An inverse problem of triple-thickness parameters determination for thermal protective clothing with Stephan–Boltzmann interface conditions
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).
Funding source: National Natural Science Foundation of China
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
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Articles in the same Issue
- Frontmatter
- Identification of the interface between acoustic and elastic waves from internal measurements
- A numerical method for an inverse source problem for parabolic equations and its application to a coefficient inverse problem
- Determination of the impulsive Sturm–Liouville operator from a set of eigenvalues
- The enclosure method for inverse obstacle scattering over a finite time interval: VI. Using shell-type initial data
- Identifying space-time dependent force on the vibrating Euler–Bernoulli beam by a boundary functional method
- A stability result for the determination of order in time-fractional diffusion equations
- Recovery of non-smooth radiative coefficient from nonlocal observation by diffusion system
- An inverse problem of triple-thickness parameters determination for thermal protective clothing with Stephan–Boltzmann interface conditions
- Direct and inverse source problems for degenerate parabolic equations
- Partial inverse problems for quadratic differential pencils on a graph with a loop
Articles in the same Issue
- Frontmatter
- Identification of the interface between acoustic and elastic waves from internal measurements
- A numerical method for an inverse source problem for parabolic equations and its application to a coefficient inverse problem
- Determination of the impulsive Sturm–Liouville operator from a set of eigenvalues
- The enclosure method for inverse obstacle scattering over a finite time interval: VI. Using shell-type initial data
- Identifying space-time dependent force on the vibrating Euler–Bernoulli beam by a boundary functional method
- A stability result for the determination of order in time-fractional diffusion equations
- Recovery of non-smooth radiative coefficient from nonlocal observation by diffusion system
- An inverse problem of triple-thickness parameters determination for thermal protective clothing with Stephan–Boltzmann interface conditions
- Direct and inverse source problems for degenerate parabolic equations
- Partial inverse problems for quadratic differential pencils on a graph with a loop