Inverse-Coefficient Problem of Heat Transfer in Layered Nanostructures

Abstract

The rapid development of electronics is leading to the creation and use of small electronic components, including nanoelements of a 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 the 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 manufacturing technology of heterostructures, 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 is formulated in an algebraic (finite difference) form under the assumption of a constant temperature within each layer due to their small thickness. The inverse problem is solved in the extreme formulation and optimized using zero-order methods that do not require calculating the derivatives of the optimized function. As a basic optimization algorithm, the Nelder–Mead method is used in combination with random restarts to search for the global minimum. The results of identifying the contact thermal resistance coefficients obtained in the context of a quasi-real experiment are presented. The accuracy of the solution of the identification problem is estimated as a function of the number of layers in the heterostructure and the measurement error. The 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 thermal conductivity coefficients of the heterostructure.