A boundary inverse problem for the process of heat and moisture transfer in multilayered region

Abstract

The paper deals with the boundary inverse problem for a system of transfer equations for heat and moisture. A system of equations describe the joint movement of moisture and heat in the multilayer region. Boundary conditions of practical importance have defined. The resulting initial boundary problem is written in dimensionless form. After that the formulation of the inverse boundary value problem in dimensionless variables is given. The result gives a quasi-linear inverse boundary problem. In the present work we have derived the conjugate system of differential equations with partial derivatives. The boundary and initial conditions of the conjugate problem are defined. A connection between the line and the conjugate problem is established. We have constructed a functional for solving the inverse boundary problem. The unknown quantities are determined from the minimum of this functional. The minimizing functional is written in the dimensionless form. An iterative method is developed to calculate the unknown boundary heat and moisture values. Iteration formulas are written in an explicit form and contain the decisions of direct and the conjugate problem. The iteration is carried out so, that the functional decreases monotonically in the calculation process. The convergence of iterative processes is controlled by a small control functions. The numerical calculations are conducted by proving the suitability of the developed method. The criterion for stopping the computing process is sufficient smallness of the dimensionless values of the functional.