Development and visualization of two dimensional transient heat diffusion using temporal scatter mapping and finite difference method

Abstract

The difficulty in visualizing transient thermal behavior often hinders students from understanding complex heat transfer processes in thermodynamics. The research objective is to develop and validate a numerical framework that synchronizes two-dimensional spatial contour maps with temporal scatter mapping using the Finite Difference Method. Validation was conducted by comparing the simulated thermal responses of twenty-one materials against their known physical properties and stability criteria. Results demonstrate that high-diffusivity materials like Gold reach equilibrium within eight seconds, while insulators like Water exhibit extreme thermal lag even after fifty seconds. To ensure physical accuracy, the tool incorporates an automated stability check based on the Fourier Number to prevent non-physical divergent results. This application enhances physics education by transforming abstract thermodynamic equations into intuitive visual evidence, thereby improving the conceptual mastery of transient processes. These findings provide a robust pedagogical tool for instructors to bridge the gap between mathematical theory and physical reality