A CATALOG OF RADIATION HEAT TRANSFER 
Derives factors by contour integration, and presents final analytical expressions. The resulting expressions contain integrals that must be evaluated numerically. Numerical integrations are carried out for particular cases, and the results are correlated and expressions are presented for various ranges of the geometric parameters. Error ranges and correlation coefficients are given for each correlation. 
Alexandrov, V.T., 1965, "Determination of the angular radiation coefficients for a system of two coaxial cylindrical bodies," Inzh. Fiz. Zh., vol. 8, no. 5, pp. 609612.
Uses numerical integration of fundamental defining relation between two elements to find factor from inner surface of outer coaxial cylinder to outer surface of inner directly opposed cylinder of the same finite length. Closed form is found for outerouter factor, and outertoinner finite area factor is found by numerical integration. Configuration factor algebra is then used to obtain factor from inner cylinder to annular ring end. 
Alciatore, David and Lipp, Stephen, 1989, "Closed form solution of the general three dimensional radiation configuration factor problem with microcomputer solution," Proc. 26th National Heat Transfer Conf., Philadelphia, ASME.
Presents general algorithm for finding factor between any threedimensional contour and a differential element. Formulation is based on the unit sphere technique of Nusselt (1928). Results of computer implementation of the method are compared with exact formulation for element to a polygon. 

Alfano, G. and Sarn , A., 1975, "Normal and hemispherical thermal emittances of cylindrical cavities," J. Heat Transfer, vol. 97, no. 3, pp. 387390, August.
Gives factors from a differential element on and normal to the axis to a differential ring element on the interior of a concentric right circular cylinder; from a differential element to a circular ring element on a parallel disk when the element is on the disk axis; from the interior surface of a circular cylinder to a differential element on and normal to the cylinder axis; and from a disk to a differential element which is on and normal to the disk axis. All are in closed form. 
Ameri, A. and Felske, J.D., 1982, "Radiation configuration factors for obliquely oriented finite length circular cylinders," Int. J. Heat Mass Transfer, vol. 33, no. 1, pp. 728736.
Numerical integration is used to compute the factors between the exteriors of two cylinders of equal radius and length, and oriented to one another in various ways. Factors between one cylinder and a second of onehalf the length of the first are also given. Most results are for rotation of cylinder two about the normal through the center or the end of the axis of cylinder one. Closed form relations derived by fitting the numerical results are presented. Graphical and some tabular data are presented. 
Ambirajan, Amrit and Venkateshan, S.P., 1993, "Accurate determination of diffuse view factors between planar surfaces," Int. J. Heat Mass Transfer, vol. 36, no. 8, pp. 2203 2208.
Uses numerical evaluation of general double integral obtained by contour integration around polygonal surfaces. Special cases of intersecting and non intersecting surfaces are discussed. Numerical results are presented for the cases of directly opposed isosceles triangles, squares, and regular pentagons, hexagons, and octagons, as well as adjoint plates of finite length at various intersection angles. Points out some errors in similar results in Feingold (1966). 
Ballance, J.O. and Donovan, J., 1973, "Radiation configuration factors for annular rings and hemispherical sectors," J. Heat Transfer, vol. 95, no. 2, pp. 275276, May.
Monte Carlo method is used to find the factors to within approximately 5 percent. 
Bartell, F.O. and Wolfe, W.L., 1975, "New approach for the design of blackbody simulators," Appl. Opt., vol. 14, no. 2, pp. 249252, February.
Includes closedform relations for factors from sphere interior to element on interior; from circular cone interior to base; and from right circular cylinder to base. 
Bernard, JeanJoseph and Genot, Jeanne, 1971a, "Diagrams for computing the radiation of axisymmetric surfaces (propulsive nozzles)," Office National d' Etudes et de Recherches Aerospatiales, Paris, France, ONERANT185 (in French).
Gives diagrams for finding exchange between exterior elements and between interior elements on various bodies of revolution. Closed form relations are not given, but auxiliary functions are presented that can be used to find equivalent configuration factors. For exterior elements, relations are given for two coaxial cones connected at their apexes; two truncated coaxial cones connected at the small ends; a cylinder connected to the small end of a circular cone; and a concentric disk normal to the cone axis at the cone apex. For interior surfaces, cases treated are two attached truncated coaxial cones; a cylinder attached to a truncated coaxial cone; and from any interior element in these assemblies to the end disks. 
Bernard, JeanJoseph and Genot, Jeanne, 1971b, "Royonnement thermique des surfaces de revolution," Int. J. Heat Mass Transfer, vol.14, no. 10, pp. 16111619, October.
