| Title:
|
Mathematical and numerical analysis of radiative heat transfer in semi-transparent media (English) |
| Author:
|
Han, Yao-Chuang |
| Author:
|
Nie, Yu-Feng |
| Author:
|
Yuan, Zhan-Bin |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
75-100 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision algorithm is developed to handle the computation of the integrals containing the visibility factor. An efficient iterative algorithm is proposed to solve the nonlinear discrete system and its convergence is also established. Numerical experiment results are also presented to verify the effectiveness and accuracy of the proposed method and algorithm. (English) |
| Keyword:
|
radiative heat transfer |
| Keyword:
|
existence and uniqueness |
| Keyword:
|
collocation-boundary element method |
| Keyword:
|
shadow detection |
| Keyword:
|
iterative nonlinear solver |
| MSC:
|
45K05 |
| MSC:
|
47G10 |
| MSC:
|
65M38 |
| MSC:
|
65N38 |
| MSC:
|
80A20 |
| idZBL:
|
Zbl 07031678 |
| idMR:
|
MR3913885 |
| DOI:
|
10.21136/AM.2019.0276-17 |
| . |
| Date available:
|
2019-02-08T10:03:58Z |
| Last updated:
|
2021-03-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147596 |
| . |
| Reference:
|
[1] Adams, M. L., Larsen, E. W.: Fast iterative methods for discrete-ordinates particle transport calculations.Progr. Nucl. Energy 40 (2002), 3-159. 10.1016/S0149-1970(01)00023-3 |
| Reference:
|
[2] Agoshkov, V.: Boundary Value Problems for Transport Equations.Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, Boston (1998). Zbl 0914.35001, MR 1638817, 10.1007/978-1-4612-1994-1 |
| Reference:
|
[3] Altaç, Z., Tekkalmaz, M.: Benchmark solutions of radiative transfer equation for three-dimensional rectangular homogeneous media.J. Quant. Spect. Rad. Transfer 109 (2008), 587-607. 10.1016/j.jqsrt.2007.07.016 |
| Reference:
|
[4] Altaç, Z., Tekkalmaz, M.: Exact solution of radiative transfer equation for three-dimensional rectangular, linearly scattering medium.J. Thermophys. Heat Transf. 25 (2011), 228-238. 10.2514/1.50910 |
| Reference:
|
[5] Atkinson, K., Chandler, G.: The collocation method for solving the radiosity equation for unoccluded surfaces.J. Integral Equations Appl. 10 (1998), 253-290. Zbl 0914.65137, MR 1656533, 10.1216/jiea/1181074231 |
| Reference:
|
[6] Atkinson, K., Chien, D. D.-K., Seol, J.: Numerical analysis of the radiosity equation using the collocation method.ETNA, Electron. Trans. Numer. Anal. 11 (2000), 94-120. Zbl 0961.65118, MR 1799026 |
| Reference:
|
[7] Białecki, R. A., Grela, Ł.: Application of the boundary element method in radiation.Mech. Teor. Stosow. 36 (1998), 347-364. Zbl 0934.74076 |
| Reference:
|
[8] Blobner, J., Białecki, R. A., Kuhn, G.: Boundary-element solution of coupled heat conduction-radiation problems in the presence of shadow zones.Numer. Heat Transfer, Part B 39 (2001), 451-478. 10.1080/104077901750188840 |
| Reference:
|
[9] Chen, S.-S., Li, B.-W., Tian, X.-Y.: Chebyshev collocation spectral domain decomposition method for coupled conductive and radiative heat transfer in a 3D L-shaped enclosure.Numer. Heat Transfer, Part B 70 (2016), 215-232. 10.1080/10407790.2016.1193398 |
| Reference:
|
[10] Cohen, M. F., Wallace, J. R.: Radiosity and Realistic Image Synthesis.Academic Press Professional, Boston (1993). Zbl 0814.68138 |
| Reference:
|
[11] Crosbie, A. L., Schrenker, R. G.: Exact expressions for radiative transfer in a three-dimensioanl rectangular geometry.J. Quant. Spect. Rad. Transfer 28 (1982), 507-526. 10.1016/0022-4073(82)90017-6 |
| Reference:
|
[12] Crosbie, A. L., Schrenker, R. G.: Radiative transfer in a two-dimensional rectangular medium exposed to diffuse radiation.J. Quant. Spect. Rad. Transfer 31 (1984), 339-372. 10.1016/0022-4073(84)90095-5 |
