Estimativa de condutâncias térmicas de contato em interfaces irregulares usando a técnica da transformada integral clássica e o método dos funcionais de reciprocidade

Abstract

The reciprocity functional method, associated to the Classic Integral Transform Technique (CITT), has been succesfully applied in obtaining analytical solutions for the inverse heat transfer problem that seeks to estimate the thermal contact conductance (TCC) distribution on the interface of a body composed of two materials. Yet, the theoretical development upon which this approach is based is not limited to the need of this interface to have a regular format. This work proposes to extend the method, thus obtaining an analytical development for the estimation of the thermal contact conductance distribution on interfaces which are not necessarily regular. Therefore, some tools will be employed, namely: the extension of the irregular physical domain to a regular physical domain in which the auxiliary problems will be analytically solved; and the application of the Gram-Schmidt orthogonalization process in order to generate an orthonormal set of functions from the solutions obtained from the auxiliary problems. Several test problems were solved using the techniques described in this work, leading to very good results, with low CPU time usage by the computational implementation.