Time-fractional telegraph equation for hydrogen diffusion during severe accident in BWRs

The aim of this work is to study the behavior of heat and mass transfer during hydrogen generation in the core of the boiling water reactor (BWR). The core of the BWR is a system highly heterogeneous where the transport processes are complex. The core is considered as an average channel of the fuel assembly, which consists of arrays of in-line fuel rod. This study considers diffusion and reaction due to generation of hydrogen during severe accident in a nuclear power plant with reactor type BWR. The temperature distribution in the nuclear fuel is obtained with a normal diffusion model, whereas that of the distribution of the hydrogen concentration is obtained with a time-fractional telegraph equation (TFTE). The TFTE allows consider the anomalous diffusion processes (non-Fickian effects), which govern the transport in heterogeneous systems.The numerical experiments were performance in an averaging channel that represents a core reactor with the fuel rod with its gap and cladding and cooling steam, in order to establish the importance of the effects of hydrogen diffusion in a severe accident scenario. The initial conditions of this scenario correspond to 100% of rated power, with scram of the reactor, and without cooling flow. The temperature of the fuel is incremented due to decay heat, and due to lack of cooling the fuel temperature increases, which eventually causes fuel cladding oxidation and hydrogen generation.The hydrogen concentration results in a reaction due to oxidation for different values of fractional coefficient, at t=0t=0 and short times were obtained. The physical meaning is discussed when the fractional coefficient tends to a value of 1 and when it tends to a value of 0.5, i.e., within the limits of validity of the fractional model proposed. According to the results obtained the hydrogen concentration is inversely proportional to the fractional coefficient. These results are relevant for decision making in terms of risk analysis in nuclear power plant with BWR.