An accurate and efficient implicit thermal network method for the steady-state temperature field

Abstract

To calculate the temperature value accurately and efficiently, an implicit thermal network method (TNM) is developed in this study. The main idea of the method is the conversion of such time-varying observed variables as the thermal resistance and the heat source into latent variables to build the implicit thermal equilibrium equation. In the implicit TNM, the steady-state temperature is taken as an independent variable, then parameters related to the steady-state temperature can be expressed as the function of the independent variable. On this basis, implicit thermal equilibrium equations can be constructed. Finally, the steady-state temperature field can be obtained by Newton’s method in optimization. To validate the performance and effectiveness of the implicit TNM, case studies and the sensitivity analysis of algorithms are conducted. The result reveals that the implicit TNM outperforms conventional TNMs, the steady-state TNM and the transient TNM, in computation accuracy, computing time and allocated memory.