Monte Carlo Method for Calculating View Factor of Truncated Cone Radiators

Document Type : Full Lenght Research Article

Authors

School of Advanced Technologies, Iran University of Science and Technology, Tehran, Iran

Abstract

To address radiative heat transfer problems, the determination of view factors is crucial. In this study, the focus is placed on the calculation of the view factor using the Monte Carlo method, specifically for truncated cone radiators. Although reference books offer theoretical relations for computing the view factor, a new approach employing the Monte Carlo method is utilized to ensure the accuracy of the general solution. To measure the accuracy, three types of cases are considered: positive, negative, and zero-angle truncated cones with a fixed disk (ring) at the base of the cone. The results are presented for various ratios between the height of the truncated cone and the radii of the ring and base side of the cone. Additionally, the impact of different angles of the truncated cone on the view factor is investigated. In the zero-angle case, five different L/r1 are examined, in the positive angle case, seven different positive angles in two different L/r1 are studied, and in the negative angle case, three negative angles in three different L/r1 are studied. For positive angles, the maximum difference between the results of Monte Carlo method and theoretical method is 42.81% and occurred in L/r1 equal to 5 and 40 degrees. While for zero-angle the maximum difference is 30.16% and occurred in L/r1 equal to 10. In the negative angle case, the maximum difference is 36.66% and occurred in L/r1 equal to 0.2 and -15 degrees.

