. Thus, By b similar to Fa, hut takes reflections into account By the definition emitted by surface i which falb directly upon j (Le., b inter of Bij, the net rate of energy loss may be written: cepted by f). The angle factor from j to t is similarly defined merely by interchanging the rolea of i and j. Thb second qi - WfAi - BijWiAi (13) angle factor will not, in general, be numerically equal to the first.- However, under the assumptions noted previously, rd. = PjiAj, where A indicates surface area. Note that a The n values of necessary to compute qi may be found by wimmmg,fthgnrptanti rates atj due to th> emission rates of