The Nonrecursive Plating Algorithm (NRPA) for Computing the Total Radiative Exchange Factors in Enclosures

REFERENCES

• E. B. Becker , G. F. Carey , and J. T. Oden , Finite Elements: An Introduction , vol. 1 , Prentice Hall , Englewood Cliffs , NJ , 1981 .
   Google Scholar
• M. M. Raaque , D. E. Klein , and J. R. Howell , Finite Elements Solution of Radiative Heat Transfer in a Two-Dimensional Rectangular Enclosure with Gray Participating Media , J. Heat Transfer , vol. 105 , pp. 933 – 934 , 1983 .
   Web of Science ®Google Scholar
• H. C. Hottel and E. S. Cohen , Radiant Heat Exchange in a Gas-Filled Enclosure: Allowance for Nonuniformity of Gas Tempereature , AIChE J. , vol. 4 , pp. 3 – 14 , 1983 .
   Google Scholar
• James J. Noble , The Zone Method: Explicit Matrix Relations for Total Exchange Areas, Int. J. Heat Mass Tranfer , vol. 18, pp. 1153–1169, 1965.
   Google Scholar
• W. W. Yuen and E. E. Takara , Development of a Generalized Zonal Method for the Analysis of Radiative Heat Transfer in Absorbing and Anisotropically Scattering Media , in K. Vafai and J. L. S. Chen (eds.), Numerical Heat Transfer , ASME HTD-vol. 130 , pp. 123 – 132 , 1990 .
   Google Scholar
• W. W. Yuen , The Multiple Absorption Coefficient Zonal Method (MACZM), an Efficient Computational Approach for the Analysis of Radiative Heat Transfer in Multidimensional Inhomogeneous Nongray Media , Numer. Heat Transfer B , vol. 49 , pp. 89 – 103 , 2006 .
   Web of Science ®Google Scholar
• W. W. Yuen , Definition and Evaluation of Mean Beam Lengths for Applications in Multidimensional Radiative Heat Transfer: A Mathematically Self-consistent Approach , J. Heat Transfer , vol. 130 , 114507 , 2008 .
   Web of Science ®Google Scholar
• B. Ghannam , M. Nemer , K. El Khoury , and W. Yuen , Experimental Validation of the Multiple Absorption Coefficient Zonal Method (MACZM) in a Dynamic Modeling of a Steel Rehating Furnace , Numer. Heat Transfer, A , vol. 58 , pp. 1 – 19 , 2010 .
   Web of Science ®Google Scholar
• N. Metropolis and S. Ulam , The Monte Carlo Method , J. Am. Stat. Assoc. , vol. 44 , nos. 247 , pp. 335 – 341 , 1949 .
   PubMed Web of Science ®Google Scholar
• J. R. Howell , The Monte Carlo Method in Radiative Heat Transfer , J. Heat Transfer , vol. 120 , pp. 547 – 560 , 1998 .
   Web of Science ®Google Scholar
• K. D. Lathrop , Use of Discrete Ordinate Methods for Solution of Photon Transport Problems , Nucl. Sci. Eng. , vol. 24 , pp. 391 – 388 , 1966 .
   Google Scholar
• M. Krook , On the Solution of Equations of Tranfer, I , Astrophys. J. , vol. 122 , pp. 488 – 497 , 1955 .
   Web of Science ®Google Scholar
• C. H. Hoyt , Radiant-Heat Transmission , in H. McAdams William (ed.), Heat Transmission, , 3rd ed. , chap. 4 , McGraw-Hill , New York , 1954 .
   Google Scholar
• G. Poljak , Analysis of Heat Interchange by Radiation between Diffuse Surfaces , Tech. Phys. USSR , vol. 1 , pp. 555 – 590 , 1935 .
   Google Scholar
• Y. Y. Jiang , A Two-Step Strategy for Numerical Simulation of Radiative Transfer with Anisotropic Scattering and Reflection , J. Quant. Spectrosc. Radiat. Transfer , vol. 109 , pp. 636 – 649 , 2008 .
   Web of Science ®Google Scholar
• B. Gebhart , Heat Transfer, , 2d ed. , pp. 150 – 163 , McGraw-Hill , New York , 1971 .
   Google Scholar
• B. Gebhart , Surface Temperature Calculations in Radiant Surroundings of Arbitrary Complexity Gray, Diffuse Radiation , Int. J. Heat Mass Transfer , vol. 3 , pp. 341 – 346 , 1961 .
