Analysis of a Fundamental Procedure for Solving the Inverse Heat Conduction Problem Applied to Simple Systems

Abstract

Heat transfer phenomena develop in various natural and artificially created processes. Fundamental laws of physics allow the transfer mechanisms to be classified; however, describing the phenomena is relatively complex, even if the analysis is limited to conduction. In particular, to determine the temperature distribution in a solid body, the definition of the boundary conditions that perturb it is required. Such conditions mathematically model a fluid’s hydrodynamic and thermodynamic behavior, and when the temperature differences are significantly high, the flow by radiation. It is then complex to define the functions of the thermal boundary conditions and solve the well-posed problem. Naturally, nonlinear system results and applying numerical methods are constant in the analysis. However, a unique solution for the thermal field in a solid does ensure. Alternatively, the scheme of the discretization of the system allows us to propose that through the knowledge of a fraction of the thermal field, the boundary condition is quantified independently of its nature. Such a procedure is called inverse analysis and has the characteristic of not satisfying the single solution criterion. However, some cases of interest can treat, and the estimate is guaranteed to be highly accurate.