Inverse Heat Transfer Analysis for Locating Internal Sources With Arbitrary Geometries Using Physics-Based Compressive Sensing

Abstract Acquiring accurate internal thermal profiles is crucial for ensuring safety, performance, and reliability of parts and components across various applications including advanced manufacturing, electronic devices, and structural health monitoring. However, existing inverse heat transfer methods often demand dense sensor coverage or struggle with ill-conditioning under sparse measurements. In this work, a modified physics-based compressive sensing (PBCS) framework is developed by incorporating sparsity-promoting techniques such as compressed sensing (CS) with the governing heat-transfer equations. By reconfiguring the PBCS method, this approach reliably locates and quantifies internal heat sources, even in complex multisource configurations, while requiring only limited external temperature data. Numerical studies demonstrate that the method achieves high-fidelity reconstructions under diverse scenarios, outperforming traditional methods that rely on denser instrumentation. By combining CS principles with thermophysical constraints, the proposed framework offers a versatile and cost-effective solution for industrial process optimization, real-time monitoring, and inverse thermal analysis.