The inverse coefficient problem of heat transfer in layered nanostructures

Abstract

The rapid development of electronics leads to the creation and use of electronic components of small dimensions, including nanoelements of complex, layered structure. The search for effective methods for cooling electronic systems dictates the need for the development of methods for the numerical analysis of heat transfer in nanostructures. A characteristic feature of energy transfer in such systems is the dominant role of contact thermal resistance at interlayer interfaces. Since the contact resistance depends on a number of factors associated with the technology of heterostructures manufacturing, it is of great importance to determine the corresponding coefficients from the results of temperature measurements.The purpose of this paper is to evaluate the possibility of reconstructing the thermal resistance coefficients at the interfaces between layers by solving the inverse problem of heat transfer.The complex of algorithms includes two major blocks — a block for solving the direct heat transfer problem in a layered nanostructure and an optimization block for solving the inverse problem. The direct problem was formulated in an algebraic (finite difference) form under the assumption of a constant temperature within each layer, which is due to the small thickness of the layers. The inverse problem was solved in the extreme formulation, the optimization was carried out using zero-order methods that do not require the calculation of the derivatives of the optimized function. As a basic optimization algorithm, the Nelder—Mead method was used in combination with random restarts to search for a global minimum.The results of the identification of the contact thermal resistance coefficients obtained in the framework of a quasi-real experiment are presented. The accuracy of the identification problem solution is estimated as a function of the number of layers in the heterostructure and the «measurements» error.The obtained results are planned to be used in the new technique of multiscale modeling of thermal regimes of the electronic component base of the microwave range, when identifying the coefficients of thermal conductivity of heterostructure.