A computational process for choosing the relaxation parameter in nonlinear SOR

Computing ◽  
1986 ◽  
Vol 37 (1) ◽  
pp. 19-29 ◽  
Author(s):  
M. E. Brewster ◽  
R. Kannan
Keyword(s):  
Relaxation Parameter ◽  
Computational Process

scholarly journals Numerical Study of a Cooling System Using Phase Change of a Refrigerant in a Thermosyphon

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3634
Author(s):  
Grzegorz Czerwiński ◽  
Jerzy Wołoszyn
Keyword(s):  
Mass Transfer ◽  
Phase Change ◽  
Heat Dissipation ◽  
Cooling System ◽  
Numerical Study ◽  
Relaxation Parameter ◽  
Phase Changes ◽  
Transfer Time ◽  
Two Phase ◽  
Time Relaxation

With the increasing trend toward the miniaturization of electronic devices, the issue of heat dissipation becomes essential. The use of phase changes in a two-phase closed thermosyphon (TPCT) enables a significant reduction in the heat generated even at high temperatures. In this paper, we propose a modification of the evaporation–condensation model implemented in ANSYS Fluent. The modification was to manipulate the value of the mass transfer time relaxation parameter for evaporation and condensation. The developed model in the form of a UDF script allowed the introduction of additional source equations, and the obtained solution is compared with the results available in the literature. The variable value of the mass transfer time relaxation parameter during condensation rc depending on the density of the liquid and vapour phase was taken into account in the calculations. However, compared to previous numerical studies, more accurate modelling of the phase change phenomenon of the medium in the thermosyphon was possible by adopting a mass transfer time relaxation parameter during evaporation re = 1. The assumption of ten-fold higher values resulted in overestimated temperature values in all sections of the thermosyphon. Hence, the coefficient re should be selected individually depending on the case under study. A too large value may cause difficulties in obtaining the convergence of solutions, which, in the case of numerical grids with many elements (especially three-dimensional), significantly increases the computation time.

Computational process optimization of array edges

2012 ◽  
Author(s):  
Bernd Küchler ◽  
Artem Shamsuarov ◽  
Thomas Mülders ◽  
Ulrich Klostermann ◽  
Seung-Hune Yang ◽  
...  
Keyword(s):  
Process Optimization ◽  
Computational Process

Analysis of Convective-Radiative Fins by Using Hybrid Spline Difference Method

2013 ◽  
Vol 284-287 ◽  
pp. 3345-3351
Author(s):  
Chi Chang Wang ◽  
Wu Jung Liao ◽  
Lu Ping Chao
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Finite Difference Method ◽  
Difference Method ◽  
Radiative Heat ◽  
High Accuracy ◽  
Spline Method ◽  
Computational Process ◽  
Numerical Accuracy ◽  
Constant Heat

This study used rectangular fins with constant heat transfer coefficient as material to discuss convective and radiative heat transfer, so as to prove that the hybrid spline difference method proposed in this study is an easy to operate method with high accuracy. According to the computational process described in this paper, the hybrid spline difference method is as simple as finite difference method and is easy to use. The complex computational process of traditional spline method can be simplified by using this method, but the numerical accuracy can be increased to second order. Therefore, the high accuracy numerical method of hybrid spline difference method replacing traditional spline method for future heat transfer analyses is expectable.

Elastic Effects on Rayleigh-Be´nard-Marangoni Convection in Liquids With Temperature-Dependent Viscosity

2009 ◽  
Author(s):  
G. N. Sekhar ◽  
G. Jayalatha
Keyword(s):  
Stress Relaxation ◽  
Variable Viscosity ◽  
Relaxation Parameter ◽  
Oscillatory Convection ◽  
Tight Coupling ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Viscoelastic Liquids ◽  
Retardation Parameter

A linear stability analysis of convection in viscoelastic liquids with temperature-dependent viscosity is studied using normal modes and Galerkin method. Stationary convection is shown to be the preferred mode of instability when the ratio of strain retardation parameter to stress relaxation parameter (elasticity ratio) is greater than unity. When the ratio is less than unity the possibility of oscillatory convection is shown to arise. Oscillatory convection is studied numerically for Rivlin-Ericksen, Walters B′, Maxwell and Jeffreys liquids by considering free-free and rigid-free isothermal/adiabatic boundaries. It is found that there is a tight coupling between the Rayleigh and Marangoni numbers, with an increase in one resulting in a decrease in the other. The effect of variable viscosity parameter is shown to destabilize the system. The problem reveals the stabilizing nature of strain retardation parameter and destabilizing nature of stress relaxation parameter, on the onset of convection. The Maxwell liquids are found to be more unstable than the one subscribing to Jeffreys description whereas the Rivlin-Ericksen and Walters B′ liquids are comparatively more stable. Rigid-free adiabatic boundary combination is found to give rise to a most stable system, whereas the free isothermal free adiabatic combination gives rise to a most unstable system. The problem has applications in non-isothermal systems having viscoelastic liquids as working media.

ENHANCING ADEQUACY OF GRADING STUDY PROJECTS ON THE BASE OF PARAMETRIC RELAXATION OF PAIRWISE COMPARISONS

2021 ◽  
Vol 1 ◽  
pp. 122-133
Author(s):  
Alexey V. Oletsky ◽  
◽  
Mikhail F. Makhno ◽  
◽  
Keyword(s):  
Center Of Mass ◽  
Estimation Algorithm ◽  
Relaxation Parameter ◽  
Connected Components ◽  
Pairwise Comparisons ◽  
Strongly Connected Components ◽  
Standard Scale ◽  
Relaxation Parameters ◽  
Strongly Connected ◽  
The One

A problem of automated assessing of students’ study projects is regarded. A heuristic algorithm based on fuzzy estimating of projects and on pairwise comparisons among them is proposed. For improving adequacy and naturalness of grades, an approach based on introducing a parameter named relaxation parameter was suggested in the paper. This enables to reduce the spread between maximum and minimum values of projects in comparison with the one in the standard scale suggested by T. Saati. Reasonable values of this parameter were selected experimentally. For estimating the best alternative, a center of mass of a fuzzy max-min composition should be calculated. An estimation algorithm for a case of non-transitive preferences based on getting strongly connected components and on pairwise comparisons between them is also suggested. In this case, relaxation parameters should be chosen separately for each subtask. So the combined technique of evaluating alternatives proposed in the paper depends of the following parameters: relaxation parameters for pairwise comparisons matrices within each strongly connected components; relaxation parameter for pairwise comparisons matrices among strongly connected components; membership function for describing the best alternative.

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