Real-time heat conduction in a self-heated composite slab by Padé filters

A study of the heat conduction through a miniature composite slab showing large differences in scale is presented. The system consists of a highly conductive thin sensing film, subjected to self-heating and encapsulated by insulating layers. The formalism of the Laplace transfer functions is used to relate the operating temperature of the coated sensing film to the unknown outermost temperatures and to self-heating. The use of Padé approximants provides approximations of these transfer functions by rational functions that are much more accurate than most of the concurrent approaches. Then the real-time evolution of the operating temperature of the sensing film is established without resorting to the Laplace inversion, but using recursive digital filters constructed from the Padé approximants. Finally, the inverse analysis that is proposed allows to regain the evolution of the outermost temperatures from the knowledge of the operating temperature, even in the presence of a significant self-heating and a nonlinear regime. The present systemic approach could be applied to optimize and accurately describe the real-time operation of many miniature resistive sensors used for example in biomedical instrumentation.