Solution of an Initial-value Problem in Linear Transport Theory
Solution of an Initial-value Problem in Linear Transport Theory

Author: Perry A. Newman

Publisher:

Published: 1971

Total Pages: 122

ISBN-13:

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The solution of an initial-value problem in linear transport theory is obtained by using the normal-mode expansion technique of Case. The problem is that of monoenergetic neutrons migrating in a thin slab surrounded by infinitely thick reflectors and the scattering is taken to be isotropic. The results obtained indicate that the reflector may give rise to a branch-cut integral term typical of a semi-infinite medium whereas the central slab may contribute a summation over discrete residue terms. Exact expressions are obtained for these discrete time eigenvalues, and numerical results showing the behavior of real time eigenvalues as a function of the material properties of the slab and reflector are presented. These eigenvalues are finite in number and may disappear into the branch cut or continuum as the material properties are varied; such disappearing eigenvalues correspond to exponentially time-decaying modes. The two largest eigenvalues can be compared with critical dimensions of slabs and spheres, and the numerical values are shown to agree with the critically results of others. In the limit of purely absorbing reflectors or a bare slab, the present solution has the same properties as have been previously reported by others who used the approach of Lehner and Wing.

Radiative Heat Transfer
Radiative Heat Transfer

Author: Michael F. Modest

Publisher: Academic Press

Published: 2013-02-20

Total Pages: 905

ISBN-13: 0123869900

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The third edition of Radiative Heat Transfer describes the basic physics of radiation heat transfer. The book provides models, methodologies, and calculations essential in solving research problems in a variety of industries, including solar and nuclear energy, nanotechnology, biomedical, and environmental. Every chapter of Radiative Heat Transfer offers uncluttered nomenclature, numerous worked examples, and a large number of problems—many based on real world situations—making it ideal for classroom use as well as for self-study. The book's 24 chapters cover the four major areas in the field: surface properties; surface transport; properties of participating media; and transfer through participating media. Within each chapter, all analytical methods are developed in substantial detail, and a number of examples show how the developed relations may be applied to practical problems. Extensive solution manual for adopting instructors Most complete text in the field of radiative heat transfer Many worked examples and end-of-chapter problems Large number of computer codes (in Fortran and C++), ranging from basic problem solving aids to sophisticated research tools Covers experimental methods

Transport Theory
Transport Theory

Author: Richard Bellman

Publisher: American Mathematical Soc.

Published: 1969

Total Pages: 340

ISBN-13: 9780821813201

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The industrial and military applications of atomic energy have stimulated much mathematical research in neutron transport theory. The possibility of controlled thermonuclear processes has similarly focussed attention upon plasmas, sometimes called the "fourth state of matter". Independently, many classical aspects of kinetic theory and radiative transfer theory have been studied both because of their basic mathematical interest and of their physical applications to areas such as upper-atmosphere meteorology - introduction.

Multi-group Discrete Sn Transport Calculation for Cylindrical Geometry
Multi-group Discrete Sn Transport Calculation for Cylindrical Geometry

Author: Ronald M. Saqui

Publisher:

Published: 1965

Total Pages: 115

ISBN-13:

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A computer code is presented for neutron transport calculations on a cylindrical geometry, gaseous core, nuclear rocket. The code is applied to a simplified reactor system model consisting of a two region right cylindrical cavity core with an effective temperature of 3980K. The calculations are performed using a five energy group, discrete S4 approximation of the Boltzmann Equation. The cylindrical form of the Boltzmann Equation is developed in detail. Application of the discrete Sn approximation to obtain the finite difference equations and the boundary conditions is shown. An iterative procedure having the total fission source production as the eigenvalue is used by the computer code to solve these equations numerically. This code is written in Fortran IV language for the IBM 7094 coupled system. The atom density results of the two systems tested are within 2.5% and 0.6% agreement with those of another code written by T.F. Plunckett of Douglas Aircraft. Although these results are good, variations in the multiplication factor and the inability to significantly effect this factor by small changes in system parameters leads to the conclusion that further tests of the code are required before it may be used in the analysis of the propulsion device. (Author).