scholarly journals Asymptotic approximation for the solution to a semi-linear elliptic problem in a thin aneurysm-type domain

2017 ◽  
Vol 15 (1) ◽  
pp. 1351-1370 ◽  
Author(s):  
Taras A. Mel’nyk ◽  
Arsen V. Klevtsovskiy

Abstract A semi-linear boundary-value problem with nonlinear Robin boundary conditions is considered in a thin 3D aneurysm-type domain that consists of thin curvilinear cylinders that are joined through an aneurysm of diameter 𝓞(ε). Using the multi-scale analysis, the asymptotic approximation for the solution is constructed and justified as the parameter ε → 0. Namely, we derive the limit problem (ε = 0) in the corresponding graph, define other terms of the asymptotic approximation and prove energetic and uniform pointwise estimates. These estimates allow us to observe the impact of the aneurysm on some properties of the solution.

Polymer ◽  
2017 ◽  
Vol 108 ◽  
pp. 163-172 ◽  
Author(s):  
Samira Fernandes Nassar ◽  
Alain Guinault ◽  
Nicolas Delpouve ◽  
Véronique Divry ◽  
Violette Ducruet ◽  
...  

2014 ◽  
Vol 187 ◽  
pp. 155-170 ◽  
Author(s):  
Marc Corbeels ◽  
Jan de Graaff ◽  
Tim Hycenth Ndah ◽  
Eric Penot ◽  
Frederic Baudron ◽  
...  

Catalysts ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 505 ◽  
Author(s):  
Hamid Reza Godini ◽  
Mohammadali Khadivi ◽  
Mohammadreza Azadi ◽  
Oliver Görke ◽  
Seyed Mahdi Jazayeri ◽  
...  

A multi-aspect analysis of low-pressure catalytic hydrogenation of CO2 for methanol production is reported in the first part (part I) of this paper. This includes an extensive review of distinguished low-pressure catalytic CO2-hydrogenation systems. Specifically, the results of the conducted systematic experimental investigation on the impacts of synthesis and micro-scale characteristics of the selected Cu/ZnO/Al2O3 model-catalysts on their activity and stability are discussed. The performance of the investigated Cu/ZnO/Al2O3 catalysts, synthesized via different methods, were tested under a targeted range of operating conditions in this research. Specifically, the performances of these tested Cu/ZnO/Al2O3 catalysts with regard to the impacts of the main operating parameters, namely H2/CO2 ratio (at stoichiometric -3-, average -6- and high -9- ratios), temperature (in the range of 160–260 °C) and the lower and upper values of physically achievable gas hourly space velocity (GHSV) (corresponding to 200 h−1 and 684 h−1, respectively), were analyzed. It was found that the catalyst prepared by the hydrolysis co-precipitation method, with a homogenously distributed copper content over its entire surface, provides a promising methanol yield of 21% at a reaction temperature of 200 °C, lowest tested GHSV, highest tested H2/CO2 ratio (9) and operating pressure (10 bar). This is in line with other promising results so far reported for this catalytic system even in pilot-plant scale, highlighting its potential for large-scale methanol production. To analyze the findings in more details, the thermal-reaction performance of the system, specifically with regard to the impact of GHSV on the CO2-conversion and methanol selectivity, and yield were experimentally investigated. Moreover, the stability of the selected catalysts, as another crucial factor for potential industrial operation of this system, was tested under continual long-term operation for 150 h, the reaction-reductive shifting-atmospheres and also even after introducing oxygen to the catalyst surface followed by hydrogen reduction-reaction tests. Only the latter state was found to affect the stable performance of the screened catalysts in this research. In addition, the reported experimental reactor performances have been analyzed in the light of equilibrium-based calculated achievable performance of this reaction system. In the performed multi-scale analysis in this research, the requirements for establishing a selective-stable catalytic performance based on the catalyst- and reactor-scale analyses have been identified. This will be combined with the techno–economic performance analysis of the industrial-scale novel integrated process, utilizing the selected catalyst in this research, in the form of an add-on catalytic system under 10 bar pressure and H2/CO2 ratio (3), for efficiently reducing the overall CO2-emission from oxidative coupling of methane reactors, as reported in the second part (part II) of this paper.


2013 ◽  
Vol 34 (9) ◽  
pp. 2078-2084 ◽  
Author(s):  
Yun-fei Wang ◽  
Du-yan Bi ◽  
De-qin Shi ◽  
Tian-jun Huang ◽  
Di Liu

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