Reduction and Correlation of Lumped Parameter Method for Thermal Models in Steady-State Conditions

The reduction of thermal mathematical models is often carried out manually, being very time consuming and error-prone. A combination of two methods for reducing and correlating the reduction results is presented. The first step consists in the reduction of the thermal model applying a matrix method, based on the manipulation of the conductive couplings matrix. A new model with the characteristics of a lumped parameter thermal model is obtained. The scope of the method — the scale of the reduction — is limited by the temperature differences between the detailed and reduced models, as well as by the differences in the heat flows across the model interfaces. This limitation is overcome by the application of the second method, for the correlation of the detailed and reduced models results. The correlation method is based on Jacobian matrix formulation and Moore-Penrose pseudoinverse, which allows the obtaining the value of the model parameters — conductive couplings — that yield correlated results. The combination of both methods in a pipeline allows the reduction and correlation of the thermal models, with little intervention of the engineer.