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Multiscale analysis in nonlinear thermal diffusion problems in composite structures

100%
Timofte C.
Open Physics
|
2010
|
vol. 8
|
issue 4
555-561
EN
The aim of this paper is to analyze the asymptotic behavior of the solution of a nonlinear problem arising in the modelling of thermal diffusion in a two-component composite material. We consider, at the microscale, a periodic structure formed by two materials with different thermal properties. We assume that we have nonlinear sources and that at the interface between the two materials the flux is continuous and depends in a dynamical nonlinear way on the jump of the temperature field. We shall be interested in describing the asymptotic behavior of the temperature field in the periodic composite as the small parameter which characterizes the sizes of our two regions tends to zero. We prove that the effective behavior of the solution of this system is governed by a new system, similar to Barenblatt’s model, with additional terms capturing the effect of the interfacial barrier, of the dynamical boundary condition, and of the nonlinear sources.
2
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A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

100%
Dinarvand S.
Open Physics
|
2009
|
vol. 7
|
issue 1
114-122
EN
The similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].
3
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The analysis of the suction/injection on the MHD Maxwell fluid past a stretching plate in the presence of nanoparticles by Lie group method

76%
Cao L., Si X., Zheng L., Pang H.
Open Physics
|
2015
|
vol. 13
|
issue 1
EN
In this paper, the magnetohydrodynamic (MHD) Maxwell fluid past a stretching plate with suction/ injection in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The dimensionless governing equations are solved numerically using Bvp4c with MATLAB, which is a collocation method equivalent to the fourth order mono-implicit Runge-Kutta method. The effects of some physical parameters, such as the elastic parameter K, the Hartmann number M, the Prandtl number Pr, the Brownian motion Nb, the thermophoresis parameter Nt and the Lewis number Le, on the velocity, temperature and nanoparticle fraction are studied numerically especially when suction and injection at the sheet are considered.
4
Content available remote

Electromagnetic plane-wave scattering from a sectorial groove in a perfectly conducting plane

64%
Tsaur D.-H., Chang K.-H.
Open Physics
|
2009
|
vol. 7
|
issue 1
160-167
EN
Scattering characteristics of plane waves by a sectorial groove in a perfectly conducting plane are investigated. Both the transverse magnetic (TM) and transverse electric (TE) polarizations of the incident wave are considered. Judicious use of the region-matching technique provides a rigorous series solution to the problem. The analyzed region is separated into two sub-regions by choosing a semi-circular auxiliary boundary. Thefield in each sub-region is expanded as a summationof proper wave functions with unknown coefficients. Enforcing the matching of conditions on the auxiliary boundary and of boundary condition on the circular-arc surface of the groove leads to a linear set of equations and the unknown coefficients are then determined. Numerical results demonstrate the influence of central angles of the sectorial groove on echo width, far-field pattern and near-field distribution. The presented geometry is easily applicable to the design and fabrication of a grating structure for optical switches and tunable filters.
5
Content available remote

Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order α

64%
Jumarie G.
Open Physics
|
2008
|
vol. 6
|
issue 3
737-753
EN
In a first stage, the paper deals with the derivation and the solution of the equation of the probability density function of a stochastic system driven simultaneously by a fractional Gaussian white noise and a fractional Poissonian white noise both of the same order. The key is the Taylor’s series of fractional order f(x + h) = E α(hαDx α)f(x) where E α() denotes the Mittag-Leffler function, and D x α is the so-called modified Riemann-Liouville fractional derivative which removes the effects of the non-zero initial value of the function under consideration. The corresponding fractional linear partial differential equation is solved by using a suitable extension of the Lagrange’s technique involving an auxiliary set of fractional differential equations. As an example, one considers a half-oscillator of fractional order driven by a fractional Poissonian noise.
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