Mathematical Expressions on the Boundary Conditions for Permeable Mechanics—Focusing on the Elastic Propagation Issue

We considered the situation where a container with a permeable boundary is immersed in a larger body of fluid of the same kind. In this paper, we found mathematical expressions at the permeable interfaceΓof a domainΩ, whereΩ⊂R3.Γis defined as a smooth two-dimensional (at least classC2) manifold inΩ. The Sennet-Frenet formulas for curves without torsion were employed to find the expressions on the interfaceΓ. We modelled the flow of Newtonian as well as non-Newtonian fluids through permeable boundaries which results in nonhomogeneous dynamic and kinematic boundary conditions. The flow is assumed to flow through the boundary only in the direction of the outer normaln, where the tangential components are assumed to be zero. These conditions take into account certain assumptions made on the curvature of the boundary regarding the surface density and the shape ofΩ; namely, that the curvature is constrained in a certain way. Stability of the rest state and uniqueness are proved for a special case where a “shear flow” is assumed.

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Research on energy efficient kinetics of drying raw material

E3S Web of Conferences ◽

10.1051/e3sconf/202021601093 ◽

2020 ◽

Vol 216 ◽

pp. 01093

Author(s):

Jasur Safarov ◽

Akhtam Khujakulov ◽

Shakhnoza Sultanova ◽

Ulugbek Khujakulov ◽

Sunil Verma

Keyword(s):

Diffusion Coefficient ◽

Diffusion Equation ◽

Boundary Conditions ◽

Energy Efficient ◽

Least Squares Method ◽

Moisture Diffusion ◽

Raw Material ◽

Special Program ◽

Mathematical Expressions ◽

Kinetics Of

In this work, at constant values of the process temperature, the kinetics of drying was considered through the Fick diffusion equation with the corresponding initial and boundary conditions. To describe the process with mathematical expressions, Fick’s equation, which expresses the value of moisture content, is reduced to a dimensionless formula. When accepting the boundary conditions of the first kind, the ratio of the moisture diffusion coefficient to the square of the determining size was determined by the least squares method using a special program with subroutines for solving partial differential equations with a sufficient number of exponents in the solution.

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Analysis of the Main Aspects Affecting Bonding in Stainless Steel Rebars Embedded in a Hydraulic Medium

Metals ◽

10.3390/met11050786 ◽

2021 ◽

Vol 11 (5) ◽

pp. 786

Author(s):

Fernando Ancio ◽

Esperanza Rodriguez-Mayorga ◽

Beatriz Hortigon

Keyword(s):

Finite Element ◽

Stainless Steel ◽

Boundary Conditions ◽

Masonry Structures ◽

Finite Element Analyses ◽

Pull Out ◽

Mathematical Expressions ◽

Special Circumstances ◽

Steel Rebars

The use of stainless steel rebars to reinforce masonry structures has become established as an eminently efficient methodology. From among the numerous techniques available, bed-joint structural repointing and superficial reinforcement with rebars or meshes attached to surfaces have become widespread, thanks to the excellent results they have produced in recent decades. Both techniques imply the use of diameters less than 6 mm and thin coverings. This article deals with the characterization of the bonding behavior of the rebar under these special circumstances. To this end, several finite element analyses have been carried out to identify the possible relationships between pull-out forces in various situations. These models allow certain conclusions to be drawn regarding the influence of the thickness of covering, boundary conditions, and geometrical aspects of the rebars in bonding. Certain mathematical expressions that relate the various conclusions from this research are finally laid out.

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MATHEMATICAL ANALYSIS OF PARALLEL CONVECTIVE EXCHANGERS WITH GENERAL LATERAL BOUNDARY CONDITIONS USING GENERALIZED GRAETZ MODES

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202513500620 ◽

2014 ◽

Vol 24 (04) ◽

pp. 627-665 ◽

Cited By ~ 2

Author(s):

JULIEN BOUYSSIER ◽

CHARLES PIERRE ◽

FRANCK PLOURABOUE

Keyword(s):

Boundary Conditions ◽

Mathematical Analysis ◽

Generalized Solutions ◽

Current Configuration ◽

Mode Decomposition ◽

Mathematical Expressions ◽

Lateral Boundary Conditions ◽

Outer Domain ◽

Longitudinal Coordinate ◽

Numerical Precision

We propose a mathematical analysis of parallel convective exchangers for any general but longitudinally invariant domains. We analyze general Dirichlet or Neumann prescribed boundary conditions at the outer solid domain. Our study provides general mathematical expressions for the solution of convection/diffusion problems. Explicit form of generalized solutions along longitudinal coordinate are found from convoluting elementary base Graetz mode with the applied sources at the boundary. In the case of adiabatic zero flux counter-current configuration, we recover the longitudinally linearly varying solution associated with the zeroth eigenmode which can be considered as the fully developed behavior for heat-exchangers. We also provide general expression for the infinite asymptotic behavior of the solutions which depends on simple parameters such as total convective flux, outer domain perimeter and the applied boundary conditions. Practical considerations associated with the numerical precision of truncated mode decomposition is also analyzed in various configurations for illustrating the versatility of the formalism. Numerical quantities of interest are investigated, such as fluid/solid internal and external fluxes.

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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