Journal of Northeastern University(Natural Science) ›› 2025, Vol. 46 ›› Issue (6): 32-39.DOI: 10.12068/j.issn.1005-3026.2025.20230325

• Materials & Metallurgy • Previous Articles     Next Articles

Improved Algorithm for Radiation Direct Exchange Area Based on Duffy Transformation to Eliminate Effects of “Singularities”

Hao-zhe ZHANG1,2, Guo-jun LI1,2, Lin-yang WEI1,2, Zhi YI1,2   

  1. 1.School of Metallurgy,Northeastern University,Shenyang 110819,China
    2.Liaoning Engineering Research Center of Process Industry Energy Saving and Low-Carbon Technologies,Northeastern University,Shenyang 110819,China. Corresponding author: LI Guo-jun,E-mail: ligj@mail. neu. edu. cn
  • Received:2023-12-07 Online:2025-06-15 Published:2025-09-01

Abstract:

When the integral method is used to solve the direct exchange area (DEA) of radiation in the zone method, the relative error is large due to the existence of “singularities”, and it usually requires a lot of computing time and has little effect to improve the calculation accuracy at “singularities”. Therefore, based on Duffy transformation method, the Duffy transformation integral formula is derived to eliminate the influence of the singularity on the calculation of DEA. The improved method and the direct Gaussian integral (DGI) method are used to solve the DEA of radiation in a two-dimensional square cavity. The results show that the completeness verification errors of the gas-zone and the surface-zone can be decreased from 3.73% and 6.70% to (4.88×10-4)% and (2.98×10-5)% respectively in the same calculation time by applying Duffy transform. In the case of the same calculation accuracy, the maximum difference in calculation time between them is 13 693 times. Therefore, the improved algorithm has significant advantages in computation speed and accuracy.

Key words: Duffy transformation, singularity problem, direct exchange area(DEA), zone method, radiative heat transfer

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