Application of the fractional neutron point kinetic equation: Start-up of a nuclear reactor

Solution of two-point reactor kinetic equations for source-driven reflected reactors using the Green's function generation method

“…surrounded by a thick graphite reflector is taken into consideration [9,13]. The kinetics parameters in subcritical condition are presented in table (1). Using the expression which relates the system reactivity with the coupling parameters, the system reactivity becomes equal to −0.003.…”

“…During the initial reactor start-up, the reactor is in a subcritical condition and the external neutron source plays a crucial role from the reactor control point of view. Since in the reactor start-up process, the average temperature of the reactor core is lower and the power added is smaller, the temperature reactivity feedback mechanism can be neglected [1][2][3].…”

Formulation and Solution of Space-Time Fractional KdV-Burgers Equation

“…Fractional calculus has gained importance during the last decades mainly due to its applications in various fields of science and engineering. Some of the areas of present day applications of fractional calculus include fluid flow, rheology, dynamical process in self-similar and porous structures, diffusive transport akin to diffusion, electrical networks, probability and statistics, control theory of dynamical systems, viscoelasticity, electro-chemistry of corrosion, chemical physics, optics, and signal processing, and so on [1][2][3][4][5][6][7].…”

Generalization of the analytical solution of neutron point kinetics equations with time-dependent external source

“…Since the reactor is in sub-critical state in the cold start-up stage, the external neutron source cannot be ignored. Due to the low average temperature in the reactor core, here, the effect of temperature feedback can be ignored [9,19]; consequently, the NPK equations with the external neutron source term for one group of delayed neutrons can be written as follows [8,11,12,16]:…”

“…Applying too much reactivity will cause a high increase in reactor power and can result in an overpressure accident in the reactor core [9]. Therefore, one should carefully study the influence of external neutron source on the reactor power [10,11]. So far, appropriate mathematical models have already been developed to study the sub-critical kinetics, such as including the constant external neutron source [6], approximation models [12][13][14] and prompt jump approximation (PJA) [9,15,16].…”