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


    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


    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


    Point Kinetic Diffusion

    Theory of point kinetic neutron diffusion equation

    Case study


    Stochastic Point Kinetic Diffusion

    Stochastic point kinetic model



    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.