The conjugate gradient method using vectorial descent parameters is used to solve the inverse problem of simultaneously estimating one boundary condition and one thermo-physical property of an heterogeneous material. The advantage of the conjugate gradient method lies in that no a priori information is needed on the variation of the unknown quantities. The heterogeneous material model under consideration consists of a matrix in imperfect contact with embedded separated particles. The first unknown of interest in this inverse problem is the constant coupling parameter Ψ which characterizes the thermal contact (conductance) behavior between the matrix and the particles. The second unknown is the time dependent applied heat flux on one external side of the matrix. As a result, this problem is concerned with a combined parameter and function estimation at the same time. Thus two descent parameters, each one corresponding to each unknown function parameter, are derived and used in the iterative process. The developed inverse analysis is based on the transient temperature measurements taken from some sensors implanted inside the matrix only during the process of heating. Several numerical test cases were performed and show that the developed method provides an accurate estimation of thermo-physical properties and boundary condition in a very short practical time.

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