Contains abridged information from Bernard and Genot (1971a). 
Bien, Darl D., 1966, "Configuration factors for thermal radiation from isothermal inner walls of cones and cylinders," J. Spacecraft Rockets, vol. 3, no. 1, pp. 155156.
Uses known disktodisk factors and configuration factor algebra to derive factors from inside surface of cone, right circular cylinder or frustum of cone to ends. 
Bobco, R.P., 1966, "Radiation from conical surfaces with nonuniform radiosity," AIAA J., vol. 4, no. 3, pp. 544546.
Derives factor from planar element in plane of base of right circular cone to cone interior in form of integral relation. Cone apex is below the element. Numerical results are presented for cone halfangles of 10^{o} and 20^{o}. See Edwards (1969) for discussion of some errors in this reference. 
Boeke, Willem and Wall, Lars, 1976, "Radiative exchange factors in rectangular spaces for the determination of mean radiant temperatures," Build. Serv. Engng., vol. 43, pp. 244 253, March.
Derives analytical expressions for configuration factors between plane rectangles contained within adjoint and opposed planes. Some tabulated factors are given. 
Bonilla, J. M., Àgueda, A., Muñoz, M. A., Vílchez, J. A., and Planas, E., 2019 " Thermal radiation model for dynamic fireballs with shadowing,” Process Safety and Environmental Protection, vol. 128, pp. 372–384., "
Provides graphical and tabular results for vertical differential element on the base plane to a sphere at a height HBabove the base plane, with shadowing by an intermediate finite plane resting on the base plane. 
Bornside, D.E. and Brown, R.A., 1990, "View factor between differingdiameter, coaxial disks blocked by a coaxial cylinder," J. Thermophys. Heat Transfer, vol. 4, no, 3, pp. 414 416, July.
Closedform solution is presented for specified geometry. 
Brewster, M. Quinn, 1992, Thermal Radiative Transfer and Properties, John Wiley & Sons, New York.
Comprehensive radiative transfer text. Appendix B presents algebraic expressions for thirteen common configurations. 
Brockmann, H., 1994, "Analytic angle factors for the radiant interchange among the surface elements of two concentric cylinders," Int. J. Heat Mass Transfer, vol. 37, no. 7, pp. 10951100.
Derives analytic expressions for factors between concentric right circular cylinders of finite equal length. Includes factors between inner and outer cylinders, outer cylinder and itself, ends and inner and outer cylinder, endtoend, and ends of radius less than outer cylinder radius to other finite areas. 
Buraczewski, Czeslaw, 1977, "Contribution to radiation theory configuration factors for rotary combustion chambers," Pol. Akad. Nauk Pr. Inst. Masz Przeplyw, no. 74, pp. 4773 (in Polish.)
Disktodisk factors are used with configuration factor algebra to generate all factors on interior of right circular cone, interior of frustum of right circular cone, interior of finite right circular cylinder, and combinations of cones and frustums of cones. 
Buraczewski, Czeslaw, and Stasiek, Jan, 1983, "Application of generalized Pythagoras theorem to calculation of configuration factors between surfaces of channels of revolution." Int. J. Heat & Fluid Flow, vol. 4, no. 3, pp. 157160, Sept.
Derives closed form relations for coaxial disks of different radii; ring elements on interior of circular cylinders to coaxial disks of the same diameter; ringelement to ringelement on interior of circular cylinder; ring element on interior of cone to coaxial disk; and ringelement to coaxial ring element, both on interior of cone. 
Buschman, Albert Jr. and Pittman, Claud M., 1961, "Configuration factors for exchange of radiant energy between axisymmetrical sections of cylinders, cones, and hemispheres and their bases," NASA TN D944.
Derives many relations for factors between combinations of differential and finite areas on the interior of right circular cylinders, right circular cones and hemispheres. Straightforward analytical integration is used, resulting in lengthy expressions in closed form. One typographical error (Eq. A14 of the reference, where Z^{4} is mistyped as Z^{2}) is corrected in the present catalog for the factor from an element on the interior of a right circular cone to a coaxial disk on the base. Some of the final results are more simply derived using disktodisk factors and configuration factor algebra, particularly the frustumdisk factors. The latter are obtained by Buschman and Pittman through the use of elliptic integrals, and this results in a tedious computation and lengthy expressions. Results are given in tabular form. 
Byrd, L.W., 1993, "View factor algebra for two arbitrary sized nonopposing parallel rectangles," J. Heat Transfer, vol. 115, no. 2, pp. 517518.
Notes that Hamilton and Morgan (1952) has an error for this configuration. 
