Physics informed neural network prediction of heat transfer mechanisms in manufactured sand for thermal energy storage systems

Manufactured sand (M-Sand) is a low-cost granular medium for sensible heat storage and characterising the internal temperature field during charging requires either dense instrumentation or a physics-consistent model. In a previous experimental study, an M-Sand packed-bed thermal energy storage unit was characterised at three flow rates – 1.00, 1.88, and 2.66 LPM–using five internal thermocouples. A physics-informed neural network was trained on this dataset while enforcing the three-dimensional transient heat conduction equation through a physics-constrained loss term. The trained model predicted temperature as a continuous function of space, time, and flow rate. The model achieved R 2 = 0.9616, RMSE = 1.493 °C, and MAE = 0.984 °C across all sensor locations and flow rates. Spatiotemporal maps showed the thermal front advanced faster laterally than axially, with an estimated front velocity of 1.8 × 10 − 5 m/s in the z-direction, consistent with the thermal diffusivity of M-Sand (α = 1.538 × 10 − 7 m 2 /s). Peak temporal heating rate reached 1.2 °C/min near the tube surface. Spatial temperature gradient maps showed peak gradients of 620 °C/m at the tube legs. Three-dimensional isosurfaces captured the progression from tube-adjacent lobes to volume-filling surfaces. The results confirm that a PINN trained on sparse experimental data from five thermocouples and three flow rates can reconstruct the full three-dimensional thermal behaviour of the M-Sand bed within the training operating functioning as a physics-consistent surrogate model that reduces the need for dense sensor instrumentation in packed-bed Thermal energy storage characterisation.