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

  • 1 School of Mathematics, Shanghai University of Finance and Economics, 200433; and School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, Shanghai, P. R. China
  • 2 School of Mathematics, Shanghai University of Finance and Economics, 200433, Shanghai, P. R. China
  • 3 Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia
  • 4 Department of Mathematics, Hokkaido University, Sapporo, Japan
  • 5 Institute of Textiles & Clothing, The Hong Kong Polytechnic University, and School of Architecture and Art, Central South University, Changsha 410075, Hong Kong, P. R. China
Tingyue Li, Sergey KabanikhinORCID iD: https://orcid.org/0000-0003-4772-1481, Gen Nakamura, Faming WangORCID iD: https://orcid.org/0000-0002-2945-4685 and Dinghua XuORCID iD: https://orcid.org/0000-0001-6418-8119

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).

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This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.

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