Numerical Method For Positive Inversion Of Heat Conduction In A Spherical Medium

In this paper,the forward and inverse problem of heat conduction in multilayer media in spherical domain and its numerical calculation method are studied.The main work is as follows:(1)Temperature and pressure correction of rock thermal conductivity is studied.The thermal conductivity of rock affects the variation of temperature field in rock,and temperature and pressure are two important factors affecting the thermal conductivity of rock.Based on the laboratory test data of sandstone under different temperature and pressure conditions,this paper studies the variation of thermal conductivity with temperature and pressure.(2)Numerical schemes and forward problems for heat conduction of multilayer media in spherical domain are studied.Firstly,under the assumption of spherical symmetry,the three-dimensional heat conduction problem is simplified to the one-dimensional radial heat conduction problem.By introducing the theory of state space and applying difference in the time domain,the state equation of one-dimensional multi-layer media heat conduction problem is established,and the transient analysis of heat conduction is carried out by combining boundary conditions and connection conditions between layers.The recursive formula between temperature and heat flow and the source term is given.Then,based on the recursive formula,the equations of temperature and heat flow are solved by combining the initial conditions and boundary conditions.Finally,numerical examples are given,and the results show that the algorithm is effective.(3)The inverse problem of heat conduction source term for multilayer media in spherical domain is studied.According to the numerical formula derivation of one-dimensional radial multilayer media heat conduction problem in spherical domain,the inverse problem of source term is transformed into the first Fredholm integral equation.Firstly,the integral equation is transformed into linear equations by discrete regularization method,and the integral equation is solved by Tikhonov regularization method.The regularization parameters are determined by Morozov deviation principle and Newton iterative method,and the discrete regularization numerical solution scheme of integral equation is derived.