Advanced Time of Death Estimation Using Non-Linear Time-Dependent Heat Loss Modeling with Spatially and Temporally Variable Coefficients
Keywords:
Time of Death Estimation, Postmortem Interval, Heat Transfer Modeling, Non-Linear PDE, Finite Element Method, Forensic Thermodynamics, Spatially Variable Coefficients, Temporally Adaptive Model, Cooling Curve Analysis, Anatomical Heat LossAbstract
Realistic post-mortem interval (PMI) or time-of-death (TOD) estimation is essential in forensic science to reconstruct event timelines. Newton’s Law of Cooling-based traditional models oversimplify cooling behavior by assuming static ambient environments and constant heat transfer coefficients, ignoring important factors like clothing insulation, regional skin conductance variations, and ambient temperature dynamics. This paper presents a new non-linear, time-varying heat loss model based on variable coefficient ordinary differential equations (ODEs) to account for spatially varying clothing layers, region-specific heat transfer rates, and dynamic ambient temperature profiles. With synthetic data generated using simulated temperature sensors and advanced numerical techniques like the fourth-order Runge-Kutta (RK4) method, the model provides unparalleled accuracy in PMI estimation. Validation with hypothetical case studies shows the model’s potential to transform forensic science by accounting for real-world complexities.
