Applications of Partial Differential Equations in Heat Transfer Modelling

Abstract

Heat transfer plays a critical role in energy, and environmental systems, where modelling is important to monitor the performance and efficiency of the system. With the rise of complex physical processes, partial differential equations were the corner stone to describe them in detail. In this paper, we will highlight the role of PDEs for numerous applications of heat transfer, including conduction, convection, radiation, and phase-change processes. Out paper examines recent case studies from many engineering domains such as solar thermal systems, phase-change solar collectors, industrial drying ovens, and electrical transformer cooling systems. The paper concludes by emphasizing future directions in physics-informed machine learning, fractional modelling, and digital twin integration for real-time thermal management.