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An inverse problem of triple-thickness parameters determination for thermal protective clothing with Stephan–Boltzmann interface conditions

  • Tingyue Li , Sergey Kabanikhin ORCID logo , Gen Nakamura , Faming Wang ORCID logo and Dinghua Xu ORCID logo EMAIL logo
Published/Copyright: March 10, 2020

Abstract

A seven-layers parabolic model with Stephan–Boltzmann interface conditions and Robin boundary conditions is mathematically formulated to describe the heat transfer process in environment-three layers clothing-air gap-body system. Based on this model, the solution to the corresponding inverse problem of simultaneous determination of triple fabric layers thickness is given in this paper, which satisfies the thermal safety requirements of human skin. By implementing a stable finite difference scheme, the thermal burn injuries on the skin of the body can be predicted. Then a kind of stochastic method, named as particle swarm optimization (PSO) algorithm, is developed to numerically solve the inverse problem. Numerical results indicate that the formulation of the model and proposed algorithm for solving the corresponding inverse problem are effective. Hence, the results in this paper will provide scientific supports for designing and manufacturing thermal protective clothing (TPC).

Award Identifier / Grant number: 11871435

Award Identifier / Grant number: 11471287

Award Identifier / Grant number: 91534113

Funding statement: The research is partially supported by National Natural Science Foundation of China (Grant No. 11871435, 11471287 and 91534113).

Acknowledgements

The fifth author expresses sincere thanks to the third author for the discussion and cooperation during his visit in June 2018 at the Hokkaido University, and to the second author for the great improvement to the manuscript during the visit in Shanghai University of Finance and Economics in May 2019.

References

[1] D. Barr, W. Gregson and T. Reilly, The thermal ergonomics of firefighting reviewed, Appl. Ergonomics 41 (2010), 161–172. 10.1016/j.apergo.2009.07.001Search in Google Scholar

[2] M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, John Wiley & Sons, Inc, New Jersey, 2005. 10.1002/0471787779Search in Google Scholar

[3] A. Cheng and H. Wang, An error estimate on a Galerkin method for modeling heat and moisture transfer in fibrous insulation, Numer. Methods for Partial Differential Equations 2 (2010), 504–517. 10.1002/num.20277Search in Google Scholar

[4] P. Chitrphiromsri and A. V. Kuznetsov, Modeling heat and moisture transport in firefighter protective clothing during flash fire exposure, Heat Mass Transf. 41 (2005), 206–215. 10.1007/s00231-004-0504-xSearch in Google Scholar

[5] J. T. Fan, X. Y. Cheng and W. W. Sun, An improved model of heat and moisture transfer with phase change and mobile condensates in fibrous insulation and comparison with experimental results, Int. J. Heat Mass Transf. 47 (2004), 2343–2352. 10.1016/j.ijheatmasstransfer.2003.10.033Search in Google Scholar

[6] J. T. Fan, Z. X. Luo and Y. Li, Heat and moisture transfer with sorption and condensation in porous clothing assemblies and numerical simulation, Int. J. Heat Mass Transf. 43 (2000), 2989–3000. 10.1016/S0017-9310(99)00235-5Search in Google Scholar

[7] J. T. Fan and X. H. Wei, Heat and moisture transfer through fibrous insulation with phase change and mobile condensates, Int. J. Heat Mass Transf. 19 (2002), 4045–4055. 10.1016/S0017-9310(02)00114-XSearch in Google Scholar

[8] B. Farnworth, Mechanisms of heat flow through clothing insulation, Textile Res. J. 53 (1983), 717–725. 10.1177/004051758305301201Search in Google Scholar

[9] A. Ghazy, Influence of thermal shrinkage on protective clothing performance during fire exposure: Numerical investigation, Mech. Eng. Res. 4 (2014), 1–15. 10.5539/mer.v4n2p1Search in Google Scholar

[10] A. Ghazy and D. J. Bergstrom, Influence of the air gap between protective clothing and skin on clothing performance during flash fire exposure, Heat Mass Transf. 47 (2011), 1275–1288. 10.1007/s00231-011-0791-ySearch in Google Scholar

[11] A. Ghazy and D. J. Bergstrom, Numerical simulation of heat transfer in firefighters’ protective clothing with multiple air gaps during flash fire exposure, Numer. Heat Transf. 61 (2012), 569–593. 10.1080/10407782.2012.666932Search in Google Scholar

[12] A. Ghazy and D. J. Bergstrom, Numerical simulation of the influence of fabric’s motion on protective clothing performance during flash fire exposure, Heat Mass Transf. 49 (2013), 775–788. 10.1007/s00231-013-1123-1Search in Google Scholar

[13] P. W. Gibson, Multiphase heat and mass transfer through hygroscopic porous media with applications to clothing materials, Fiber. 53 (1996), 183–194. 10.2115/fiber.53.5_183Search in Google Scholar

[14] F. C. Henriques and A. R. Moritz, Studies of thermal injuries I: The conduction of heat to, and through skin, and the temperatures attained therein, a theoretical and experimental investigation, Amer. J. Pathol. 23 (1947), 531–549. Search in Google Scholar

