Smoothed Particle Hydrodynamics for Heat Transfer in Plates: Analytical Validation and Geometric Effects of Internal Heat Sources

Kurniawan, Riski

Journal of the Indonesian Mathematical Society
Vol. 32 No. 2 (2026): JUNE

Accurate simulation of heat transfer is essential in many engineering applications. This study investigates heat transfer on thin plates by solving two-dimensional heat equations using the Smoothed Particle Hydrodynamics (SPH) method. The accuracy of the formulation is evaluated by comparing SPH results with analytical solutions for Dirichlet and Neumann boundary conditions, where small nRMSE values confirm good agreement. The method is then applied to plates with internal heat sources of different but equal-area geometries, showing that the star-shaped source yields the fastest heat transfer. These findings highlight the flexibility of SPH for modeling heat equations under complex geometries and boundary conditions.