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).

中文翻译：

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Stephan-Boltzmann界面条件下热防护服三重参数确定的反问题

摘要 建立了具有Stephan-Boltzmann界面条件和Robin边界条件的七层抛物线模型来描述环境-三层服装-气隙-体系统的传热过程。基于该模型，本文给出了同时测定三层织物厚度的相应逆问题的解，满足人体皮肤的热安全要求。通过实施稳定的有限差分方案，可以预测身体皮肤上的热烧伤。然后开发了一种称为粒子群优化（PSO）算法的随机方法来数值求解逆问题。数值结果表明，该模型的建立和所提出的求解相应逆问题的算法是有效的。因此，本文的研究结果将为设计和制造热防护服（TPC）提供科学支持。