A novel mathematical model is proposed, based on thermodynamics and transport phenomena fundamentals, that aims to capture the hydrogen pressure, temperature and molar volume evolution during a hydrogen vehicle's fill-up process. Hydrogen's thermodynamic properties are calculated through the use of the generic cubic equation of state and residual properties. The obtained model gives rise to a set of differential-algebraic equations (DAE), which are then simulated using a hybrid Newton/Runge-Kutta method. The model's pressure, temperature, volume, and mass flowrate predictions match, within 2%, corresponding experimental data obtained, during a fill-up process, from a fuel cell vehicle's and the fueling station's storage tanks. The model also elucidates the two mechanisms contributing to the temperature increase in the vehicle storage tank: heating by Joule-Thomson expansion and heating by compression. It is shown that Joule-Thomson heating dominates at the beginning of the fill-up process, while compression heating-dominates towards the end of the fill-up process. Copyright (C) 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.