Comment on “New method to obtain periodic solutions of period two and three of a rational difference equation” [Nonlinear Dyn 79:241–250]

In this paper, we discuss the results of Elsayed (Nonlinear Dyn 79:241–250, 2015) for periodic solution of period two and three of rational difference equation. Also, we study the existence of periodic solutions of some difference equation by using old method and new method and comparison of results. The results obtained here correct and improve some known results in Elsayed (Nonlinear Dyn 79:241–250, 2015). Some numerical examples will be given to illustrate our results.     

Comment on “Exponential ultimate boundedness of fractional-order differential system via periodically intermittent control” [Nonlinear Dyn 2019;92(2), 247–265]

Nonlinear Dynamics - In this note, some points to paper (Xu L.G., Liu W.,” Hu ”H.X.:“Exponential ultimate boundedness of fractional-order differential system via periodically...     

Comments on the Paper “Non-Darcian Forced-Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium” by O. Aydin and A. Kaya,Transport in Porous Media,doi:10.1007/s11242-007-9200-x, 2008

In a very recent paper by Aydin and Kaya (Transp. Porous Media (to appear), 2008) the combined effects of viscous dissipation and surface mass flux on the forced-convection boundary-layer flow was considered. However, as the present Note shows, the thermal boundary condition imposed at the outer edge of the boundary-layer by Aydin and Kaya is incompatible with the energy equation, and thus the results of their paper are in error.     

Comments on “Adaptive fuzzy H ∞ tracking design of SISO uncertain nonlinear fractional order time-delay systems” [Nonlinear Dyn. 69 (2012) 1639–1650]

In this paper, it is shown that the closed-loop system stability analysis in the main theorem of the paper (Lin et al. in Nonlinear Dyn. 69:1639?C1650, 2012) contains two essential errors. We demonstrate that the authors of the above paper have carelessly dealt with the derivation and integration procedures of the fractional-order equations as common ordinary differential equations.     

Comment on “Mixed convection boundary layer flow over a horizontal plate with thermal radiation” by A. Ishak, Heat Mass Transfer, DOI 10.1007/s00231-009-0552-3

In a recent paper of Ishak (Heat Mass Transfer, doi:10.1007/s00231-009-0552-3, 2009) the similarity solutions of the title problem have been investigated numerically in some detail. The present note shows, however, that with the aid of a simple rescaling of the Prandtl number, the results reported by Ishak can easily be recovered from the well known solution of the same problem, without the effect of thermal radiation.     

Comment on “Combined Forced and Free Convective Flow in a Vertical Porous Channel: The Effects of Viscous Dissipation and Pressure Work” by A. Barletta and D. A. Nield,Transport in Porous Media,DOI 10.1007/s11242-008-9320-y, 2009

In a recent article by Barletta and Nield (Transport in Porous Media, DOI , 2009), the title problem for the fully developed parallel flow regime was considered assuming isoflux/isothermal wall conditions. For the limiting cases of the forced and the free convection, analytical solutions were reported; for the general case, numerical solutions were reported. The aim of the present note is (i) to give an analytical solution for the full problem in terms of the Weierstrass elliptic P-function, (ii) to illustrate this general approach by two easily manageable examples, and (iii) to rise a couple of questions of basic physical interest concerning the interplay between the viscous dissipation and the pressure work. In this context, the concept of “eigenflow” introduced by Barletta and Nield is discussed in some detail.     

Comment on the paper “Transient MHD free convective flow past an infinite vertical plate embedded in a porous medium with viscous dissipation,Siva Reddy Sheri,R. Srinivasa Raju,Meccanica, DOI 10.1007/s11012-015-0285-y”

A numerical investigation of transient magnetohydrodynamic free convection flow past an infinite vertical plate embedded in a porous medium with viscous dissipation is presented in the above paper. The governing differential equations are transformed into a set of non-linear coupled partial differential equations and are solved numerically using the finite element method. Numerical results for the velocity, temperature and concentration profiles within the boundary layer are presented and discussed.     

Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part II. Application to InxGa1−xAs/InP system

Cracking phenomena in tensile-strained In_xGa_1?xAs epitaxial film on an InP substrate are analyzed via the formulation given in Part I [Lee, S., Choi, S.T., Earmme, Y.Y., 2006. Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part I. Mathematical formulation. International Journal of Solids and Structures 43, 3401–3413], where the solution for a dislocation in an anisotropic trimaterial is used as a fundamental solution and the crack is modeled by the continuous distribution of dislocations. Misfit strains and stresses are evaluated as a function of indium content x in an In_xGa_1?xAs/InP system. A single crack and periodic cracks, respectively, induced by the misfit stresses are considered. The crack opening profile, the crack mouth displacement, and the energy release rate as a function of the crack length are obtained. The critical conditions for a single crack and periodic cracks, respectively, are thus obtained, and are found to depend on the film thickness, the crack length, and the period of the cracks. The results of these analyses are also compared with published data obtained from experiments.     

Letter to the Editor: Comments on the Paper “Inertia Effects in High-Rate Flow Through Heterogeneous Porous Media” by M. Fourar, R. Lenormand, M. Karimi-Fard, and R. Horne, Transport in Porous Media, DOI 10.1007/s11242-004-6800-6, 2005

In a recent article, Fourar et al. (Transp Porous Med, 2005, doi:10.1007/s11242-004-6800-6) analyzed the effect of heterogeneity in the permeability distribution on Forchheimer flow in porous media. They derived expressions to calculate the effective inertial coefficient in serial layers, parallel layers, and two-dimensional correlated media. Here, we highlight an inconsistency in their first-order expression for serial layers and extend their findings by providing closed-form expressions for the effective inertial coefficient in the case of a lognormal permeability distribution.     

Corrigendum of “Similarity analysis in magnetohydrodynamics: Hall effects on free convection flow and mass transfer past a semi-infinite vertical flat plate” [International Journal of Non-Linear Mechanics 38 (2003) 513–520]

The problem of steady, laminar mixed convection heat and mass transfer past a semi-infinite vertical plate in the presence of Hall current has been studied. The governing partial differential equations describing the problem are transformed to a system of non-linear ordinary differential equations with appropriate boundary conditions using Lie's method of infinitesimal transformation groups. The non-linear ordinary differential equations are solved numerically using Chebyshev spectral method. The effects of various parameters on the velocity profiles, temperature and concentration profiles are presented and discussed. This work is an extension and correction for the paper by Megahed et al. [1], published in International Journal of Non-Linear Mechanics 38 (2003) 513–520.     

Comments on “Effects of temperature dependent fluid properties and variable Prandtl number on the transient convective flow due to a porous rotating disk by M. S. Alam,S. M. Chapal Hossain,M. M. Rahman [Meccanica (2014) 49:2439–2451]”

In this letter, we submit our comments on recently published paper titled “Effects of temperature dependent fluid properties and variable Prandtl number on the transient convective flow due to a porous rotating disk by Alam et al. (Meccanica 49: 2439–2451, 2014)”. Authors of this paper have attempted to present similarity solutions in the paper. We comment in this letter is that the similarity transformations considered in Alam et al. (Meccanica 49: 2439–2451, 2014) are not correct and thus results are leading to invalid conclusions.