Campbell, James P. and McConnell, Dudley G., 1968, "Radiantinterchange configuration factors for spherical and conical surfaces to spheres," NASA TN D4457.
Provides extensive graphs and factors between spheres of equal radius, between a sphere and a spherical cap on a sphere of equal radius, and between a sphere and a coaxial cone with apex toward the sphere. Results are for sphere separations of 0 to 10 radii in steps of one radius, and for cap angles of 0 to 90^{o}. Cone results are given for cone semiangles of 15^{o}, 30^{o}, 45^{o} and 60^{o}; cone base radii in the range of 0 to1 sphere radius; and for cone apex to sphere surface separations of 0, 1, 2, 4, 6, 8, and 10 sphere radii. All results were calculated numerically. 
Chekhovskii, I.R.; Sirotkin, V.V.; ChuDunChu, Yu. V.; and Chebanov, V.A., 1979, "Determination of radiative view factors for rectangles of different sizes," High Temp., July (Trans. of Russian original, vol. 17, no. 1, Jan.Feb., 1979)
Configuration factor algebra and integration of analytical expressions are used to find factors between rectangles in parallel planes and in perpendicular planes. Form is more complex than given by Ehlert and Smith or Gross, Spindler and Hahne (1981) 
Chung, B.T.F. and Kermani, M.M., 1989, "Radiation view factors from a finite rectangular plate," J. Heat Transfer, vol. 111, no. 4, pp. 11151117, November.
Derives general relation for configuration factor from tilted differential element to a nonintersecting rectangle, and then uses integration to obtain algebraic factor from a tilted differential strip to a nonintersecting rectangle. (See also Hamilton and Morgan.) The latter factor is then used to generate factors between a rectangular plate and other finite objects. Specifically discussed are the factors from a rectangular plate to a second plate, or to a solid cylinder. These factors involve an integral that is to be evaluated numerically. Particular graphical results are presented for factor from rectangular plate a tilted right triangular plate. 
Chung, B.T.F., Kermani, M.M., and Naraghi, M.H.N., 1984, "A formulation of radiation view factors from conical surfaces," AIAA J., vol. 22, no. 3, pp. 429436, March.
Provides closedform factors between differential elements and cones and frustums of cones, and between cones and various surfaces of revolution that are on a common axis with the cone. 
Chung, B.T.F. and Naraghi, M.H.N., 1982, "A simpler formulation for radiative view factors from spheres to a class of axisymmetric bodies" J. Heat Transfer, vol. 104, no. 1, pp. 201204, February.
Derives simple formulation for exchange between exterior of a sphere and exterior of a coaxial body of revolution. Uses formulation to derive closedform expressions for a number of such geometries, and provides graphical results for some ranges of parameters. Receiving bodies include spheres, spherical caps, cones, ellipsoids and paraboloids. 
Chung, B.T.F. and Naraghi, M.H.N., 1981, "Some exact solutions for radiation view factors from spheres," AIAA J. vol. 19, pp. 10771081, August.
Factors in closed form are derived from the exterior of a sphere to the exterior surfaces of a cylinder, from a sphere to a coaxial differential ring, and from a sphere to a coaxial non intersecting or intersecting disk. Graphical and tabular results are presented for a wide range of parameters. 
Chung, B.T.F. and Sumitra, P.S., 1972, "Radiation shape factors from plane point sources," J. Heat Transfer, vol. 94, no. 3, pp. 328330, August.
Using the method of Feingold and Gupta (1970), authors use idea of surrounding a planar element that has its projection inscribed on the sphere interior. Factors from a planar element to a sphere, to the interior of a cylinder lying on the normal to the element, to an isosceles triangle, to a ring element, and to a disk segment are presented. Also, the factor from a spherical element to a sphere is derived. All results are in closed form. Some graphical results are presented. 
Chung, T.J. and Kim, J.Y., 1982, "Radiation view factors by finite elements," J. Heat Transfer, vol. 104, pp. 792.
Uses finite elements plus Gaussian integration to formulate configuration factors between irregular geometries, and shows accuracy of the method by comparison of numerical calculation with values for known factors between opposed squares and between two planes sharing a common edge at various angles. 
Cox, Richard L., 1976, Radiative heat transfer in arrays of parallel cylinders, Ph.D. Dissertation, Department of Chemical Engineering, University of Tennessee, Knoxville.
Crossedstring method is used to find factors between infinitely long cylinders in equilateral triangular and square arrays. Results are also given for factors when tubes are spirally wrapped with cylinders of smaller diameter. 
Crawford, Martin, 1972, "Configuration factor between two unequal, parallel, coaxial squares," paper no. ASME 72WA/HT16.
