Describing function theory as applied to thermal and neutronic problems

Thesis/Dissertation · Sat Jan 01 00:00:00 EST 1983

OSTI ID:6912160

Nassersharif, B

Describing functions have traditionally been used to obtain the solutions of systems of ordinary differential equations. In this work the describing function concept has been extended to include nonlinear, distributed parameter partial differential equations. A three-stage solution algorithm is presented which can be applied to any nonlinear partial differential equation. Two generalized integral transforms were developed as the T-transform for the time domain and the B-transform for the spatial domain. The thermal diffusion describing function (TDDF) is developed for conduction of heat in solids and a general iterative solution along with convergence criteria is presented. The proposed solution method is used to solve the problem of heat transfer in nuclear fuel rods with annular fuel pellets. As a special instance the solid cylindrical fuel pellet is examined. A computer program is written which uses the describing function concept for computing fuel pin temperatures in the radial direction during reactor transients. The second problem investigated was the neutron diffusion equation which is intrinsically different from the first case. Although, for most situations, it can be treated as a linear differential equation, the describing function method is still applicable. A describing function solution is derived for two possible cases: constant diffusion coefficient and variable diffusion coefficient. Two classes of describing functions are defined for each case which portray the leakage and absorption phenomena. For the specific case of a slab reactor criticality problem the comparison between analytical and describing function solutions revealed an excellent agreement.

• Research Organization: Oregon State Univ., Corvallis (USA)
• OSTI ID: 6912160
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
22 GENERAL STUDIES OF NUCLEAR REACTORS
PARTIAL DIFFERENTIAL EQUATIONS
NONLINEAR PROBLEMS
REACTORS
HEAT TRANSFER
NEUTRON TRANSPORT
ALGORITHMS
ANNULAR FUEL ELEMENTS
COMPUTER CODES
CRITICALITY
INTEGRAL TRANSFORMATIONS
NEUTRON DIFFUSION EQUATION
TEMPERATURE DEPENDENCE
THERMAL DIFFUSION
TRANSIENTS
DIFFERENTIAL EQUATIONS
DIFFUSION
ENERGY TRANSFER
EQUATIONS
FUEL ELEMENTS
MATHEMATICAL LOGIC
NEUTRAL-PARTICLE TRANSPORT
RADIATION TRANSPORT
REACTOR COMPONENTS
TRANSFORMATIONS
658000* - Mathematical Physics- (-1987)
220100 - Nuclear Reactor Technology- Theory & Calculation