scholarly journals Transient Thermal Field Analysis in ACCC Power Lines by the Green’s Function Method

Energies ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 280
Author(s):  
Jerzy Gołębiowski ◽  
Marek Zaręba
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Thermal Field ◽  
Continuity Condition ◽  
Field Analysis ◽  
Parabolic Differential Equations ◽  
Steady State Current ◽  
Core Line ◽  
Transient Thermal

The paper investigates the dynamics of the thermal field of the ACCC (aluminum conductor composite core) line. The system was heated by solar radiation and current flow. Conductor cooling was modeled using the total heat transfer coefficient as the sum of convective and radiative components. The temperature increase generated by the current is described by a system of parabolic differential equations with an appropriate set of boundary, initial and continuity condition. The mentioned boundary-initial problem was solved by a modified Green’s method, adapted to the layered structure of the system. For this purpose, Green’s functions, as the kernels of integral operators inverse to differential ones, were determined. Aluminum resistivity and heat transfer coefficient change significantly with temperature. For this reason, the solution to the problem is presented in the form of a lower and upper estimation of the heating curve and local time constant. A steady-state current rating was also determined. The results are presented graphically and verified by other methods (power balance and finite element). The physical interpretation of the presented solution is also given.

Method of analysis of asymmetrical thermal field in a double insulated wire

2017 ◽  
Vol 36 (4) ◽  
pp. 1075-1088
Author(s):  
Jerzy Golebiowski ◽  
Marek Zareba
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Axial Symmetry ◽  
Thermal Field ◽  
Scalar Fields ◽  
Content Type ◽  
Steady State Current ◽  
The Wire

Purpose The purpose of this article is investigating the impact of the spatially variable heat transfer coefficient on the thermal field in the double insulated wire. Design/methodology/approach The effect of the air boundary layer was modelled by means of changing the total heat transfer coefficient on the external perimeter of the wire. This leads to an elliptical boundary problem with Hankel’s condition dependent on the angular coordinate. The eigenfunctions of the problem were determined analytically. On the other hand, the unknown coefficients of eigenfunctions and the constants were calculated numerically by solving a respective system of algebraic equations. The steady state current rating was determined with an iterative method. Findings By means of the presented method, the thermal field distribution deprived of axial symmetry in the double insulated wire was determined. The obtained results have good physical interpretation and were verified with the finite element method (by means of NISA v. 16 software). The determined values of the steady-state current rating were compared with those calculated by means of the equivalent heat transfer coefficient method and the International Electrotechnical Commission (IEC) standard. Research limitations/implications The method is applied to analyse scalar fields in layered cylindrical structures. This could be expanded to the case of a wire of any number of insulation layers. What is more, one could also consider heat sources without axial symmetry and located within the external area. Originality/value The analytical method of determining a thermal field deprived of axial symmetry in heterogeneous cylindrical system (the wire composed of three different materials) was developed.

Parallel analysis of thermal field in a layered DC cable part I

2013 ◽  
Vol 24 (1) ◽  
pp. 58-72 ◽  
Author(s):  
Jerzy Golebiowski ◽  
Robert Piotr Bycul
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Finite Difference ◽  
Transfer Coefficient ◽  
Parallel Algorithm ◽  
Conjugate Gradient ◽  
Thermal Field ◽  
Initial Boundary ◽  
Content Type ◽  
Time Decomposition