Analytical closedform expression is derived for the title geometry. Graphical results and some limiting expressions are given. 
Cunningham, F.G., 1961, "Power input to a small flat plate from a difffusely reflecting sphere, with application to an Earth satellite," NASA TN D710 (corrected copy).
Derives closedform expressions for factor between arbitrarily oriented differential element and sphere. Some graphs of results are given. Also see Hauptmann and Modest (1980). 
Currie, I.G. and Martin, W.W., 1980, "Temperature calculations for shell enclosures subjected to thermal radiation," Computat. Methods Appl. Mech. Engng, vol. 21, no. 1, pp. 75 79, January.
Presents factors between a differential element and a ring element on various combinations of surfaces in an enclosure made up of a coaxial directly opposed cylinder contained completely within the frustum of a cone; i.e., the smallest frustum end is larger than the cylinder diameter. The expressions given as "view factors" are actually the kernels of double integrals that must be carried out to get the final configuration factors between surfaces and ring elements. The integration of the complex algebraic kernels are not carried out in closed form. 
DiLaura, D.L., 1999, "New procedures for calculating diffuse and nondiffuse radiative exchange form factors," ASME Paper C99107, Proc. 33rd. National Heat Transfer Conf., Albuquerque, August.
Casts double area integral describing areaarea configuration factors into a secondorder tensor, which is further transformed into a double contour integral. Several forms of the integrals are derived, some of which have superior convergence characteristics in comparison with standard contour integration. Comparison of computed and analytical results is shown for two squares with a common edge at various enclosed angles. 
Dummer, R.S. and Breckenridge, W.T. Jr., 1963, "Radiation configuration factors catalog," General Dynamics/Astronautics Rept. ERRAN224, February.
Dunkle, R.V., 1963, "Configuration factors for radiant heattransfer calculations involving people," J. Heat Transfer, vol. 85, no. 1, pp. 7176, February.
Measurements using a mechanical formfactor integrator are used to derive empirical relations for factors from points on various surfaces to standing or sitting persons. These are then integrated to find factors from a person to various room walls and the ceiling. The empirical relation for the pointtostandingperson factor has a mean deviation from measured values of 5.6 percent, and a maximum deviation of 19.4 percent. For the seated person, the empirical relation differs from the measured factor by a mean deviation of 6.6 percent, and a maximum deviation of 22 percent. Surfacetositting person results are given in closed form, but standing person results could not be integrated in closed form, so graphical results are presented. 
Edwards, D.K., 1969, "Comment on "Radiation from conical surfaces with nonuniform radiosity," AIAA J., vol. 7, no. 8, pp. 16561659.
Shows that graphs given by Bobco (1966) are in error when planar element is near to cone. Presents revised graphs for cone halfangles of 10^{o} and 20^{o} for various spacings of planar element from cone and a range of dimensionless cone lengths from 1 to 100. 
Eddy, T.L. and Nielsson, G.E., 1988, "Radiation shape factors for channels with varying cross section," J. Heat Transfer, vol. 110, no. 1, pp. 264266, February.
Discusses factors in circular ducts of varying radius r(x) , and formulates the effects of blockage between differential and finite areas on the duct surface separated by a distance x. Extends these results to ducts that transition from circular to rectangular crosssection, and treats cases of circular to rectangular elements, rectangular to circular elements, and rectangular to rectangular elements. See also Modest (1988). 
Ehlert, J. R. and Smith, T.F., 1993, "View Factors for Perpendicular and Parallel, Rectangular Plates," J. Thermophys. Heat Trans., vol. 7, no. 1, pp. 173174.
Simpler forms than Gross, Spindler, and Hahne (1981) for parallel and perpendicular rectangles. TL 900 J68. 
Eichberger, J.I., 1985, "Calculation of geometric configuration factors in an enclosure whose boundary is given by an arbitrary polygon in the plane," Warmeund Stoff bertragung, vol. 19, no. 4, p. 269.
Prescribes a computer algorithm for applying the crossedstring method in twodimensional enclosures with blocking and shading. 
Emery, A.F.; Johansson, O.; Lobo, M.; and Abrous, A, 1991, "A comparative study of methods for computing the diffuse radiation viewfactors for complex structures," J. Heat Transfer, vol. 113, no. 2, pp. 413422, May.
Paper is devoted to studying the accuracy and computation time required to compute configuration factors among various surfaces with and without obstruction. Comparisons are among Monte Carlo, double area integration, a modified contour integration, the hemicube method, and a specialized algorithm. Concludes that Monte Carlo may be the best choice for computing factors as well as gaining insight into the level of computational effort required to achieve a given accuracy. In cases with significant blockage by multiple nonintersecting surfaces, double area integration was efficient, and other methods showed advantage in particular situations as well.(Also see Rushmeier et al.) 
