Investigating the Effect of Different Conventional Regularization Methods on Convergence in Moving Boundary Inverse Heat Conduction Problems

In this paper, the temperature of a moving surface is determined with a moving, finite element-based inverse method. In order to overcome the ill-condition of moving inverse problems, three different conventional regularization methods are used: Levenberg, Marquardt and Modified Levenberg. The moving mesh is generated employing the transfinite mapping technique. The proposed algorithms are used in the estimation of surface temperature on a moving boundary in the burning process of a homogenous solid fuel. The measurements obtained inside the solid media are used to circumvent problems associated with the sensor and the receding surface. As the surface recedes, the sensors are swept over by the thermal penetration depth. The produced oscillations occurring at certain intervals in the solution are a phenomenon associated with this process. It is shown that regularization delays convergence and, therefore, the use of normal analysis is sufficient. The method can be used successfully for a wide range of thermal diffusivity coefficients.