1st Edition

Neutron Diffusion Concepts and Uncertainty Analysis for Engineers and Scientists

By S. Chakraverty, Sukanta Nayak Copyright 2017
    196 Pages
    by CRC Press

    194 Pages 80 B/W Illustrations
    by CRC Press

    This book is designed for a systematic understanding of nuclear diffusion theory along with fuzzy/interval/stochastic uncertainty. This will serve to be a benchmark book for graduate & postgraduate students, teachers, engineers and researchers throughout the globe.





    In view of the recent developments in nuclear engineering, it is important to study the basic concepts of this field along with the diffusion processes for nuclear reactor design. Also, it is known that uncertainty is a must in every field of engineering and science and, in particular, with regards to nuclear-related problems. As such, one may need to understand the nuclear diffusion principles/theories corresponding with reliable and efficient techniques for the solution of such uncertain problems. Accordingly this book aims to provide a new direction for readers with basic concepts of reactor physics as well as neutron diffusion theory. On the other hand, it also includes uncertainty (in terms of fuzzy, interval, stochastic) and their applications in nuclear diffusion problems in a systematic manner, along with recent developments. The underlying concepts of the presented methods in this book may very well be used/extended to various other engineering disciplines viz. electronics, marine, chemical, mining engineering and other sciences such as physics, chemistry, biotechnology etc. This book then can be widely applied wherever one wants to model their physical problems in terms of non-probabilistic methods viz. fuzzy/stochastic for the true essence of the real problems.



    Basic Reactor Principles



    Atomic Structure



    Binding energy



    Nuclear fusion



    Nuclear fission



    Radioactivity



    Principles, Production, and interaction of neutrons with matter



    Production of neutrons



    Neutron reactions and radiation



    Inelastic and elastic scattering of neutrons



    Maxwell-Boltzmann distribution



    Neutron diffusion theory



    Cross section of neutron reactions



    Rates of neutron reactions



    Fission neutrons



    Prompt neutrons



    Delayed neutrons



    Neutron transport and diffusion equation



    Fundamentals of Uncertainty



    Probabilistic uncertainty



    Non-probabilistic uncertainty



    Interval uncertainty



    Fuzzy uncertainty



    Uncertain Neutron diffusion



    Uncertain factors involved in neutron diffusion theory



    Modeling of uncertain neutron diffusion equations



    One group model



    Analytical methods



    Numerical methods



    Finite difference method



    Finite element method



    Conclusion



    Uncertain One Group Model



    Interval arithmetic and Fuzzy Finite Element Method (FFEM)



    Formulation of the uncertain stiffness matrices and force vectors



    Bare square homogeneous reactor



    Multi group model



    Uncertain factors involved in multi group neutron diffusion theory



    Formulation of uncertain multi group neutron diffusion equations



    Uncertain Multi Group Model



    Fuzzy finite element for coupled differential equations



    Fuzzy multi group neutron diffusion equation



    Case study



    Results and discussion



    Conclusion



    Point Kinetic Diffusion



    Theory of point kinetic neutron diffusion equation



    Case study



    Conclusion



    Stochastic Point Kinetic Diffusion



    Stochastic point kinetic model



    Eu

    Biography

    Dr. S. Chakraverty has over 25 years of experience as a researcher and teacher. Currently he is working at the National Institute of Technology, Rourkela, Odisha as a full Professor and Head of the Department of Mathematics. Prior to this he was with CSIR Central Building Research Institute, Roorkee, India. After graduating from St. Columba’s College (Ranchi University), he obtained his M. Sc in Mathematics and M. Phil in Computer Applications from the University of Roorkee (now the Indian Institute of Technology Roorkee), earning First Position in the University honors. Dr. Chakraverty received his Ph. D. from IIT Roorkee in 1992. Thereafter he did his post-doctoral research at Institute of Sound and Vibration Research (ISVR), University of Southampton, U.K. and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He was also a visiting professor at Concordia and McGill Universities, Canada, during 1997-1999 and visiting professor of University of Johannesburg, South Africa during 2011-2014.



    Sukanta Nayak received his B.Sc. (Mathematics) from Government Autonomous College, Rourkela in 2008 and M.Sc. (Mathematics) from National Institute of Technology, Rourkela in 2010. He has done his Ph. D. (Mathematics) from National Institute of Technology, Rourkela in 2016. He is the awardee of P. G. level scholarship, Government of Odisha in 2008 and qualified GATE, Government of India, in 2012. Currently he is doing his post-doctoral research at the University of Johannesburg, South Africa. He has published 9 research papers in international peer-reviewed journals, and 2 book chapters.