Farnbach, J.S., 1967, "Radiant interchange between spheres: Accuracy of the pointsource approximation," Sandia Laboratories Tech. Memo. SCTM364, Albuquerque, June.
Numerically calculates exact factors between sphere exteriors, and compares results with those obtained by assuming one sphere to be a point source. Range of computed factors and the differences found are shown graphically as a function of separation distance to emitting sphere radius ratio D with receiving to emitting sphere radius ratio R as a parameter. Results are given for R = 1, 2, 5, 10 and 20, with D varying from 2 to 12, 3 to 13, 6 to 16, 11 to 21, and 21 to 31, respectively. 
Feingold, A., 1978, "A new look at radiation configuration factors between disks," J. Heat Transfer, vol. 100, no. 4, pp. 742744, November.
Uses inscribed nonintersecting circular disks on sphere interior to derive disktodisk factors in a simple way. Any two such nonintersecting disks are analyzed. 
Feingold, A., 1966, "Radiantinterchange configuration factors between various selected plane surfaces," Proc. Roy. Soc. London, ser. A, vol. 292, no. 1428, pp. 5160.
Tables of factor values for rectangles with a common edge and at an arbitrary included angle are presented, and show that the tabulated results of Hamilton and Morgan (1952) have considerable error, although the equation from which they are calculated is correct. Discusses effect of truncation and roundoff errors in factor calculation. Uses configuration factor algebra to derive factors between opposed regular polygons, and between the surfaces in a hexagonal honeycomb. Points out that small errors in configuration factor values can far overshadow the effects of assuming diffuse surface properties on radiative transfer calculation. (See also Ambirajan and Venkateshan (1993).) 
Feingold, A. and Gupta, K.G., 1970, "New analytical approach to the evaluation of configuration factors in radiation from spheres and infinitely long cylinders," J. Heat Transfer, vol. 92, no. 1, pp. 6976, February.
Contains discussion of some previous factors that have errors, and presents closedform expressions for a number of factors, particularly for surfaces of revolution, that were previously available only by numerical integration. Notes many cases where factors are valid even for non diffuse originating surface, and points out that, for spheretodisk factors, the solutions are independent of the sphere diameter. Some interesting use of symmetry in these problems allows bypassing of numerical or difficult analytical evaluations. 
Felske, J.D., 1981, Personal communication, August 25.
Unpublished results for the factor between infinite parallel cylinders of unequal diameters. Simple closedform expression is obtained by curve fit, and is within 6 percent of the exact analytical result for all ranges of parameters. 
Felske, J.D., 1978, "Approximate radiation shape factors between spheres," J. Heat Transfer, vol. 100, no. 3, pp. 547548, August.
Develops a closedform approximate solution for spheretosphere factors for all ranges of parameters, accurate to within 5.8 percent at worst, with much smaller error on average, in comparison with exact numerical solution. 
Garot, Catherine and Gendre, Patrick, 1979, "Computation of view factors used in radiant energy exchanges in axisymmetric geometry," In: Numerical methods in thermal problems; Proc. First Int. Conf., pp. 99108, July 26, Pineridge Press, Ltd., Swansea, Wales.
Discusses numerical evaluation of factors in axisymmetric geometries and methods to eliminate impossible factors caused by blockage by intervening surfaces or by orientation of surfaces so their radiating surfaces cannot see oneanother. Formulates limits for various cases. Results are computed for concentric spheres, and compare within 1 percent of analytical result. 
Glicksman, L.R., 1972, "Approximations for configuration factors between cylinders," unpublished report, MIT.
According to Ameri and Felske (1982), this reference contains a closedform approximation for the factor between cylinders of equal radius and finite length. (This is the only reference that the compiler of this bibliography did not have in hand during annotation.) 
Goetze, Dieter and Grosch, Charles B., 1962, "Earthemitted infrared radiation incident a satellite," J. Aerospace Sci., vol. 29, no. 5, pp. 521524.
Provides closedform expressions for configuration factor from exterior of sphere to arbitrarily oriented planar element. Vector algebra is used to simplify arguments of integrals, which are then evaluated. Graphical results for the configuration factor times p are presented for three spheretoelement distances and for various element tilt angles relative to the line connecting the element and the sphere center. 
Grier, Norman T., 1969, "Tabulations of configuration factors between any two spheres and their parts," NASA SP 3050, (420 pp.)