| Reference:
|
[13] Eberwien, U., Duenser, C., Moser, W.: Efficient calculation of internal results in 2D elasticity BEM.Eng. Anal. Bound. Elem. 29 (2005), 447-453. Zbl 1182.74214, 10.1016/j.enganabound.2005.01.008 |
| Reference:
|
[14] Emery, A. F., Johansson, O., Lobo, M., Abrous, A.: A comparative study of methods for computing the diffuse radiation viewfactors for complex structures.J. Heat Transfer 113 (1991), 413-422. 10.1115/1.2910577 |
| Reference:
|
[15] Hansen, O.: The local behavior of the solution of the radiosity equation at the vertices of polyhedral domains in $\Bbb R^3$.SIAM J. Math. Anal. 33 (2001), 718-750. Zbl 1001.45002, MR 1871418, 10.1137/S0036141000378103 |
| Reference:
|
[16] Howell, J. R., Mengüç, M. P., Siegel, R.: Thermal Radiation Heat Transfer.CRC Press, Boca Raton (2010). 10.1201/9781439894552 |
| Reference:
|
[17] Hsu, P.-F., Tan, Z.: Radiative and combined-mode heat transfer within L-shaped nonhomogeneous and nongray participating media.Numer. Heat Transfer, Part A 31 (1997), 819-835. 10.1080/10407789708914066 |
| Reference:
|
[18] Kress, R.: Linear Integral Equations.Applied Mathematical Sciences 82, Springer, New York (2014). Zbl 1328.45001, MR 3184286, 10.1007/978-1-4614-9593-2 |
| Reference:
|
[19] Laitinen, M. T., Tiihonen, T.: Integro-differential equation modelling heat transfer in conducting, radiating and semitransparent materials.Math. Methods Appl. Sci. 21 (1998), 375-392. Zbl 0958.80003, MR 1608072, 10.1002/(SICI)1099-1476(19980325)21:5<375::AID-MMA953>3.0.CO;2-U |
| Reference:
|
[20] Li, B. Q., Cui, X., Song, S. P.: The Galerkin boundary element solution for thermal radiation problems.Eng. Anal. Bound. Elem. 28 (2004), 881-892. Zbl 1066.80008, 10.1016/j.enganabound.2004.01.009 |
| Reference:
|
[21] Malalasekera, W. M., James, E. H.: Radiative heat transfer calculations in three-dimensional complex geometries.ASME J. Heat Transfer 118 (1996), 225-228. 10.1115/1.2824045 |
| Reference:
|
[22] Modest, M. F.: Radiative Heat Transfer.Academic Press, Oxford (2013). 10.1016/C2010-0-65874-3 |
| Reference:
|
[23] Qatanani, N. A., Daraghmeh, A.: Asymptotic error analysis for the heat radiation boundary integral equation.Eur. J. Math. Sci. 2 (2013), 51-61. |
| Reference:
|
[24] Sun, B., Zheng, D., Klimpke, B., Yildir, B.: Modified boundary element method for radiative heat transfer analyses in emitting, absorbing and scattering media.Eng. Anal. Bound. Elem. 21 (1998), 93-104. Zbl 0936.80006, 10.1016/S0955-7997(97)00068-4 |
| Reference:
|
[25] Tan, Z.: Radiative heat transfer in multidimensional emitting, absorbing, and anisotropic scattering media: mathematical formulation and numerical method.J. Heat Transfer 111 (1989), 141-147. 10.1115/1.3250636 |
| Reference:
|
[26] Thynell, S. T.: The integral form of the equation of transfer in finite, two-dimensional, cylindrical media.J. Quant. Spect. Rad. Transfer 42 (1989), 117-136. 10.1016/0022-4073(89)90094-0 |
| Reference:
|
[27] Tiihonen, T.: Stefan-Boltzmann radiation on non-convex surfaces.Math. Methods Appl. Sci. 20 (1997), 47-57. Zbl 0872.35044, MR 1429330, 10.1002/(SICI)1099-1476(19970110)20:1<47::AID-MMA847>3.0.CO;2-B |
| Reference:
|
[28] Trivic, D. N., Amon, C. H.: Modeling the 3-D radiation of anisotropically scattering media by two different numerical methods.Int. J. Heat Mass Transfer 51 (2008), 2711-2732. Zbl 1143.80329, 10.1016/j.ijheatmasstransfer.2007.10.015 |
| Reference:
|
[29] Viskanta, R.: Radiation transfer and interaction of convection with radiation heat transfer.Adv. Heat Transfer 3 (1966), 175-251. Zbl 0139.23801, 10.1016/s0065-2717(08)70052-2 |
| Reference:
|
[30] Watt, A.: Fundamentals of Three-Dimensional Computer Graphics.Addison-Wesley Publishing Company, Wokingham (1989). Zbl 0702.68099 |
| . |
