2D FLAT PLATE HEAT CONDUCTION WITH CONSTANT THERMAL CONDUCTIVITY: IMPLEMENTING THE ALTERNATING DIRECTION IMPLICIT METHOD

The heat equation is widely used in engineering applications to predict temperature distribution in materials subjected to heating or cooling, such as in high-temperature furnaces and pipeline-based heat networks. This study applies the alternating direction implicit (ADI) method to solve a two-dimensional heat conduction problem and evaluates its accuracy through grid convergence and error analysis. Results indicate that finer grid resolutions improve numerical accuracy, with absolute errors decreasing from 15.523 (for a grid size of 110) to 0.493 (for a grid size of 190) at the centre of the plate. Computational efficiency analysis reveals a trade-off, as execution times increase from 0.089907s to 0.432780s for the same grid refinements. These findings confirm the ADI method’s reliability for thermal simulations, offering a balanced approach between precision and computational cost. The study concludes that the ADI method is a robust and efficient tool for modelling heat conduction in engineering applications.