{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T19:11:27Z","timestamp":1772737887136,"version":"3.50.1"},"reference-count":26,"publisher":"ASME International","issue":"1","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[1997,2,1]]},"abstract":"<jats:p>The discrete transfer method, often employed to calculate radiative heat transfer in combustion chambers, is not conservative. The reason for this behavior is examined and a conservative formulation is proposed and evaluated. A simple treatment of isotropic scattering media is also presented. The original and the conservative formulation of the method are applied to two-dimensional and three-dimensional enclosures containing a participating medium. It is shown that the accuracy of the original and the conservative formulation is very similar, but the proposed formulation has the advantage of ensuring energy conservation.<\/jats:p>","DOI":"10.1115\/1.2824076","type":"journal-article","created":{"date-parts":[[2008,2,25]],"date-time":"2008-02-25T23:46:03Z","timestamp":1203983163000},"page":"118-128","update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":60,"title":["A Conservative Formulation of the Discrete Transfer Method"],"prefix":"10.1115","volume":"119","author":[{"given":"P. J.","family":"Coelho","sequence":"first","affiliation":[{"name":"Mechanical Engineering Department, Instituto Superior Te\u00b4cnico, Technical University of Lisbon, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal"}]},{"given":"M. G.","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, Instituto Superior Te\u00b4cnico, Technical University of Lisbon, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal"}]}],"member":"33","published-online":{"date-parts":[[1997,2,1]]},"reference":[{"key":"2019100320385339000_r1","doi-asserted-by":"crossref","unstructured":"Boyd, R. K., and Kent, J. H., 1986, \u201cThree-dimensional Furnace Computer Modelling,\u201d 21st Symposium (Int.) on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 265\u2013274.","DOI":"10.1016\/S0082-0784(88)80254-6"},{"key":"2019100320385339000_r2","unstructured":"Bressloff, N. W., Moss, J. B., and Rubini, P. A., 1995, \u201cApplication of a New Weighting Set for the Discrete Transfer Radiation Model,\u201d Proceedings, 3rd European Conference on Industrial Furnaces and Boilers, Lisbon, Portugal."},{"key":"2019100320385339000_r3","unstructured":"Carlson, B. G., and Lathrop, K. 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S., and PatankarS., 1993, \u201cRay Effect and False Scattering in the Discrete Ordinates Method,\u201d Numerical Heat Transfer, Part B, Vol. 24, pp. 373\u2013389.","DOI":"10.1080\/10407799308955899"},{"key":"2019100320385339000_r7","doi-asserted-by":"crossref","unstructured":"Chai\n              J. C.\n            , LeeH. S., and PatankarS. V., 1994, \u201cFinite Volume Method for Radiation Heat Transfer,\u201d Journal of Thermophysics and Heat Transfer, Vol. 8, pp. 419\u2013425.","DOI":"10.2514\/3.559"},{"key":"2019100320385339000_r8","unstructured":"Coelho, M. G., Gonc\u00b8alves, J. M., and Carvalho, M. G., 1995, \u201cA Comparative Study of Radiation Models for Coupled Fluid Flow\/Heat Transfer Problems,\u201d Proceedings, 9th International Conference for Numerical Methods in Thermal Problems, Vol. IX, Part 1, R. W. Lewis and P. 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R., 1968, \u201cApplication of Monte Carlo to Heat Transfer Problems,\u201d Advances in Heat Transfer, J. P. Hartnett and T. F. Irvine, eds., Vol. 5, Academic Press, New York.","DOI":"10.1016\/S0065-2717(08)70128-X"},{"key":"2019100320385339000_r16","doi-asserted-by":"crossref","unstructured":"Jamaluddin\n              A. S.\n            , and SmithP. J., 1988, \u201cPredicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinates Method,\u201d Combustion Science and Technology, Vol. 59, pp. 321\u2013340.","DOI":"10.1080\/00102208808947103"},{"key":"2019100320385339000_r17","doi-asserted-by":"crossref","unstructured":"Lathrop\n              K. D.\n            \n          , 1968, \u201cRay Effects in Discrete Ordinates Equations,\u201d Nuclear Science and Engineering, Vol. 32, pp. 357\u2013369.","DOI":"10.13182\/NSE68-4"},{"key":"2019100320385339000_r18","doi-asserted-by":"crossref","unstructured":"Lockwood, F. C., and Shah, N. 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