Improved Lumped Models for a One-Dimensional Nonlinear Heat Conduction Problem

2007 ◽  
Author(s):  
Ge Su ◽  
Zheng Tan ◽  
Jian Su
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Distributed Parameter ◽  
Nonlinear Heat Conduction ◽  
Lumped Model ◽  
One Dimensional ◽  
Average Temperature ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Lumped Models

This work reports improved lumped-parameter models for a class of one-dimensional nonlinear heat conduction problems in a slab, cylinder or sphere with linearly temperature-dependent thermal conductivity and subject to combined convective and radiative boundary condition. The improved lumped models are obtained through two point Hermite approximations for integrals. It is shown by comparison with numerical solution of the original distributed parameter models that the higher order lumped models (H1, 1/H0, 0 approximation for slab and cylinder, H2, 1/H0, 0 for sphere) yield significant improvement of average temperature predictions over the classical lumped model.

Rewetting Analysis of a PWR Fuel Slab Using Improved Lumped Models

2020 ◽  
Author(s):  
Gustavo Pereira ◽  
Jian Su
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Internal Heat ◽  
Longitudinal Direction ◽  
Slab Thickness ◽  
Two Dimensional ◽  
Average Temperature ◽  
Lumped Parameter ◽  
Lumped Models ◽  
Steady Heat Conduction

Abstract This work analyzes the rewetting of a PWR fuel slab using improved lumped parameter formulations based on Hermite approximations for integrals. The time-dependent two-dimensional rewetting problem is transformed into a quasi-steady heat conduction problem in a reference system moving with the rewetting front by assuming a constant rewetting velocity. The lumped parameter formulations are applied in the slab thickness direction, reducing the two-dimensional problem into a one-dimensional heat conduction equation in the longitudinal direction. The rewetting velocity is obtained by combining the analytical solutions of the average temperature distributions in the reflooded wet region and the liquid deficient dry region at the rewetting front. The Peclet number is obtained as a function of the Biot numbers, dimensionless internal heat generation rate, and dimensionless initial temperatures. The obtained solutions compare favorably with available solutions in the literature.

Improved Lumped Model for Transient Heat Conduction in a Heat Generating Cylinder With Temperature-Dependent Thermophysical Properties

Volume 4 ◽  
2004 ◽  
Author(s):  
Auro C. Pontedeiro ◽  
Renato M. Cotta ◽  
Jian Su
Keyword(s):  
Heat Conduction ◽  
Physical Properties ◽  
Transient Heat Conduction ◽  
Reactor Accident ◽  
Temperature Dependent ◽  
Lumped Model ◽  
Average Temperature ◽  
Lumped Models ◽  
Testing Case ◽  
Thermo Physical Properties

This paper presents improved lumped-differential formulations for one dimensional transient heat conduction in a heat generating cylinder with temperature-dependent thermo-physical properties. Two points Hermite approximations for integrals (H1,1/H1,1) are used to approximate the average temperature and the heat flux in the radial direction. As a testing case, transient heat conduction in a nuclear fuel rod was computed with the thermo-physical properties represented by correlations from MATPRO — a Library of Materials Properties for Light-Water-Reactor Accident Analysis. The problem was formulated and solved using the symbolic/numerical computation software system MATHEMATICA. The solution of the proposed improved lumped models is validated by a numerical solution of the original distributed parameter formulation.

Transient Heat Transfer Solution Using Improved Lumped Model

2015 ◽  
Vol 813-814 ◽  
pp. 773-775
Author(s):  
Anmol Chatrath ◽  
Neel Kanth Grover
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
High Temperature ◽  
Temperature Gradient ◽  
Biot Number ◽  
Transient State ◽  
Difference Model ◽  
Lumped Model ◽  
One Dimensional ◽  
Average Temperature

In present study, transient state one-dimensional heat conduction is analyzed using polynomial approximation method. In comparison with the classical lumped model, an improved lumped model have been employed as the classical lumped model is applicable for biot number of less than 0.1 and it cannot be used for high temperature gradient. An improved lumped model has been employed for sphere to calculate average temperature as a function of time for higher and lower values of biot number. The study shows that the lumped model provides better accuracy as compared to finite difference model.

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