Hybrid integral transform solution for the analysis of drying in spherical capillary-porous solids based on Luikov equations with pressure gradient

2013 ◽  
Vol 71 ◽  
pp. 216-236 ◽  
Author(s):  
Renata S.G. Conceição ◽  
Emanuel N. Macêdo ◽  
Lucília B.D. Pereira ◽  
João N.N. Quaresma
Keyword(s):  
Pressure Gradient ◽  
Integral Transform ◽  
Porous Solids ◽  
Hybrid Integral

scholarly journals PARABOLIC BOUNDARY VALUE PROBLEMS IN A PIECEWISE HOMOGENEOUS WEDGE-SHAPED SOLID CYLINDER

2020 ◽  
Vol 8 (2) ◽  
pp. 40-55
Author(s):  
A. Gromyk ◽  
I. Konet ◽  
T. Pylypyuk
Keyword(s):  
Boundary Value Problems ◽  
Integral Transform ◽  
Boundary Value ◽  
Initial Boundary ◽  
Integral Transforms ◽  
Initial Boundary Value Problems ◽  
Parabolic Boundary ◽  
Hybrid Integral ◽  
Initial Boundary Value ◽  
Parabolic Boundary Value Problems

The unique exact analytical solutions of parabolic boundary value problems of mathematical physics in piecewise homogeneous wedge-shaped solid cylinder were constructed at first time by the method of integral and hybrid integral transforms in combination with the method of main solutions (matrices of influence and Green matrices). The cases of assigning on the verge of the wedge the boundary conditions of Dirichlet and Neumann and their possible combinations (Dirichlet – Neumann, Neumann – Dirichlet) are considered. Finite integral Fourier transform by an angular variable $\varphi \in (0; \varphi_0)$, a Fourier integral transform on the Cartesian segment $(-l_1;l_2)$ by an applicative variable $z$ and a hybrid integral transform of the Hankel type of the first kind on a segment $(0;R)$ of the polar axis with $n$ points of conjugation by an radial variable $r$ were used to construct solutions of investigated initial-boundary value problems. The consistent application of integral transforms by geometric variables allows us to reduce the three-dimensional initial boundary-value problems of conjugation to the Cauchy problem for a regular linear inhomogeneous 1st order differential equation whose unique solution is written in a closed form. The application of inverse integral transforms restores explicitly the solution of the considered problems through their integral image. The structure of the solution of the problem in the case of setting the Neumann boundary conditions on the wedge edges is analyzed. Exact analytical formulas for the components of the main solutions are written and the theorem on the existence of a single bounded classical solution of the problem is formulated. The obtained solutions are algorithmic in nature and can be used (using numerical methods) in solving applied problems.

scholarly journals A review of hybrid integral transform solutions in fluid flow problems with heat or mass transfer and under Navier–Stokes equations formulation

2019 ◽  
Vol 76 (2) ◽  
pp. 60-87 ◽  
Author(s):  
Renato M. Cotta ◽  
Kleber M. Lisboa ◽  
Marcos F. Curi ◽  
Stavroula Balabani ◽  
João N. N. Quaresma ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Integral Transform ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Hybrid Integral

Activated Prominences; Mechanisms for Activation and Eruption

1979 ◽  
Vol 44 ◽  
pp. 307-313
Author(s):  
D.S. Spicer
Keyword(s):  
Pressure Gradient ◽  
Density Gradient ◽  
Current Density ◽  
Convective Instability ◽  
Tearing Mode ◽  
Magnetic Shear ◽  
Long Wavelength ◽  
Ideal Mhd ◽  
Gradient Change ◽  
Accelerated Particles

A possible relationship between the hot prominence transition sheath, increased internal turbulent and/or helical motion prior to prominence eruption and the prominence eruption (“disparition brusque”) is discussed. The associated darkening of the filament or brightening of the prominence is interpreted as a change in the prominence’s internal pressure gradient which, if of the correct sign, can lead to short wavelength turbulent convection within the prominence. Associated with such a pressure gradient change may be the alteration of the current density gradient within the prominence. Such a change in the current density gradient may also be due to the relative motion of the neighbouring plages thereby increasing the magnetic shear within the prominence, i.e., steepening the current density gradient. Depending on the magnitude of the current density gradient, i.e., magnetic shear, disruption of the prominence can occur by either a long wavelength ideal MHD helical (“kink”) convective instability and/or a long wavelength resistive helical (“kink”) convective instability (tearing mode). The long wavelength ideal MHD helical instability will lead to helical rotation and thus unwinding due to diamagnetic effects and plasma ejections due to convection. The long wavelength resistive helical instability will lead to both unwinding and plasma ejections, but also to accelerated plasma flow, long wavelength magnetic field filamentation, accelerated particles and long wavelength heating internal to the prominence.

An Attack on the Contamination Problem in the Electron Microscope

1967 ◽  
Vol 25 ◽  
pp. 368-368
Author(s):  
J. J. Kelsch ◽  
A. Holtz
Keyword(s):  
Electron Microscope ◽  
Pressure Gradient ◽  
Ionization Potential ◽  
Simple Solution ◽  
Specimen Surface ◽  
Contamination Rate ◽  
Local Pressure ◽  
High Ionization ◽  
Hydrocarbon Molecules ◽  
Contamination Problem

A simple solution to the serious problem of specimen contamination in the electron microscope is presented. This is accomplished by the introduction of clean helium into the vacuum exactly at the specimen position. The local pressure gradient thus established inhibits the migration of hydrocarbon molecules to the specimen surface. The high ionization potential of He permits the use of relatively large volumes of the gas, without interfering with gun stability. The contamination rate is reduced on metal samples by a factor of 10.

Hydration Chamber for Jeolco 200 Kv Microscope

1970 ◽  
Vol 28 ◽  
pp. 542-543
Author(s):  
V. R. Matricardi ◽  
G. G. Hausner ◽  
D. F. Parsons
Keyword(s):  
Electron Microscope ◽  
Water Vapor ◽  
Vapor Pressure ◽  
Pressure Gradient ◽  
Room Temperature ◽  
List Type ◽  
Type Number ◽  
Equilibrium Vapor Pressure

In order to observe room temperature hydrated specimens in an electron microscope, the following conditions should be satisfied: The specimen should be surrounded by water vapor as close as possible to the equilibrium vapor pressure corresponding to the temperature of the specimen.The specimen grid should be inserted, focused and photo graphed in the shortest possible time in order to minimize dehydration.The full area of the specimen grid should be visible in order to minimize the number of changes of specimen required.There should be no pressure gradient across the grid so that specimens can be straddled across holes.Leakage of water vapor to the column should be minimized.

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