A Difference Method for Calculating the Heat Flux on an Inaccessible Boundary in a Heat Conduction Problem

The continuation problem for the heat equation is considered. Determining the heat flux on an inaccessible boundary reduces to an inverse problem. An implicit difference scheme is used for the numerical solution of the inverse problem. At each time step, the heat flux on the inaccessible boundary is calculated for the difference analog of the elliptic equation by an economical direct method. The proposed algorithm substantially expands the range of problems being solved and can be used to create devices capable of real-time determination of the heat flux on parts of inhomogeneous structures inaccessible for measurements, for example, on the inner radius of pipes made of various materials.