394
5 Numerical Models for Pebble-Bed Heat Transfer
36. Rycroft, Chris H. 2009. Voro++ a three-dimensional voronoi cell library in c++. Chaos 19
(4): 041111.
37. Feingold, A., and K.G. Gupta. 1970. New analytical approach to the evaluation of configuration factors in radiation from spheres and infinitely long cylinders. Journal of Heat Transfer
92 (1): 69.
38. Niessen, H., and S. Ball. 2000. Heat transport and afterheat removal for gas cooled reactors
under accident conditions. IAEA-TECDOC-1163. International Atomic Energy Agency.
39. Yanhua Zheng, J., E. Lapins, L. Shi Laurien, and Z. Zhang. 2012. Thermal hydraulic analysis of a pebble-bed modular high temperature gas-cooled reactor with attica3d and thermix
codes. Nuclear Engineering and Design 246: 286–297. Selected and expanded papers from
International Conference Nuclear Energy for New Europe, Sept 6–9. Slovenia: Portoro.
40. Howell, J.R. 1982. A catalog of radiation configuration factors. McGraw-Hill.
41. Tanaka, S. 2008. Exact view-factor analysis for radiation from a sphere to another sphere
linked with a coaxial cylinder. Review of the Faculty of Maritime Sciences 5: 85–92.
42. Walton, G.N. 2002. Calculation of obstructed view factors by adaptive integration. Gaithersburg: National Institute of Standards and Technology.
43. Feng, Y.T., and K. Han. 2012. An accurate evaluation of geometric view factors for modelling
radiative heat transfer in randomly packed beds of equally sized spheres. International Journal
of Heat & Mass Transfer 55 (23–24): 6374–6383.
44. Jamesd, Maltby, and Burns Patrickj. 1991. Performance, accuracy, and convergence in a threedimensional monte carlo radiative heat transfer simulation. Numerical Heat Transfer Part B
Fundamentals 19 (2): 191–209.
45. Walker, T. 2014. The use of primitives in the calculation of radiative view factors. Sydney:
University of Sydney.
46. Singh, B.P., and M. Kaviany. 1994. Effect of solid conductivity on radiative heat transfer in
packed beds. International Journal of Heat & Mass Transfer 37 (16): 1159–1168.
47. Van Antwerpen, W., P.G. Rousseau, and Toit C.G. Du. 2012. Multi-sphere unit cell model
to calculate the effective thermal conductivity in packed pebble beds of mono-sized spheres.
Nuclear Engineering & Design 247: 183–201.
48. Nguyen, V.D., C. Cogné, M. Guessasma, E. Bellenger, and J. Fortin. 2011. Discrete modeling
of granular flow with thermal transfer: Application to the discharge of silos. Applied Thermal
Engineering 29 (8): 1846–1853.
49. Gusarov, A.V. 2010. Model of radiative heat transfer in heterogeneous multiphase media.
Physical Review B Condensed Matter 81 (6): 064202.
50. Gilbert, E.N. 1962. Random subdivisions of space into crystals. Annals of Mathematical
Statistics 33 (3): 958–972.
51. Moller, J. 1989. Random tessellations in RD. Advances in Applied Probability 21 (1): 37–73.
52. Lucarini, V. 2009. Three-dimensional random voronoi tessellations: From cubic crystal lattices to poisson point processes. Journal of Statistical Physics 134: 185–206.
53. Yang, R.Y., R.P. Zou, and A.B. Yu. 2002. Voronoi tessellation of the packing of fine uniform
spheres. Physical Review E Statistical, Nonlinear, and Soft Matter Physics 65 (4 Pt 1): 041302.
54. Cheng, G.J., and A.B. Yu. 2013. Particle scale evaluation of the effective thermal conductivity from the structure of a packed bed: Radiation heat transfer. Industrial & Engineering
Chemistry Research 52 (34): 12202–12211.
55. De Beer, M., C.G. Du Toit, and P.G. Rousseau. 2017. A methodology to investigate the
contribution of conduction and radiation heat transfer to the effective thermal conductivity of
packed graphite pebble beds, including the wall effect. Nuclear Engineering & Design 314:
67–81.
56. Talukdar, Prabal, and Subhash C. Mishra. 2003. Transient conduction-radiation interaction in
a planar packed bed with variable porosity. Numerical Heat Transfer 44 (3): 281–297.
57. Jhy-Wen, Wu, and Hsin-Sen Chu. 1999. Combined conduction and radiation heat transfer in
plane-parallel packed beds with variable porosity. Journal of Quantitative Spectroscopy and
Radiative Transfer 61 (4): 443–452.
