chap13-radiationexchangebetweensurfaces传热传质

13 Radiation exchange between surfacesn Introduction Radiative exchange between two or more surfaces depends strongly on the surface geometries and orientations, as well as on their radiative properties and temperatures. Initially, we assume that the surfaces are separated by a nonparticipating medium. A vacuum meets these requirements exactly, and most gases meet them to an excellent approximation.13 Radiation exchange between surfacesn Objectives To establish geometrical features of the radiation exchange problem by developing the notion of a view factor.To develop procedures for predicting radiative exchange between surfaces that form an enclosure, first under the assumption that all of the surfaces may be approximated as blackbodies and subsequently under the less restrictive assumption that all of the surfaces may be approximated as diffuse and gray.13.1 The view factorn 13.1.1 The view factor integral The view factor Fij is defined as the fraction of the radiation leaving surface i that is intercepted by surface j. To develop a general expression for Fij, we consider the arbitrarily oriented surfaces Ai and Aj of Figure 13.1. Elemental areas on each surface,dAi and dAj, are connected by a line of length R, which forms the polar angles i and j, respectively,with the surface normals ni and nj. The values of R, i and j vary with the position of the elemental areas on Ai and Aj.n From the definition of the radiation intensity and Equation 12.5, the rate at which radiation leaves dAi and is intercepted by dAj may be expressed aswhere Ii is the tensity of the radiation leaving surface i and dj-i is the solid angle subtended by dAj when viewed from dAi. With dj-i =(cos j dAj)/R2 from Equation 12.213.1.1 The view factor integraln Assuming that surface i emits and reflects diffusely and and substituting from Equation 12.24, n the total rate at which radiation leaves surface i and is intercepted by j may then be obtained by integrating over the two surfaces.13.1.1 The view factor integraln From the definition of the view factor as the fraction of the radiation that leaves Ai and is intercepted by Aj,n it follows that13.1.1 The view factor integraln similarly, the view factor Fji is defined as the fraction of the radiation that leaves Aj and is intercepted by Ai.Either Equation 13.1 or 13.2 may be used to determine the view factor associated with any two surfaces that are diffuse emitters and reflectors and have uniform radiosity. 13.1.1 The view factor integral13.1.2 View factor relationsn Equating the integrals appearing in Equations 13.1 and 13.2,This expression,termed the reciprocity relation, is useful in determining one view factor from knowledge of the other.n Another important view factor relation pertains the surfaces of an enclosure (Figure 13.2). From the definition of the view factor, the summation ruleFigure 13.2 Radiation exchange in an enclosure.n The term Fii appearing in this summation represents the fraction of the radiation that leaves surface i and is directly intercepted by i. If the surface is concave, it sees itself and Fii is nonzero. However, for a plane or convex surface, Fii =0.n To calculate radiation exchange in an enclosure of N surfaces, a total of N2 view factors is needed. This requirement becomes evident when the view factors are arranged in the matrix form.13.1.2 View factor relationsn However, all the view factors need not be calculated directly. A total of N view factors may be obtained from the N equations associated with application of the summation rule, Equation 13.4, to each of the surfaces in the enclosure. 13.1.2 View factor relationsn In addition,N(N-1)/2 view factors may be obtained from the N(N-1)/2 applications of the reciprocity relation. Accordingly,only N2-N- N(N-1)/2 = N(N-1)/2 view factors need be determined directly. n For example,in a three-surface enclosure this requirement corresponds to only 3(3-1)/2=3 view factors. 13.1.2 View factor relationsn Fig. 13.3, two-surface enclosure. Although the enclosure is characterized by N2=4 view factors (F11, F12, F22, F21 ), only N(N-1)/2=1 view factor need be determined directly. n In this case such a determination may be made by inspection. F12=1. n From the reciprocity relation, Equation 13.313.1.2 View factor relationsn From the summation rule,we also obtainin which case F11 =0,andin which case13.1.2 View factor relationsFigure 13.3 View factors for the enclosure formed by two spheres.n For more complicated geometries,the view factor may be determined by solving the double integral of Equation 13.1. n Results for several common geometries are presented in Tables 13.1 and 13.2 and Figures 13.4 to 13.6. The configurations of Table 13.1 are assumed to be infinitely long (in a direction perpendicular to the page) and are hence two-dimensional. The configurations of Table 13.2 and Figures 13.4 to 13.6 are three-dimensional. 13.1.2 View factor relationsn It is useful to note that the results of Figures 13.4 to 13.6 may be used to determine other view factors. For example, the view factor for an end surface of a cylinder relative to the lateral surface may be obtained by using the results of Figure 13.5 with the summation rule.13.1.2 View factor relationsn The first relation concerns the additive nature of the view factor for a subdivided surface and may be inferred from Figure 13.7. Considering radiation from surface i to surface j, which is divided into n components, it is evident thatwhere the parentheses around a subscript indicate that it is a composite