Adaptive Observer for Space-Fractional Partial Differential Model of Gas Pressures in Fractured Media

2021 ◽  
Author(s):  
Lilia Ghaffour ◽  
Taous-Meriem Laleg-Kirati
Keyword(s):  
Fractured Media ◽  
Adaptive Observer ◽  
Partial Differential ◽  
Differential Model ◽  
Gas Pressures

scholarly journals An improved lumped model for freezing of a freely suspended supercooled water droplet in air stream

2021 ◽  
Vol 130 (1) ◽  
Author(s):  
Emerson B. dos Anjos ◽  
Carolina P. Naveira-Cotta ◽  
Manish K. Tiwari ◽  
Renato M. Cotta ◽  
Igor S. Carvalho
Keyword(s):  
Water Droplet ◽  
Supercooled Water ◽  
Freezing Process ◽  
Partial Differential ◽  
Interface Position ◽  
Spherical Droplet ◽  
Differential Model ◽  
Differential Formulation ◽  
Air Stream ◽  
Freely Suspended

AbstractThis work deals with the mathematical modeling of the transient freezing process of a supercooled water droplet in a cold air stream. The aim is to develop a simple yet accurate lumped-differential model for the energy balance for a freely suspended water droplet undergoing solidification, that allows for cost effective computations of the temperatures and freezing front evolution along the whole process. The complete freezing process was described by four distinct stages, namely, supercooling, recalescence, solidification, and cooling. At each stage, the Coupled Integral Equations Approach (CIEA) is employed, which reduces the partial differential equation for the temperature distribution within the spherical droplet into coupled ordinary differential equations for dimensionless boundary temperatures and the moving interface position. The resulting lumped-differential model is expected to offer improved accuracy with respect to the classical lumped system analysis, since boundary conditions are accounted for in the averaging process through Hermite approximations for integrals. The results of the CIEA were verified using a recently advanced accurate hybrid numerical-analytical solution through the Generalized Integral Transform Technique (GITT), for the full partial differential formulation, and comparisons with numerical and experimental results from the literature. After verification and validation of the proposed model, a parametric analysis is implemented, for different conditions of airflow velocity and droplet radius, which lead to variations in the Biot numbers that allow to inspect for their influence on the accuracy of the improved lumped-differential formulation.

A Partial Differential Model for the Pyrolysis of Materials with Movable Residual Layer

2005 ◽  
Vol 12 (2) ◽  
pp. 77-83
Author(s):  
John Z. Lin ◽  
T. T. Chow ◽  
You Fei ◽  
Zhou Jianjun ◽  
Zou Yanghui
Keyword(s):  
Residual Layer ◽  
Partial Differential ◽  
Differential Model

Principles of Low-Vacuum SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1304-1305
Author(s):  
Klaus-Ruediger Peters
Keyword(s):  
New Technologies ◽  
High Vacuum ◽  
Optical Microscope ◽  
Specimen Surface ◽  
Electrical Field ◽  
Gaseous Environment ◽  
New Information ◽  
Gas Molecules ◽  
New Interactions ◽  
Gas Pressures

Only recently it became possible to expand scanning electron microscopy to low vacuum and atmospheric pressure through the introduction of several new technologies. In principle, only the specimen is provided with a controlled gaseous environment while the optical microscope column is kept at high vacuum. In the specimen chamber, the gas can generate new interactions with i) the probe electrons, ii) the specimen surface, and iii) the specimen-specific signal electrons. The results of these interactions yield new information about specimen surfaces not accessible to conventional high vacuum SEM. Several microscope types are available differing from each other by the maximum available gas pressure and the types of signals which can be used for investigation of specimen properties.Electrical non-conductors can be easily imaged despite charge accumulations at and beneath their surface. At high gas pressures between 10-2 and 2 torr, gas molecules are ionized in the electrical field between the specimen surface and the surrounding microscope parts through signal electrons and, to a certain extent, probe electrons. The gas provides a stable ion flux for a surface charge equalization if sufficient gas ions are provided.

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