Extensive tables of factors between combinations of spherical caps, patches, bands, and entire spheres. Spheres are of different radii and spacing. Results are obtained by numerical integration in a bispherical coordinate system. Parts of spheres are tabulated by areas that subtend angles in increments of 15^{o}, and for radius ratios from 0.01 to 1 in intervals of 0.1 between 0.1 and 1. Distance between centers of spheres varies from (1.001+r_{2}/r_{1})r_{1} to 100r_{1}, where r_{1} is the radius of the larger sphere. 
Grier, Norman T. and Sommers, Ralph D., 1969, "View factors for toroids and their parts," NASA TN D5006.
Extensive numerically computed results are presented in tables and graphs for factors involving various parts of the surface of a toroid. The factors given are between differential elements and "rim" bands; differential elements and opposed radial segments; finite bands or segments and the entire toroid; and between the toroid and itself. Factors are given for parametric values of bands in increments of 10^{o} width, and of the ratio (toroidal crosssection radius/toroid radius) for 0.01, 0.1, 0.2,...0.8, 0.9, 0.99. See also Sommers and Grier (1969). 
Gross, U., Spindler, K., and Hahne, E., 1981, "Shape factor equations for radiation heat transfer between plane rectangular surfaces of arbitrary position and size with rectangular boundaries," Lett. Heat Mass Transfer, vol. 8, pp. 219227.
Provides a closedform solution to the title factor for the cases of rectangles lying in parallel or perpendicular planes and having parallel or perpendicular edges. The rectangles may be of arbitrary size and location within the planes. Solution is also given for the case when the planes containing the rectangles intersect at an arbitrary angle; however, the solution contains a single integral that must be evaluated numerically. These solutions eliminate the tedious configuration factor algebra that must otherwise be applied to the simple adjacent or opposed rectangle factors to obtain these results, and which may generate large roundoff errors [see Feingold (1966)]. Also see Ehlert and Smith and Byrd. 
Guelzim, A., Souil, J.M., and Vantelon, J.P., 1993, "Suitable configuration factors for radiation calculation concerning tilted flames," J. Heat Transfer, vol. 115, no. 2, pp. 489492, May.
Factors are given in closed form between differential elements in various configurations to tilted cylinders with faces parallel to the base plane. 
Hahne, E. and Bassiouni, M.K., 1980, "The angle factor for radiant interchange within a constant radius cylindrical enclosure," Lett. Heat Mass Transfer, vol. 7, pp. 303309.
Derives factor from onehalf of interior of finitelength right circular cylinder to the opposite half using contour integration, and presents closedform expressions and graphical results. 
Haller, Henry C. and Stockman, Norbert O., 1963, "A note on fintube view factors," J. Heat Transfer, vol. 85, no. 4, pp. 380381, November.
Derives factor from planar element on longitudinal fin to infinitely long tube, and corrects errors in derivation in some earlier published works. 
Hamilton, D.C. and Morgan, W.R., 1952, "Radiantinterchange configuration factors," NASA TN 2836.
One of the classic compilations of configuration factors. Has a few typographical errors [see, e.g., Feingold (1966), Feingold and Gupta (1970), and Byrd.] Catalogs twelve different differential area to finite area factors, five differential strip to finite area factors, and eleven finite area to finite area factors. Some of the factors are generated by configuration factor algebra from a smaller set of calculated or derived factors. This is a pioneering work in cataloguing useful information. 
Hauptmann, E.G., 1968, "Angle factors between a small flat plate and a diffusely radiating sphere," AIAA J., vol. 6, no. 5, pp. 938939, May.
Provides simpler derivation than Cunningham (1961) to find relations for title configuration. 
He, F., Shi, J., Zhou, L., and Li, X., 2018, “Monte Carlo calculation of view factors between some complex surfaces: Rectangular plane and parallel cylinder, rectangular plane and torus, especially coldrolled strip and Wshaped radiant tube in continuous annealing furnace,” Int. J. Thermal Sci., vol. 134, pp. 465474.
Holcomb, R.S. and Lynch, F.E., 1967, "Thermal radiation performance of a finned tube with a reflector," Rept. ORNLTM1613, Oak Ridge National Laboratory.
Hottel, H.C., 1931, "Radiant heat transmission between surfaces separated by nonabsorbing media," Trans. ASME, vol. 53, FSP53196, pp. 265273.
Jakob, Max, 1957, Heat Transfer, vol. 2, John Wiley & Sons, New York.
Kezios, Stothe P. and Wulff, Wolfgang, 1966, "Radiative heat transfer through openings of variable crosssection," Proc. Third Int. Heat Transfer Conf., AIChE, vol. 5, pp. 207 218.