Purpose – The paper aims to propose a parallel algorithm in order to increase speed and efficiency of an analysis of transient thermal field in layered DC cables. Design/methodology/approach – Initial-boundary problem of thermal field was discretized by means of implicit finite difference method in cylindrical coordinates. A two-stage time decomposition method was applied to introduce parallel computations. An assumed duration of the transient state was decomposed. The system of algebraic equations was being solved with the use of a conjugate gradient method (with diagonal preconditioning) in all time intervals simultaneously. Findings – A method for solving (with the use of parallel computing system) the transient heat conduction equation in a DC cable consisting of arbitrary number of material layers was given. The dependence of the convective heat transfer coefficient on the location on the perimeter of the cable and on its surface temperature (which introduced non-linearity in the boundary condition) was taken into account. The influence of the determined field on the efficiency of the heat source was also taken into consideration in the model. Research limitations/implications – The main limitation is induced by cylindrical and coaxial structure of the consecutive layers of the system. Thermal field is generated by direct current flow only. The length of the fragment of the cable under consideration should be much greater than its diameter. Practical implications – The time-spatial distribution of thermal field in the cross-section of the cable can be used for analysis of its reliability and for determination of important characteristics and parameters of the system. Originality/value – A parallel algorithm of solving initial-boundary parabolic problem was proposed as a result of synthesis of three methods (finite difference, time decomposition and conjugate gradient). An algorithm of minimization of disturbances of the solution introduced at the division points was given. Equations approximating real distribution of heat transfer coefficient from the surface of the cable were proposed.

Transient Thermal Behavior of Hot–Mix Asphalt Pavement

2011 ◽  
Vol 110-116 ◽  
pp. 400-407
Author(s):  
A. F. Khadrawi ◽  
Ahmad Al-Shyyab ◽  
Saad A. Abo-Qudais
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Thermal Behavior ◽  
Transfer Coefficient ◽  
Hot Mix Asphalt ◽  
Fatigue Cracks ◽  
Incident Radiation ◽  
Transfer Model ◽  
Transient Thermal ◽  
The Impact

A heat transfer model was developed to predict a transient thermal behavior of asphalt concrete during service life at different weather conditions. The developed model has the capability to predict the distribution of temperature field with respect to time within the Hot-Mix asphalt body based on surrounding environmental conditions. This will greatly help pavement engineers to select the suitable asphalt grade to achieve the best pavement performance and avoid pavement distresses might be caused due to extreme pavement temperatures. These distresses include fatigue cracks, rutting, and thermal cracking. The resulted model required data on asphalt mixture, incident radiation, surface, and ambient temperatures in addition to thermal properties of Hot-Mix asphalt including absorptivity, heat transfer coefficient, and the emissivity. A sensitivity analyses wasperformed to study the impact of a number of thermalenvironmental and pavement geometric parameters on predicted temperature responses. The results of analysis indicated that the incident radiation, absorptivity, and the heat transfer coefficient have the most significant effect on Hot-Mix asphalt temperature. Also, the emissivity has insignificant effect on surface temperature Hot-Mix asphalt.

Evaporation of lignin-lean black liquor

TAPPI Journal ◽  
2015 ◽  
Vol 14 (7) ◽  
pp. 441-450
Author(s):  
HENRIK WALLMO, ◽  
ULF ANDERSSON ◽  
MATHIAS GOURDON ◽  
MARTIN WIMBY
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Black Liquor ◽  
Salt Content ◽  
Solubility Limit ◽  
Lignin Removal ◽  
Kraft Black Liquor ◽  
Black Liquors ◽  
The Heat Transfer Coefficient

Many of the pulp mill biorefinery concepts recently presented include removal of lignin from black liquor. In this work, the aim was to study how the change in liquor chemistry affected the evaporation of kraft black liquor when lignin was removed using the LignoBoost process. Lignin was removed from a softwood kraft black liquor and four different black liquors were studied: one reference black liquor (with no lignin extracted); two ligninlean black liquors with a lignin removal rate of 5.5% and 21%, respectively; and one liquor with maximum lignin removal of 60%. Evaporation tests were carried out at the research evaporator in Chalmers University of Technology. Studied parameters were liquor viscosity, boiling point rise, heat transfer coefficient, scaling propensity, changes in liquor chemical composition, and tube incrustation. It was found that the solubility limit for incrustation changed towards lower dry solids for the lignin-lean black liquors due to an increased salt content. The scaling obtained on the tubes was easily cleaned with thin liquor at 105°C. It was also shown that the liquor viscosity decreased exponentially with increased lignin outtake and hence, the heat transfer coefficient increased with increased lignin outtake. Long term tests, operated about 6 percentage dry solids units above the solubility limit for incrustation for all liquors, showed that the heat transfer coefficient increased from 650 W/m2K for the reference liquor to 1500 W/m2K for the liquor with highest lignin separation degree, 60%.

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