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Closed-form solution of a two-dimensional fuel temperature model for TRIGA-type reactors

Conference:

Abstract

If azimuthal power density variations are ignored, the steady-state temperature distribution within a TRIGA-type fuel element is given by the solution of the Poisson equation in two dimensions (r and z) . This paper presents a closed-form solution of this equation as a function of the axial and radial power density profiles, the conductivity of the U-ZrH, the inlet temperature, specific heat and flow rate of the coolant, and the overall heat transfer coefficient. The method begins with the development of a system of linear ordinary differential equations describing mass and energy balances in the fuel and coolant. From the solution of this system, an expression for the second derivative of the fuel temperature distribution in the axial (z) direction is found. Substitution of this expression into the Poisson equation for T(r,z) reduces it from a partial differential equation to an ordinary differential equation in r, which is subsequently solved in closed-form. The results of typical calculations using the model are presented. (author)
Authors:
Rivard, J B [1] 
  1. Sandia Laboratories (United States)
Publication Date:
Jul 01, 1974
Product Type:
Conference
Report Number:
INIS-US-09N0328; TOC-5
Resource Relation:
Conference: 3. TRIGA owners' conference, Albuquerque, NM (United States), 25-27 Feb 1974; Other Information: Country of input: International Atomic Energy Agency (IAEA); 1 fig; Related Information: In: 3. TRIGA owners' conference. Papers and abstracts, 432 pages.
Subject:
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS; COOLANTS; ENERGY BALANCE; FLOW RATE; HEAT TRANSFER; NUCLEAR FUELS; POISSON EQUATION; POWER DENSITY; SPECIFIC HEAT; STEADY-STATE CONDITIONS; TEMPERATURE DISTRIBUTION; TRIGA TYPE REACTORS; TWO-DIMENSIONAL CALCULATIONS
OSTI ID:
21217733
Research Organizations:
General Atomic Co., San Diego, CA (United States)
Country of Origin:
United States
Language:
English
Other Identifying Numbers:
TRN: US09N0340086517
Availability:
Available from INIS in electronic form
Submitting Site:
INIS
Size:
page(s) 2.43-2.49
Announcement Date:
Oct 19, 2009

Conference:

Citation Formats

Rivard, J B. Closed-form solution of a two-dimensional fuel temperature model for TRIGA-type reactors. United States: N. p., 1974. Web.
Rivard, J B. Closed-form solution of a two-dimensional fuel temperature model for TRIGA-type reactors. United States.
Rivard, J B. 1974. "Closed-form solution of a two-dimensional fuel temperature model for TRIGA-type reactors." United States.
@misc{etde_21217733,
title = {Closed-form solution of a two-dimensional fuel temperature model for TRIGA-type reactors}
author = {Rivard, J B}
abstractNote = {If azimuthal power density variations are ignored, the steady-state temperature distribution within a TRIGA-type fuel element is given by the solution of the Poisson equation in two dimensions (r and z) . This paper presents a closed-form solution of this equation as a function of the axial and radial power density profiles, the conductivity of the U-ZrH, the inlet temperature, specific heat and flow rate of the coolant, and the overall heat transfer coefficient. The method begins with the development of a system of linear ordinary differential equations describing mass and energy balances in the fuel and coolant. From the solution of this system, an expression for the second derivative of the fuel temperature distribution in the axial (z) direction is found. Substitution of this expression into the Poisson equation for T(r,z) reduces it from a partial differential equation to an ordinary differential equation in r, which is subsequently solved in closed-form. The results of typical calculations using the model are presented. (author)}
place = {United States}
year = {1974}
month = {Jul}
}