Kuroda, Z. and Munakata, T., 1979, "Mathematical evaluation of the configuration factors between a plane and one or two rows of tubes," Kagaku Sooti (Chemical Apparatus, Japan), pp. 5458, November (in Japanese).
Mathiak, F.U., 1985, "Berechnung von konfigurationsfactoren polygonal berandeter ebener gebiete (Calculation of formfactors for plane areas with polygonal boundaries)," Warme und Stoff bertragung, vol. 19, no. 4, pp. 273278.
Minowa, M., 19961999, "Studies of effective radiation area and radiation configuration factors of a pig," J. Soc. Ag. Structures (Japan); "Part 1: Effective radiation area of a pig based on the surfacemodel," vol. 27, no. 3, (Ser. no. 71), pp. 155161, December, 1996; "Part 2: Configuration factors of a 27 kg pig to rectangular planes on the side, front or rear wall," vol. 29, no. 1, (Ser. no. 77), pp. 18, June, 1998; "Part 3: Configuration factors of a 27 kg pig to rectangular planes on the ceiling or floor," vol. 29, no. 1, (Ser. no. 77), pp. 914, June, 1998; "Part 4: Configuration factors of a 65 kg pig to rectangular planes and comparisons to a 27 kg pig," vol. 29, no. 3, (Ser. no. 79), pp. 137149, December, 1998; "Part 5: Configuration factors of an 88 kg pig to surrounding rectangular planes and configuration factor characteristics of fattening pigs," vol. 30, no. 2, (Ser. no. 82), pp. 145156, Sept., 1999.
Mirhosseini, M. and Saboonchi, A., 2011; “View factor calculation using the Monte Carlo method for a 3D strip element to a circular cylinder,” Int. Communications Heat Mass Transfer, vol. 38, pp. 821826.
Mudan, K.S., 1987 "Geometric View Factors for Thermal Radiation Hazard Assessment," Fire Safety J., vol. 12, pp. 8996.
Naraghi, M.H.N. and Chung, B.T.F., 1982, "Radiation configuration between disks and a class of axisymmetric bodies," J. Heat Transfer, vol. 104, no. 3, pp. 426431, August.
O'Brien, P.F. and Luning, R.B., 1970, "Experimental study of luminous transfer in architectural systems," Illum. Engng, vol. 65, no. 4, pp. 193198, April.
Siegel, Robert and Howell, John R., 2010, Thermal Radiation Heat Transfer, 6th ed., Taylor and FrancisHemisphere, Washington.
Sparrow, E.M., 1962, "A new and simpler formulation for radiative angle factors," J. Heat Transfer, vol. 85, no. 2, pp. 8188, May.
Sparrow, E.M. and Heinisch, R.P., 1970, "The normal emittance of circular cylindrical cavities," Appl. Opt., vol. 9, no. 11, pp. 25692572, November.
Sparrow, E.M.; Miller, G.B.; and Jonsson, V.K., 1962, "Radiative effectiveness of annular finned space radiators, including mutual irradiation between radiator elements," J. Aerospace Sci., vol. 29, no. 11, pp. 12911299.

Toups, K.A., 1965, "A general computer program for the determination of radiant interchange configuration and form factors CONFACI," North American Aviation, Inc. Rept. SID65 10431 (NASA CR65256), October.
Tripp, W.; Hwang, C.; and Crank, R.E., 1962, "Radiation shape factors for plane surfaces and spheres, circles, or cylinders" (Spec. Rept. 16) Kansas State Univ. Bull., vol. 46, no. 4.
Derives closedform solution for factor from sphere to rectangle with one corner on and normal to sphere axis. Derives relationships for factor from outside of right circular cylinder to right triangle in base plane with one vertex on axis, and from disk to right triangle in parallel plane with one vertex on disk axis. The latter two relations contain one integral that is evaluated numerically. Graphs are presented of all results. Examples of using configuration factor algebra to generate factors from spheres, cylinders, and disks to displaced planar areas are presented. 
Tseng, J.W.C. and Strieder, W., 1990, "View factors from wall to random dispersed solid bed transport," J. Heat Transfer, vol. 112, no. 3, pp. 816819.
Derives relations in integral form for the configuration factor from a plane surface to a randomly packed bed of spheres of uniform diameter as a function of bed thickness and void fraction. Provide similar results for factor from a plane wall to a bed of randomly packed cylinders of equal diameter that are parallel to the wall and to each other. Results for the latter case are compared with results for a plane wall to cylinders arranged in staggered rows with equal spacing between cylinder spacing (pitch). 
Tso, C.P. and Mahulikar, S.P., 1999, "View factors between finite length rings on an interior cylindrical shell," AIAA J. Thermophysics Heat Transfer, vol. 13, no. 3, pp. 375379.