5 Numerical Models for Pebble-Bed Heat Transfer
36. Rycroft, Chris H. 2009. Voro++ a three-dimensional voronoi cell library in c++. Chaos 19
(4): 041111.
37. Feingold, A., and K.G. Gupta. 1970. New analytical approach to the evaluation of configuration factors in radiation from spheres and infinitely long cylinders. Journal of Heat Transfer
92 (1): 69.
38. Niessen, H., and S. Ball. 2000. Heat transport and afterheat removal for gas cooled reactors
under accident conditions. IAEA-TECDOC-1163. International Atomic Energy Agency.
39. Yanhua Zheng, J., E. Lapins, L. Shi Laurien, and Z. Zhang. 2012. Thermal hydraulic analysis of a pebble-bed modular high temperature gas-cooled reactor with attica3d and thermix
codes. Nuclear Engineering and Design 246: 286–297. Selected and expanded papers from
International Conference Nuclear Energy for New Europe, Sept 6–9. Slovenia: Portoro.
40. Howell, J.R. 1982. A catalog of radiation configuration factors. McGraw-Hill.
41. Tanaka, S. 2008. Exact view-factor analysis for radiation from a sphere to another sphere
linked with a coaxial cylinder. Review of the Faculty of Maritime Sciences 5: 85–92.
42. Walton, G.N. 2002. Calculation of obstructed view factors by adaptive integration. Gaithersburg: National Institute of Standards and Technology.
43. Feng, Y.T., and K. Han. 2012. An accurate evaluation of geometric view factors for modelling
radiative heat transfer in randomly packed beds of equally sized spheres. International Journal
of Heat & Mass Transfer 55 (23–24): 6374–6383.
44. Jamesd, Maltby, and Burns Patrickj. 1991. Performance, accuracy, and convergence in a threedimensional monte carlo radiative heat transfer simulation. Numerical Heat Transfer Part B
Fundamentals 19 (2): 191–209.
45. Walker, T. 2014. The use of primitives in the calculation of radiative view factors. Sydney:
University of Sydney.
46. Singh, B.P., and M. Kaviany. 1994. Effect of solid conductivity on radiative heat transfer in
packed beds. International Journal of Heat & Mass Transfer 37 (16): 1159–1168.
47. Van Antwerpen, W., P.G. Rousseau, and Toit C.G. Du. 2012. Multi-sphere unit cell model
to calculate the effective thermal conductivity in packed pebble beds of mono-sized spheres.
Nuclear Engineering & Design 247: 183–201.
48. Nguyen, V.D., C. Cogné, M. Guessasma, E. Bellenger, and J. Fortin. 2011. Discrete modeling
of granular flow with thermal transfer: Application to the discharge of silos. Applied Thermal
Engineering 29 (8): 1846–1853.
49. Gusarov, A.V. 2010. Model of radiative heat transfer in heterogeneous multiphase media.
Physical Review B Condensed Matter 81 (6): 064202.
50. Gilbert, E.N. 1962. Random subdivisions of space into crystals. Annals of Mathematical
Statistics 33 (3): 958–972.
51. Moller, J. 1989. Random tessellations in RD. Advances in Applied Probability 21 (1): 37–73.
52. Lucarini, V. 2009. Three-dimensional random voronoi tessellations: From cubic crystal lattices to poisson point processes. Journal of Statistical Physics 134: 185–206.
53. Yang, R.Y., R.P. Zou, and A.B. Yu. 2002. Voronoi tessellation of the packing of fine uniform
spheres. Physical Review E Statistical, Nonlinear, and Soft Matter Physics 65 (4 Pt 1): 041302.
54. Cheng, G.J., and A.B. Yu. 2013. Particle scale evaluation of the effective thermal conductivity from the structure of a packed bed: Radiation heat transfer. Industrial & Engineering
Chemistry Research 52 (34): 12202–12211.
55. De Beer, M., C.G. Du Toit, and P.G. Rousseau. 2017. A methodology to investigate the
contribution of conduction and radiation heat transfer to the effective thermal conductivity of
packed graphite pebble beds, including the wall effect. Nuclear Engineering & Design 314:
67–81.
56. Talukdar, Prabal, and Subhash C. Mishra. 2003. Transient conduction-radiation interaction in
a planar packed bed with variable porosity. Numerical Heat Transfer 44 (3): 281–297.
57. Jhy-Wen, Wu, and Hsin-Sen Chu. 1999. Combined conduction and radiation heat transfer in
plane-parallel packed beds with variable porosity. Journal of Quantitative Spectroscopy and
Radiative Transfer 61 (4): 443–452.