International Scientific Journal


The radiative heat transfer in a high temperature granular bed of binary-size mixture was explored in this paper. The effective view factor between particles decreases exponentially with the increase in particle interval, increases with the increase in the size of the absorption particle but is hardly affected by the volume ratio of the mixture. The effective thermal conductivity of granular bed was further deduced basing on the characteristic of the effective view factor. It is indicated that the thermal conductivity is proportional to the particle size and temperature cubed, and increases with the increase in the particle size ratio and volume ratio. Finally, modified calculation correlations of the effective view factor and effective thermal conductivity were developed for binary-size bed based on the simulation results, and good accuracy of less than 0.01 and 10% had been achieved, respectively.
PAPER REVISED: 2022-04-20
PAPER ACCEPTED: 2022-04-28
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 6, PAGES [5095 - 5108]
  1. Antwerpen, W. V., et al., A Review of Correlations to Model the Packing Structure and Effective Thermal Conductivity in Packed Beds of Mono-sized Spherical Particles, Nuclear Engineering & Design, 240 (2010), 7, pp. 1803-1818
  2. Zhang, Z., et al., Design Aspects of The Chinese Modular High-Temperature Gas-Cooled Reactor HTR-PM, Nuclear Engineering and Design, 236 (2006), 5-6, pp. 485-490
  3. Liu, J., et al., Thermal Energy Recovery from High-Temperature Blast Furnace Slag Particles, International Communications in Heat and Mass Transfer, 1 (2015), 69, pp. 23-28
  4. Stenberg, V., et al., Evaluation of Bed-To-Tube Surface Heat Transfer Coefficient for A Horizontal Tube in Bubbling Fluidized Bed at High Temperature, Powder Technology, 352 (2019), pp. 488-500
  5. Pitso, M. L., Characterisation of Long Range Radiation Heat Transfer in Packed Pebble Beds, Ph. D. thesis, North-West University, Evanston, USA, 2011
  6. Felske, J. D., Approximate Radiation Shape Factors Between Two Spheres, Journal of Heat Transfer, 100 (1978), 3, pp. 547-548
  7. Howell, J. R., The Monte Carlo Method in Radiative Heat Transfer, Journal of Heat Transfer, 120 (1998), 3, pp. 547-560
  8. Wu, H., et al., Numerical Simulation of Heat Transfer in Packed Pebble Beds: CFD-DEM Coupled with Particle Thermal Radiation, International Journal of Heat and Mass Transfer, 110 (2017), pp. 393-405
  9. Wu, H., et al., Analysis and Evaluations of Four Models of Thermal Radiation for Densely Packed Granular Systems, Chemical Engineering Science, 211 (2020). p. 115309
  10. Chen, J. C., et al., Radiant Heat Transfer in Packed Beds, AIChE Journal, 9 (1963), 1, pp. 35-41
  11. Argo, W. B., Smith J. M., Heat Transfer in Packed Beds, Chemical Engineering Progress, 49 (1953), pp. 443-451
  12. Wakao, N., Kato, K., Effective Thermal Conductivity of Packed Beds, Journal of Chemical Engineering of Japan, 2 (1969), 1, pp. 24-33
  13. Kasparek, G., Vortmeyer, D., Wärmestrahlung in Schüttungen aus Kugeln Mit Vernachlässigbarem Wärmeleitwiderstand, Wärme-und Stoffübertragung, 9 (1976), 2, pp. 117-128
  14. Vortmeyer, D., Radiation in packed solids, Proceedings, 6th International Heat Transfer Conf., Toronto, Canada, 1978, Vol. 6, pp. 525-529
  15. Antwerpen, W. V., et al., Multi-sphere Unit Cell Model to Calculate the Effective Thermal Conductivity in Packed Pebble Beds of Mono-sized Spheres, Nuclear Engineering & Design, 247 (2012), 6, pp. 183-201
  16. Johnson, E., et al., A Monte Carlo Method to Solve for Radiative Effective Thermal Conductivity for Particle Beds of Various Solid Fractions and Emissivities, Journal of Quantitative Spectroscopy and Radiative Transfer, 250 (2020), pp. 107014
  17. Zhou, J., et al., A Boundary Element Method for Evaluation of the Effective Thermal Conductivity of Packed Beds, Journal of Heat Transfer, 129 (2007), pp. 363-371
  18. Singh, B. P., Kaviany M., Effect of Solid Conductivity on Radiative Heat Transfer in Packed Beds, International Journal of Heat & Mass Transfer, 37 (1994), 16, p. 1159-1168
  19. Chen, L., et al., Effective Thermal Property Estimation of Unitary Pebble Beds Based on a CFD-DEM Coupled Method for A Fusion Blanket, Plasma Science and Technology, 17 (2015), 12, pp. 1083-1087
  20. Chen, L., et al., Investigation of Effective Thermal Conductivity for Pebble Beds by One-way Coupled CFD-DEM Method for CFETR WCCB, Fusion Engineering and Design, 106 (2016), pp. 1-8
  21. Mandal, D., et al., Void Fraction and Effective Thermal Conductivity of Binary Particulate Bed, Fusion Engineering and Design, 88 (2013), 4, pp. 216-225
  22. Lai, J. F., et al.. Bayesian Inference for Solving a Class of Heat Conduction Problems, Thermal Science, 25 (2021), 3B, pp. 2135-2142
  23. Wang, T., et al., A Local Average Method for Stochastic Thermal Analysis Under Heat Conduction Conditions, Thermal Science, 23 (2019), 2B, pp. 899-911
  24. Yan, Z. Z., et al., A New Method For Solving a Class of Heat Conduction Equations, Thermal science, 19 (2015), 4, pp. 1205-1210
  25. Colomer, G., et al., Three-Dimensional Numerical Simulation of Convection and Radiation in A Differentially Heated Cavity Using the Discrete Ordinates Method, International Journal of Heat and Mass Transfer, 47 (2004), 2, pp. 257-69
  26. Chai, J. C., et al., Finite Volume Method for Radiation Heat Transfer, Journal of Thermophysics & Heat Transfer, 8 (1994), 3, pp. 419-425
  27. Fokou, A., et al., Radiation Distribution in Inhomogeneous Atmosphere-Ocean System by Discrete Spherical Harmonics Method, Journal of Quantitative Spectroscopy and Radiative Transfer, 270 (2021), 5, pp. 107707
  28. Byun, D. Y., et al., Thermal Radiation in A Discretely Heated Irregular Geometry Using the Monte-Carlo, Finite Volume, and Modified Discrete Ordinates Interpolation Method, Numerical Heat Transfer: Part A: Applications, 37 (2000), 1, pp. 1-8
  29. Zehner, P., Schlünder, E. U., Einfluß der Wärmestrahlung und des Druckes auf den Wärmetransport in nicht durchströmten Schüttungen, Chemie Ingenieur Technik, 44 (1972), 23, pp. 1303-1308
  30. Breitbach, G., Barthels, H., The Radiant Heat Transfer in the High Temperature Reactor Core after Failure of the Afterheat Removal Systems, Nuclear Technology, 49 (1980), 3, pp. 392-399

© 2023 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence