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.

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.

scholarly journals Dynamics of Rising Bubbles in a Quiescent Slag Bath with Varying Thermo-Physical Properties

2020 ◽  
Vol 51 (6) ◽  
pp. 2843-2861
Author(s):  
D. Obiso ◽  
D. H. Schwitalla ◽  
I. Korobeinikov ◽  
B. Meyer ◽  
M. Reuter ◽  
...  
Keyword(s):  
Physical Properties ◽  
Bubble Dynamics ◽  
Fluid Dynamic ◽  
Temperature Gradients ◽  
Slag Bath ◽  
Bubble Motion ◽  
Temperature Dependent ◽  
Slag Properties ◽  
Temperature Dependent Properties ◽  
Thermo Physical Properties

AbstractThe motion of bubbles in a liquid slag bath with temperature gradients is investigated by means of 3D fluid dynamic computations. The goal of the work is to describe the dynamics of the rising bubbles, taking into account the temperature dependency of the thermo-physical properties of the slag. Attention is paid to the modeling approach used for the slag properties and how this affects the simulation of the bubble motion. In particular, the usage of constant values is compared to the usage of temperature-dependent data, taken from models available in the literature and from in-house experimental measurements. Although the present study focuses on temperature gradients, the consideration of varying thermo-physical properties is greatly relevant for the fluid dynamic modeling of reactive slag baths, since the same effect is given by heterogeneous species and solid fraction distributions. CFD is applied to evaluate the bubble dynamics in terms of the rising path, terminal bubble shape, and velocity, the gas–liquid interface area, and the appearance of break-up phenomena. It is shown that the presence of a thermal gradient strongly acts on the gas–liquid interaction when the temperature-dependent properties are considered. Furthermore, the use of literature models and experimental data produces different results, demonstrating the importance of correctly modeling the slag’s thermo-physical properties.

Optimal Removal of Experimental Points to Determine Apparent Thermal Diffusivity of Canned Products

2014 ◽  
Vol 10 (2) ◽  
pp. 223-231 ◽  
Author(s):  
Wilton P. da Silva ◽  
Cleide M. D. P. S. Silva ◽  
Marcos A. A. Lins ◽  
Waldemir S. da Costa
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Analytical Solution ◽  
Heat Conduction Equation ◽  
Transient Heat Conduction ◽  
Agar Gel ◽  
Precision And Accuracy ◽  
Thermo Physical Properties

Abstract To describe the transient heat conduction from or to a product, its thermo-physical properties must be known. If the boundary condition of the heat conduction equation is of the first kind, the process is governed by the thermal diffusivity α. Normally this property is determined by fit of the analytical solution with only the first term of the series to an experimental dataset of the temperature versus time, in which the temperature is measured in a known position. In this case, the value obtained for α contains errors due to the consideration of only one term and the inclusion of the first experimental points in the fit. This article presents an algorithm based on optimal removal of experimental points to minimize errors in the determination of α. The algorithm was validated and applied to heating of Agar gel. The precision and accuracy of the obtained result were, respectively, 0.38 and 0.6%.

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