SP3Solution versus Diffusion Solution in Pin-by-Pin Calculations and Conclusions Concerning Advanced Methods

2014 ◽  
Vol 43 (1-7) ◽  
pp. 214-239 ◽  
Author(s):  
D. Litskevich ◽  
B. Merk
Keyword(s):  
Processes ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 544 ◽  
Author(s):  
Z. Baicha ◽  
M.J. Salar-García ◽  
V.M. Ortiz-Martínez ◽  
F.J. Hernández-Fernández ◽  
A.P. de los Ríos ◽  
...  

In the last few years, the use of ionic liquid-based membranes has gained importance in a wide variety of separation processes due to the unique properties of ionic liquids. The aim of this work is to analyze the transport of nutrients through polymer inclusion membranes based on different concentrations of methyltrioctylammonium chloride, in order to broaden the application range of these kinds of membranes. Calcium chloride (CaCl2) and sodium hydrogen phosphate (Na2HPO4) nutrients were used at the concentration of 1 g·L−1 in the feeding phase. The evolution of the concentration in the receiving phase over time (168 h) was monitored and the experimental data fitted to a diffusion-solution transport model. The results show very low permeation values for CaCl2. By contrast, in the case of Na2HPO4 the permeation values were higher and increase as the amount of ionic liquid in the membrane also increases. The surface of the membranes was characterized before and after being used in the separation process by scanning electron microscopy coupled to energy dispersive X-Ray spectroscopy (SEM–EDX) and elemental mapping analysis. The SEM–EDX images show that the polymer inclusion membranes studied are stable to aqueous solution contacting phases and therefore, they might be used for the selective transport of nutrients in separation processes.


1983 ◽  
Vol 105 (2) ◽  
pp. 333-340 ◽  
Author(s):  
A. C. Ratzel ◽  
J. R. Howell

Radiative energy transfer in a gray absorbing and emitting medium is considered in a two-dimensional rectangular enclosure using the P-N differential approximation. The two-dimensional moment of intensity partial differential equations (PDE’s) are combined to yield a single second-order PDE for the P-1 approximation and four coupled second-order PDE’s for the P-3 approximation. P-1 approximation results are obtained from separation of variables solutions, and P-3 results are obtained numerically using successive-over-relaxation methods. The P-N approximation results are compared with numerical Hottel zone results and with results from an approximation method developed by Modest. The studies show that the P-3 approximation can be used to predict emissive power distributions and heat transfer rates in two-dimensional media with opacities of unity or greater. The P-1 approximation is identical to the diffusion solution and is thus applicable only if the medium is optically dense.


1994 ◽  
Vol 367 ◽  
Author(s):  
M.E. Glicksman ◽  
M.B. Koss ◽  
L.T. Bushnell ◽  
J.C. Lacombe ◽  
E.A. Winsa

AbstractDendritic growth is the most ubiquitous form of crystal growth encountered when metals and alloys solidify under low thermal gradients. The growth of thermal dendrites in pure melts is generally acknowledged to be controlled by the diffusive transport of latent heat from the moving crystal-melt interface into its supercooled melt. However, this formulation is incomplete, and the physics of an additional selection rule, coupled to the transport solution, is necessary to predict uniquely the dendrite tip velocity and radius of curvature as a function of the supercooling. Unfortunately, experimental confirmation or evidence is ambiguous, because dendritic growth can be severely complicated by buoyancy induced convection. Recent experiments performed in the microgravity environment of the space shuttle Columbia (STS-62) quantitatively show that convection alters tip velocities and radii of curvature of succinonitrile (SCN) dendrites. In addition, these data can be used to evaluate how well the Ivantsov diffusion solution, coupled to a scaling constant, matches the dendritic growth data under microgravity conditions.


The physically important conduction-diffusion problem for the Boussinesq equations is considered. It is shown that provided the solution satisfies a set of weak a priori bounds then the conduction-diffusion solution to the final value problem for the Boussinesq equations is stable on compact subintervals of a finite time interval. Uniqueness of a solution to the final value problem is also established.


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