Identification of the thermal conductivity and heat capacity in unsteady nonlinear heat conduction problems using the boundary element method
The authors investigate the simultaneous estimation of the temperature-dependent conductivity and heat capacity starting from boundary and initial data supplemented by interior temperature measurements. The unknown temperature solution and unspecified boundary values are required. The mathematical formulation is based on a one-dimensional plane time-dependent nonlinear parabolic initial-boundary value problem of the Dirichlet type. The solution of the direct problem is initiated via a Kirchhoff transformation followed by a boundary element time-marching technique. The inverse problem is approached via a boundary element method employed in an iterative procedure requiring the minimization of a nonlinear least squares functional. Test examples are considered to illustrate the applicability and feasibility of the method.
nonlinear parabolic initial-boundary value problem
scientific article; zbMATH DE number 937214