Definition and Evaluation of Mean Beam Lengths for Applications in Multidimensional Radiative Heat Transfer: A Mathematically Self-Consistent Approach

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Walter W. Yuen
Keyword(s):  
Radiative Heat ◽  
Radiation Effect ◽  
Three Dimensional ◽  
Beam Length ◽  
Zonal Method ◽  
One Dimensional ◽  
Functional Behavior ◽  
Self Consistent ◽  
Multiple Absorption ◽  
Consistent Approach

A set of mathematically self-consistent definitions of mean beam length is introduced to account for surface-surface, surface-volume, and volume-volume radiative exchanges in general three-dimensional inhomogeneous medium. Based on these definitions, the generic exchange factor (GEF) formulated by the recently introduced multiple-absorption-coefficient-zonal-method (MACZM) can be written in an equivalent one-dimensional form. The functional behavior of the proposed mean beam lengths is shown to be readily correlated by either simple algebraic relations or neural network based correlations. They can be implemented directly with MACZM in general computational code to account for the radiation effect in complex three-dimensional systems. In addition, these definitions of mean beam length can also be used to assess the accuracy of the conventional mean beam length concept currently used by the practicing engineering community.

scholarly journals Josephson oscillations in split one-dimensional Bose gases

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Yuri Daniel van Nieuwkerk ◽  
Jörg Schmiedmayer ◽  
Fabian Essler
Keyword(s):  
Three Dimensional ◽  
Time Dependent ◽  
Dimensional Theory ◽  
Bose Gases ◽  
Microscopic Description ◽  
One Dimensional ◽  
Hartree Fock ◽  
Equilibrium Dynamics ◽  
Self Consistent ◽  
Double Well Potential

We consider the non-equilibrium dynamics of a weakly interacting Bose gas tightly confined to a highly elongated double well potential. We use a self-consistent time-dependent Hartree--Fock approximation in combination with a projection of the full three-dimensional theory to several coupled one-dimensional channels. This allows us to model the time-dependent splitting and phase imprinting of a gas initially confined to a single quasi one-dimensional potential well and obtain a microscopic description of the ensuing damped Josephson oscillations.

CAN DIFFUSION MODEL LOCALIZATION IN OPEN MEDIA?

2012 ◽  
Vol 11 ◽  
pp. 96-101
Author(s):  
CHU-SHUN TIAN ◽  
SAI-KIT CHEUNG ◽  
ZHAO-QING ZHANG
Keyword(s):  
Field Theory ◽  
Diffusion Model ◽  
First Principles ◽  
Anderson Localization ◽  
Three Dimensional ◽  
One Dimensional ◽  
Wave Transport ◽  
Self Consistent ◽  
Local Diffusion ◽  
Localized Waves

We employed a first-principles theory – the supersymmetric field theory – formulated for wave transport in very general open media to study static transport of waves in quasi-one-dimensional localized samples. We predicted analytically and confirmed numerically that in these systems, localized waves display an unconventional diffusive phenomenon. Different from the prevailing self-consistent local diffusion model, our theory is capable of capturing all disorder-induced resonant transmissions, which give rise to significant enhancement of local diffusion inside a localized sample. Our theory should be able to be generalized to two- and three-dimensional open media, and open a new direction in the study of Anderson localization in open media.

Development of a Multiple Absorption Coefficient Zonal Method (MACZM) for Application to Radiative Heat Transfer in Multi-Dimensional Inhomogeneous Non-Gray Media

Volume 4 ◽  
2004 ◽  
Author(s):  
Walter W. Yuen
Keyword(s):  
Heat Transfer ◽  
Absorption Coefficient ◽  
Radiative Heat Transfer ◽  
Steam Explosion ◽  
Radiative Heat ◽  
Zonal Method ◽  
Fine Grid ◽  
Element Computation ◽  
Multiple Absorption ◽  
Finite Element Computation

The formulation of a multiple absorption coefficient zonal method (MACZM) is presented. The method can be directly applied to a fine-grid finite-difference or finite-element computation and is thus an effective approach to generate accurate assessment of the importance of radiative heat transfer in multi-dimensional inhomogeneous, non-gray media. The feasibility of the method is demonstrated by calculating the radiative exchange between a high temperature (∼3000 K) molten nuclear fuel (UO2) and water (with a large variation in absorption coefficient from the visible to the infrared) in a highly 3-D and inhomogeneous environment simulating the premixing phase of a steam explosion.

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