Nonlinear Inverse Heat Transfer Problem

Abstract

Abstract In this work, a method for finding nonlinear heat-conducting characteristics of soil is developed. Two-layer complexes of containers were created, the side faces of which are thermally insulated, so the 1D thermal conductivity equation is used. A temperature sensor is placed at the junction of the two media, and a mixed boundary value problem is solved in each area. In order to provide the inverse coefficient problem with initial data, two temperature sensors are used: one sensor was placed at the open border of the container and recorded the soil temperature at this border, and the second sensor was placed at a short distance from the border, which recorded the air temperature. The measurements were carried out in the time interval (0,4t max ). First, the initial-boundary value problem of thermal conductivity with nonlinear coefficients is investigated by the finite difference method. Two types of difference schemes are constructed: linearized and nonlinear. The linearized difference scheme is implemented numerically by the scalar Thomas method, and the nonlinear difference problem is solved by the Newton method. The solution of the linearized difference problem was taken as the initial approximation of the Newton method. To find the thermophysical parameters, the corresponding functional is minimized using the gradient descent method. In addition, all thermophysical characteristics (8 coefficients) were found for a two-layer container with sand and chernozem.