A numeric-analytic method of solving a nonlinear problem of heat conduction for a right prism

1993 ◽  
Vol 64 (3) ◽  
pp. 984-987
Author(s):  
E. G. Grits'ko ◽  
L. M. Zhuravchak
Keyword(s):  
Heat Conduction ◽  
Nonlinear Problem ◽  
Analytic Method

A catastrophe-theory study of a two-chamber model for a tokamak scrape-off and divertor

1989 ◽  
Vol 42 (1) ◽  
pp. 59-74
Author(s):  
Alkesh Punjabi
Keyword(s):  
Heat Conduction ◽  
Catastrophe Theory ◽  
Geometric Mean ◽  
Plasma Transport ◽  
Analytic Method ◽  
Mode Transition ◽  
Threshold Values ◽  
Electron Heat ◽  
Chamber Model ◽  
Field Lines

The two-chamber model (TCM) of Singer and Langer is employed to study the plasma transport in the scrape-off and divertor regions of a tokamak. Collisiondominated transport along the field lines is considered, with a. geometric-mean flux-limited expression for parallel electron heat conduction. An analytic method for the catastrophe-theory study of the TCM is developed. Maxwell convention for the catastrophes is adopted. Catastrophes occur when the energy flux entering the divertor chamber from the main plasma scrape-off, the recycling coefficient and the ratio of electron temperatures in the scape-off to that in the divertor exceed some threshold values. It is seen that the behaviour of the plasma during these catastrophes is in qualitative agreement with the experimentally observed features of the plasma during the H-mode transition.

A Novel Method for Transient Heat Conduction in a Quasi-Periodic Structure With Nonlinear Defects

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Haichao Cui ◽  
Qiang Gao ◽  
Xiaolan Li ◽  
Huajiang Ouyang
Keyword(s):  
Heat Conduction ◽  
Periodic Structure ◽  
Nonlinear Problem ◽  
Superposition Principle ◽  
Nonlinear Problems ◽  
Transient Heat Conduction ◽  
Small Scale ◽  
Novel Method ◽  
Physical Features ◽  
Small Scale Structures

Abstract This paper proposes an efficient numerical method for transient heat conduction in a quasi-periodic structure with nonlinear defects. According to the physical features of transient heat conduction, a quasi-superposition principle for transient heat conduction in a quasi-periodic structure with nonlinear defects is presented, and then a new method is developed to separate the above nonlinear problem to be solved into a linear problem of a perfect periodic structure and nonlinear problems of some small-scale structures with defects. As the scale of nonlinear problem to be solved is significantly reduced and low computational resource is required, outstanding efficiency is achieved. Finally, a numerical example shows that the proposed method is effective and accurate.

Nonlinear problem of heat conduction for a heat-sensitive sphere

1992 ◽  
Vol 62 (1) ◽  
pp. 103-106
Author(s):  
Yu. M. Kolyano ◽  
E. G. Ivanik ◽  
O. V. Sikora
Keyword(s):  
Heat Conduction ◽  
Nonlinear Problem
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