Uses configuration factor algebra with the factors of Brockmann to provide factors among rings on the interior surface of an outer cylinder in the presence of a central concentric cylinder. 
Usiskin, C.M. and Siegel, R., 1960, "Thermal radiation from a cylindrical enclosure with specified wall heat flux," J. Heat Transfer, vol. 82, no. 4, pp. 369374.
Uses factor from ring element on inside of cylinder to disk in thermal analysis. 
van Leersum, J., 1989, "A method for determining a consistent set of radiation view factors from a set generated by a nonexact method," Int. J. Heat Fluid Flow, vol. 10, no. 1, p 83.
Presents compatibility requirements for set of factors needed for enclosure analysis that will meet the requirement of overall energy conservation for the enclosure. 
Wakao, Noriaki; Kato, Koichi; and Furuya, Nobuo, 1969, "View factor between two hemispheres in contact and radiation heat transfer coefficient in packed beds," Int. J. Heat Mass Transfer, vol. 12, pp. 118120.
Numerical integration of analytical relation for factor between differential element on the surface of one hemisphere to a second coaxial hemisphere is used to find hemispherehemisphere factors. Hemisphere bases are parallel. Results are presented for radius ratios of 1 to 10. 
Wang, Joseph C.Y.; Lin, Sui; Lee, PaiMow; Dai, WeiLiang; and Lou, YouShi, 1986, "Radiantinterchange configuration factors inside segments of frustum enclosures of right circular cones," Int. Comm. Heat Mass Transfer, vol. 13, pp. 423432.
Presents numerically computed figures for factors between segments on parallel disks of different radii and between an isosceles trapezoid and the segment of a disk that intersects the trapezoid at right angle. 
Watts, R.G., 1965, "Radiant heat transfer to Earth satellites," J. Heat Transfer, vol. 87, no. 3, pp. 369373, August.
Derives relations for factors from large sphere to small sphere, small hemisphere, small cylinder, or small ellipsoid. "Small" means that the angle between the line connecting any point on the small body and the sphere center and the line from the same point to an arbitrary point on the sphere can be considered invariant over the receiving body. Closed forms are given for the receiving body being a sphere or hemisphere. Numerical evaluation is used in other cases. All results are a factor of 4 times larger than for the configuration factor as used in this catalog because the sphere surface area is taken as p r^{2} rather than 4p r^{2}. 
Wiebelt, John A., 1966, Engineering Radiation Heat Transfer, Holt, Rinehart & Winston, New York.
Contains catalog of factors excerpted from Hamilton and Morgan (1952), and a chapter on configuration factors. 
Wiebelt, J.A. and Ruo, S.Y., 1963, "Radiantinterchange configuration factors for finite right circular cylinder to rectangular plane," Int. J. Heat Mass Transfer, vol. 6, no. 2, pp. 143146.
Numerically computed factors are presented as graphs for various parametric values of rectangle size and spacing. Factors are judged by authors to have possible errors of approximately 5 percent. 
Wong, H.Y., 1977, Handbook of Essential Formulae and Data on Heat Transfer for Engineers, Longman Group, London.
Catalog of 33 factors for common geometries given mostly as closedform expressions. 
Yang, L., Chen, W., Luo, L., and Zhao, X., 2014, "Calculation of Radiation Heat Transfer View Factors Among Fuel Rod Bundles Based on CFD Method," Annals of Nuclear Energy, vol. 71, pp. 462466.
Computes factors using both the discrete ordinates and discrete transfer methods in a commercial CFD code. Compares results with previous analytical expressions for simple parallel cylinder arrays and presents numerical results for one case of a control rod surrounded by fuel rods of different diameter. 
Yarbrough, David W. and Lee, ChonLin, 1984, "Monte Carlo calculation of radiation view factors," in Integral Methods in Sciences and Engineering, Payne, Fred R. et al., eds, Harper and Rowe/Hemisphere, New York, pp. 563574.
Uses Monte Carlo to compute factors for various simple geometries, and compares with analytical solutions. Presents original results for strip on finite length rectangular fin to parallel cylinder and from cylinder of finite length placed at focus of parallel paraboloid. All results are calculated to be within +/ 5 percent. 
Yuen, W.W., 1980, "A simplified approach to shapefactor calculation between threedimensional planar objects," AIAA J. Heat Transfer, vol. 102, no. 2, pp. 386388.
Derives general relation for factor between arbitrarily arranged general polygons based on contour integration. Presents some numerical results. 
Send mail to: John Howell
University of Texas at Austin