This paper presents a special transformation of variables to reduce a double integral into three single integrals and its use for calculating Direct Exchange Areas (DEA) in Zonal method. This technique was originally presented for calculation of DEA using a uniform zone system in a cylindrical enclosure. However, non-uniform zones are needed for applications with large thermal gradients. Thus we extended this technique to calculate the DEA for non-uniform zones in an axisymmetrical cylinder system. At least six times of saving in computational time was observed in calculating DEA compared with cases without transforming of variables. It is shown that accuracy and efficiency of estimation of radiation heat flux is improved when using a non-uniform zone system. Reasonable accuracy of all DEA are calculated without resorting to the conservative equations. Results compared well with analytical solutions and numerical results of previous researchers. A brief discussion of its application in calculating DEA in a 3-D rectangular enclosure is also provided.

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