An Inverse Method to Determine Boundary Temperature and Heat Flux for a 2D Steady State Heat Conduction Problem

Inverse determination of temperature and heat flux on an inaccessible surface of a solid has been widely employed in engineering and research. In this paper a new inverse method was used to predict local boundary temperature and heat flux distributions for a 2D steady heat conduction problem based on temperature measurements at interior wall sample points. The method is a non-iterative meshless boundary allocation method (BAM) using the principle of superposition for linear problems. A case study showed that the BAM method predicts the boundary temperature and heat flux with about the same accuracy as Beck’s function specified method but uses less computing time. Error analysis of thermocouple position and measurement was also carried out. More difficult problems such as those with multiple materials and non-rectangular geometries can also be treated by BAM.