A Class Of Abnormal Heat Transfer Models And Related Inverse Problems Of Parameters Determination

The so-called" complex phenomena",such as abnormal heat conduction and diffusion,are usually not be well explained by the classical model of the integral partial differential equation.It is not successful to adjust the parameters or take a nonlinearization treatment of the classical model equation.Meanwhile the anomalous diffusion including fractional deriva-tive is consistent with such experimental phenomena.In this paper,a heat transfer model with fractional differential equation and Riemann-Liouville fractional Robin boundary condi-tions is established to describe the heat transfer inside/on the boundary of isotropic materials in high temperature environment.Based on this,the heat transfer model of TPC(Thermal Protective Clothing)system and the inverse problem of parameters determination are stud-ied.This paper is mainly composed of the following five parts:In the first chapter,a brief introduction of research background and significance on fractional diffusion equations and some preliminary knowledge about fractional derivatives is given.Meanwhile,the results of previous research and content of this paper are also briefly described.In the second chapter,the space fractional heat transfer model of single layer TPC is established by the theory of Continuous Time Random Walk.In order to better describe the heat exchange on the boundary,the fractional Robin boundary condition is adopted on the boundary.The well-posedness of the model is analyzed.Based on the variational form of the model,the energy estimation and uniqueness of the weak solution are given.In the third chapter,the shifted Grunwald-Letnikov formula is adopted to approximate fractional derivative.Convergence rate of the numerical algorithm for the Robin problem with exact/noisy initial-boundary value conditions is derived.The numerical simulations validate the rationality of the proposed model.In the fourth chapter,based on the proposed fractional model,the heat transfer mech-anism and burn criteria of skin layer,some inverse problems of the relevant parameter-s determination are proposed under the design objectives of less than primary/secondary burns.Namely the inverse problems are formulated by TPC thickness,porosity and thermal conductivity determination.The numerical simulation results show the rationality of the proposed models and effectiveness of the algorithms.In the last chapter,the research content and innovation of this paper are summarized,and the next research direction is also pointed out.