   Google Scholar
• S. Maruyama and Y. Takeuchi , A Fast Method of Radiative Heat Transfer Analysis between Arbitrary Three-Dimensional Bodies Composed of Specular and Diffuse Surfaces , Numer. Heat Transfer A , vol. 39 , pp. 761 – 776 , 2001 .
   Web of Science ®Google Scholar
• D. K. Edwards , The Plating Algorithm for Radiation Script-F Transfer Factor , ASME J. Heat Transfer , vol. 108 , pp. 237 – 238 , 1986 .
   Web of Science ®Google Scholar
• G. El Hitti , M. Nemer , and K. El Khoury , Reducing CPU Time for Radiative Exchange and Transient Heat Transfer Analysis Using Zone Method , Numer. Heat Transfer B , vol. 56 , pp. 23 – 37 , 2009 .
   Web of Science ®Google Scholar
• G. El Hitti , M. Nemer , K. El Khoury , and D. Clodic , The Replating Algorithm for Radiation Total Exchange Area Calculation , Numer. Heat Transfer B , vol. 57 , pp. 110 – 125 , 2010 .
   Web of Science ®Google Scholar
• V. Strassen ., Gaussian Elimination is Not Optimal , Numer. Math. , vol. 13 , pp. 354 – 356 , 1969 .
   Web of Science ®Google Scholar
• S. Winograd . On Multiplication of 2 × 2 Matrices , Linear Algebra Appl. , vol. 4 , pp. 381 – 388 , 1971 .
   Google Scholar
• D. Coppersmith and S. Winograd , Matrix Multiplicaiton via Arithmetic Progressions , J. Symbolic Comput. , vol. 9 , pp. 251 – 280 , 1990 .
   Web of Science ®Google Scholar
• H. Cohn and C. Umans , A Group-Theoretic Approach to Fast Matrix Multiplication, in Foundations of Computer Science, 26th Annual IEEE Symposiumon, Cambridge, MA, IEE Computer Society, pp. 438-449 , 2003 .
   Google Scholar
• H. Cohn , R. Kleinberg , B. Szegedy , and C. Umans , Group-Theroretic Algorithms for Matric Multiplication, in Foundations of Computer Science, 46th Annual IEEE Symp. , pp. 23–25, 2005.
   Google Scholar
• W. Cai and K. El Khoury , Radiative Heat Transfer Model in Industrial Enclosures by Ray-Tracing, in Proc. 4th Int. Symp. Heat Transfer, Beijing, China , 1996 .
   Google Scholar
• J. Laderman , V. Y. Pan , and H. X. Sha , On Practical Algorithms for Accelerated Matrix Multiplication , Linear Algebra Appl. , vol. 162 , pp. 557 – 588 , 1992 .
   Web of Science ®Google Scholar
• I. Kaporin , A Practical Algorithm for Faster Matrix Multiplication , J. Numer. Linear Algebra Appl. , vol. 6 , no. 8 , pp. 469 – 510 , 1999 .
   Google Scholar
• I. Kaporin , The Aggregation and Cancellation Techniques as a Practical Tool for Faster Matrix Multiplication , J. Theor. Comput. Sci. , vol. 315 , no. 2–3 , pp. 469 – 510 , 2004 .
   Web of Science ®Google Scholar
• G. El Hitti , M. Nemer , and K. El Khoury , Transient Radiation and Conduction Heat Transfer in Glass Sheets by the Thin Layer Approximation , J. Heat Transfer , vol. 132 (2) , pp. 204 – 210 , 2011 .
   Google Scholar
• B. Ghannam , M. Nemer , K. El Khoury , and W. Yuen , Experimental Validation of the Multiple Absorption Coefficient Zonal Method (MACZM) in a Dynamic Modeling of a Steel Reheating Furnace , Numerical Heat Transfer, A , vol. 58 , pp. 1 – 19 , 2010 .
   Web of Science ®Google Scholar
• B. Ghannam , M. Nemer , K. El Khoury , and W. Yuen , An Efficient CPU-GPU Implementation of the Multiple Absorption Coefficient Zonal Method (MACZM) , Numer. Heat Transfer, B , vol. 32 , no. 6 , pp. 439 – 461 , 2012 .
   Google Scholar
• NVIDIA, CUDA Technology, http://www.nvidia.com/CUDA , 2007 .
   Google Scholar
• David B. Kirk and Wen-mei W. Hwu , Programming Massively Parallel Processors: A Hands-on Approach (Applications of GPU Computing Series) , Elsevier , 2010 .
   Google Scholar
• The OpenMP website, www.openmp.org.
   Google Scholar