Fractal neutrons diffusion equation: Uniformization of heat and fuel burn-up in nuclear reactor

Abstract

In this study, the fractal neutrons diffusion equation is constructed based on the concept of fractal anisotropy and product-like fractal measure introduced by Li and Ostoja-Starzewski using the method of dimensional regularization. In this approach, the global forms of dynamical equations are cast in forms involving integer-order integrals while the local forms are expressed by partial differential equations with derivatives of integer order. This theory is characterized by an effective buckling which varies with distance and a diffusion damping characterized by a spatially variable coefficient. These terms are major in nuclear reactor physics since the magnitude of energy dissipation in fission depends on the position and nature of interaction. We have discussed the cases of parallelepiped and finite cylinder reactors. In both geometrical types of reactors, it was observed that the ratio of the maximum flux to the average flux is too small since the uniformization of the heat fabrication and the fuel burn-up in the nuclear reactor is potential. This has important consequences on safety of the fuel operation and on the types of nuclear materials used in nuclear engineering reactors. Further details are discussed as well.