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References

[1]   Rezaei, A., Hadibafekr, S., Khalilian, M., Chitsaz, A., Mirzaee, I. and Shirvani, H., 2023. A Comprehensive numerical study on using lobed cross-sections in spiral heat exchanger: Fluid flow and heat transfer analysis. International Journal of Thermal Sciences, 193, p. 108464, doi:10.1016/j.ijthermalsci.2023.108464.
[2]   Sans, M., Farges, O., Schick, V. and Parent, G., 2022. Solving transient coupled conductive and radiative transfers in porous media with a Monte Carlo Method: Characterization of thermal conductivity of foams using a numerical Flash Method. International Journal of Thermal Sciences, 179, p. 107656, doi:10.1016/j.ijthermalsci.2022.107656.
[3]   Palluotto, L., Dumont, N., Rodrigues, P., Gicquel, O. and Vicquelin, R., 2019. Assessment of randomized Quasi-Monte Carlo method efficiency in radiative heat transfer simulations. Journal of Quantitative Spectroscopy and Radiative Transfer, 236, p. 106570, doi:10.1016/j.jqsrt.2019.07.013.
[4]   Shi, Y., Song, P. and Sun, W., 2020. An asymptotic preserving unified gas kinetic particle method for radiative transfer equations. Journal of Computational Physics, 420, p. 109687, doi:10.1016/j.jcp.2020.109687.
[5]   Maltby, J. D. and Burns, P. J., 1991. Performance, accuracy, and convergence in a three-dimensional monte carlo radiative heat transfer simulation. Numerical Heat Transfer, Part B: Fundamentals, 19(2), p. 191–209, doi:10.1080/10407799108944963.
[6]   Miyahara, S. and Kobayashi, S., 1995. Numerical calculation of view factors for an axially symmetrical geometry. Numerical Heat Transfer, Part B: Fundamentals, 28(4), p. 437–453, doi:10.1080/10407799508928843.
[7]   Quaky, D. L., Welty, J. R. and Drost, M. K., 1997. Monte carlo simulation of radiation heat transfer from an infinite plane to parallel rows of infinitely long tubes —hottel extended. Numerical Heat Transfer, Part A: Applications, 31(2), p. 131–142, doi:10.1080/10407789708914029.
[8]   Hong, S. H. and Welty,  J.R., 1999. Monte carlo simulation of radiation heat transfer in a three-dimensional enclosure containing a circular cylinder. Numerical Heat Transfer, Part A: Applications, 36(4), p. 395–409, doi:10.1080/104077899274714.
[9]   Mazumder, S. and Kersch, A., 2000. A fast monte carlo scheme for thermal radiation in semiconductor processing applications. Numerical Heat Transfer, Part B: Fundamentals, 37(2), p. 185–199, doi:10.1080/104077900275486.
[10] Xia, X. L., Ren, D. P. and Tan, H. P., 2006. A curve monte carlo method for radiative heat transfer in absorbing and scattering gradient-index medium. Numerical Heat Transfer, Part B: Fundamentals, 50(2), p. 181–192, doi:10.1080/10407790500459387.
[11] Schweiger, H., Oliva, A., Costa, M. and Perez Segarra, C. D., 1999. A monte carlo method for the simulation of transient radiation heat transfer: application to compound honeycomb transparent insulation. Numerical Heat Transfer, Part B: Fundamentals, 35(1), p. 113–136, doi:10.1080/104077999276036.
[12] Mirhosseini, M. and Saboonchi, A., 2011. View factor calculation using the Monte Carlo method for a 3D strip element to circular cylinder. International Communications in Heat and Mass Transfer, 38(6), p. 821–826, doi:10.1016/j.icheatmasstransfer.2011.03.022.
[13] Mirhosseini, M. and Saboonchi, A., 2011. Monte Carlo method for calculating local configuration factor for the practical case in material processing. International communications in heat and mass transfer, 38(8), pp. 1142-1147. doi.org/10.1016/j.icheatmasstransfer.2011.05.003
[14] Wei, Q. and Jiang, Y., 2004. Simple approach to evaluate the view factors between internal heat sources and their environment. Annual ASHRAE conference, Nashville, TN, Transactions 2004, 110.
[15] Walker, T., Xue, S.-C., and Barton, G.W., 2010. Numerical Determination of Radiative View Factors Using Ray Tracing. ASME Journal of Heat and Mass Transfer 132, p. 072702. doi.org/10.1115/1.4000974
[16] Ravishankar, M., Mazumder, S., and Sankar, M., 2010. Application of the modified differential approximation for radiative transfer to arbitrary geometry. Journal of Quantitative Spectroscopy and Radiative Transfer 111, p. 2052. doi.org/10.1016/j.jqsrt.2010.05.020
[17] Arambakam, R., Hosseini, S. A., Vahedi Tafreshi, H. and Pourdeyhimi, B., 2011. A Monte Carlo simulation of radiative heat through fibrous media: Effects of boundary conditions and microstructural parameters. International Journal of Thermal Sciences, 50(6), p. 935, doi:10.1016/j.ijthermalsci.2011.01.015.
[18] Mazumder, S. and Ravishankar, M., 2012. General procedure for calculation of diffuse view factors between arbitrary planar polygons. International Journal of Heat and Mass Transfer, 55(23–24), p. 7330–7335.
[19] Matthew, A. D., Tan, C. K., Roach, P. A., Ward, J., Broughton, J. and Heeley, A., 2014. Calculation of the radiative heat-exchange areas in a large-scale furnace with the use of the monte carlo method. Journal of Engineering Physics and Thermophysics, 87(3), p. 732–742, doi:10.1007/s10891-014-1067-4.
[20] Wang, Z.H., 2014. Monte Carlo simulations of radiative heat exchange in a street canyon with trees. Solar Energy, 110, p. 704–713, doi:10.1016/j.solener.2014.10.012.
[21] Hajji, A. R., Mirhosseini, M., Saboonchi, A. and Moosavi, A., 2015. Different methods for calculating a view factor in radiative applications: Strip to in-plane parallel semi-cylinder. Journal of Engineering Thermophysics, 24(2), p. 169–180, doi:10.1134/S1810232815020071.
[22] Liu, Y. W., An, L. S. and Wu, R. j., 2016. Analysis of radiative energy loss in a polysilicon CVD reactor using Monte Carlo ray tracing method. Applied Thermal Engineering, 93, p. 269–278, doi:10.1016/j.applthermaleng.2015.09.046.
[23] Frank, A., Heidemann, W. and Spindler, K., 2016. Modeling of the surface-to-surface radiation exchange using a Monte Carlo method. Journal of Physics: Conference Series, 745(3), p. 032143, doi:10.1088/1742-6596/745/3/032143.
[24] Cortés, E., Gaviño, D., Calderón-Vásquez, I., García, J., Estay, D., Cardemil, J. M. and Barraza, R., 2023. An enhanced and optimized Monte Carlo method to calculate view factors in packed beds. Applied Thermal Engineering, 219, p. 119391, doi:10.1016/j.applthermaleng.2022.119391.
[25] Cumber, P., 2023. Calculating View Factor Systems with Internal Surfaces Using a Hybrid Monte-Carlo Method. http://dx.doi.org/10.2139/ssrn.4562214
[26] Sparrow, E. M., 1963. A New and Simpler Formulation for Radiative Angle Factors. ASME Journal of Heat and Mass Transfer, 85(2), p. 81–87, doi:10.1115/1.3686058.
[27] Howell, J. R., A Catalog of Radiation Configuration Factors, McGraw-Hill, New York, USA, 1982, p. 136. http://www.thermalradiation.net/sectionc/C-49.html (Available online: 12/21/2023)

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  • Receive Date: 20 May 2023
  • Revise Date: 21 December 2023
  • Accept Date: 24 December 2023

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