[15] J. R. Lawson, W. D. Walton, N. P. Bryner and F. K. Amon, Estimates of thermal properties for fire fighters’ protective clothing materials, preprint (2005). 10.6028/NIST.IR.7282Search in Google Scholar

[16] W. E. Mell and J. R. Lawson, A heat transfer model for firefighters’ protective clothing, Fire Technol. 36 (2000), 39–68. 10.1023/A:1015429820426Search in Google Scholar

[17] M. F. Modest, Radiative Heat transfer, 2nd ed., Academic Press, Boston, 2003. 10.1016/B978-012503163-9/50023-0Search in Google Scholar

[18] G. Song, Modeling thermal protection outfits for fire exposures, Ph.D. thesis, North Carolina State University, 2003. Search in Google Scholar

[19] G. W. Song, R. L. Barker, H. Hamouda, A. V. Kuznetsov, P. Chitrphiromsri and R. V. Grimes, Modeling the thermal protective performance of heat resistant garments in flash fire exposures, Textile Res. J. 74 (2004), 1033–1040. 10.1177/004051750407401201Search in Google Scholar

[20] G. W. Song, P. Chitrphiromsri and D. Ding, Numerical simulations of heat and moisure transport in thermal protective clothing under flash fire conditions, Int. J. Occupational Safety & Ergonomics Jose 14 (2008), 89–106. 10.1080/10803548.2008.11076752Search in Google Scholar PubMed

[21] A. M. Stoll and M. A. Chianta, Method and rating system for evaluation of thermal protection, Aerospace Medicine 11 (1969), 1232–1238. Search in Google Scholar

[22] Y. Su, J. Z. He and J. Li, An improved model to analyze radiative heat transfer in flame-resistant fabrics exposed to low-level radiation, Textile Res. J. 16 (2016), 1953–1967. 10.1177/0040517516660892Search in Google Scholar

[23] D. A. Torvi and J. D. Dale, Heat transfer in thin fibrous materials under high heat flux, Fire Technol. 35 (1999), 210–231. 10.1023/A:1015484426361Search in Google Scholar

[24] D. A. Torvi, D. J. Douglas and B. Faulkner, Influence of air gaps on bench-top test results of flame resistant fabrics, J. Fire Protection Eng. 10 (1999), 1–12. 10.1177/104239159901000101Search in Google Scholar

[25] Udayraj and F. Wang, A three-dimensional conjugate heat transfer model for thermal protective clothing, Int. J. Thermal Sci. 130 (2018), 28–46. 10.1016/j.ijthermalsci.2018.04.005Search in Google Scholar

[26] J. Vershoor and P. Greebler, Heat transfer by gas conduction and radiation in fibrous insulation, Trans. Amer. Math. Soc. Mech. Eng. 74 (1952), 961–968. 10.1115/1.4015979Search in Google Scholar

[27] D. H. Xu, Mathemtical Modeling of Heat and Moisture Transfer within Textiles and Corresponding Inverse Problems of Textile Material Design, Science Press, Beijing, 2014. Search in Google Scholar

[28] D. H. Xu, R. L. Chen and M. B. Ge, Inverse problems of textile material design based on comfort of clothing, Commun. Appl. Comput. Math. 3 (2012), 332–341. Search in Google Scholar

[29] D. H. Xu, Y. B. Chen and X. H. Zhou, Type design for textile materials under low temperature: Modeling, numerical algorithm and simulation, Int. J Heat Mass Transf. 60 (2013), 582–590. 10.1016/j.ijheatmasstransfer.2012.12.063Search in Google Scholar

[30] D. H. Xu, J. X. Cheng, Y. B. Chen and M. B. Ge, An inverse problem of thickness design for bilayer textile materials under low temperature, J. Phys. Conf. Ser. 290 (2011), Article ID 12018. 10.1088/1742-6596/290/1/012018Search in Google Scholar

[31] D. H. Xu and M. B. Ge, Thickness determination in textile material design: dynamic modeling and numerical algorithms, Inverse Problems 28 (2012), Article ID 035011. 10.1088/0266-5611/28/3/035011Search in Google Scholar

[32] D. H. Xu, L. Wen and B. Xu, An inverse problems of bilayer textile thickness determination in dynamic heat and moisture transfer, Appl. Anal. 93 (2013), 445–465. 10.1080/00036811.2013.835042Search in Google Scholar

[33] Y. H. Xu, D. H. Xu, L. P. Zhang and X. H. Zhou, A new inverse problem for the determination of textile fabrics, Inverse Probl. Sci. Eng. 23 (2015), 635–650. 10.1080/17415977.2014.933827Search in Google Scholar

[34] G. F. Yang, M. Yamamoto and J. Cheng, Heat transfer in composite materials with Stefan–Boltzmann interface conditions, Math. Methods Appl. Sci. 11 (2010), 1297–1314. Search in Google Scholar

Received: 2019-09-11
Accepted: 2019-12-18
Published Online: 2020-03-10
Published in Print: 2020-06-01

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