Conjugate Natural Convection in a Porous Enclosure Sandwiched by Finite Walls Under the Influence of Non-uniform Heat Generation and Radiation

Conjugate natural convection in a square porous enclosure sandwiched by finite walls under the influence of non-uniform heat generation and radiation is studied numerically in the present article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures, while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the ratio of wall thickness to its width $(0.02 \le D \le 0.3)$ ( 0.02 ≤ D ≤ 0.3 ) , the wall to porous thermal conductivity ratio $(0.1 \le k_\mathrm{r} \le 10.0)$ ( 0.1 ≤ k r ≤ 10.0 ) , the internal heating $(0 \le \gamma \le 5)$ ( 0 ≤ γ ≤ 5 ) , and the local heating exponent parameters $(1 \le \lambda \le 20)$ ( 1 ≤ λ ≤ 20 ) . It is found that the average Nusselt number on the hot and cold interfaces increases with increasing the radiation intensity. Very high non-uniformity heating does not affect the average Nusselt number at very thick walls.     

Efficacy of variational iteration method for chaotic Genesio system – Classical and multistage approach

This is a case study of solving the Genesio system by using the classical variational iteration method (VIM) and a newly modified version called the multistage VIM (MVIM). VIM is an analytical technique that grants us a continuous representation of the approximate solution, which allows better information of the solution over the time interval. Unlike its counterpart, numerical techniques, such as the Runge–Kutta method, provide solutions only at two ends of the time interval (with condition that the selected time interval is adequately small for convergence). Furthermore, it offers approximate solutions in a discretized form, making it complicated in achieving a continuous representation. The explicit solutions through VIM and MVIM are compared with the numerical analysis of the fourth-order Runge–Kutta method (RK4). VIM had been successfully applied to linear and nonlinear systems of non-chaotic in nature and this had been testified by numerous scientists lately. Our intention is to determine whether VIM is also a feasible method in solving a chaotic system like Genesio. At the same time, MVIM will be applied to gauge its accuracy compared to VIM and RK4. Since, for most situations, the validity domain of the solutions is often an issue, we will consider a reasonably large time frame in our work.     

Solution of prey–predator problem by numeric–analytic technique

In this paper, an analytical expression for the solution of the prey–predator problem by an adaptation of the classical Adomian decomposition method (ADM). The ADM is treated as an algorithm for approximating the solution of the problem in a sequence of time intervals, i.e. the classical ADM is converted into a hybrid numeric–analytic method called the multistage ADM (MADM). Numerical comparisons with the classical ADM, and the classical fourth-order Rungge–Kutta (RK4) methods are presented.     

Series Solutions of Systems of Nonlinear Fractional Differential Equations

Differential equations of fractional order appear in many applications in physics, chemistry and engineering. An effective and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method (ADM) solution as special cases.      

Near-edge X-ray absorption fine structure spectroscopy and structural properties of Ni-doped CeO2 nanoparticles

Ni-doped CeO₂ nanoparticles were prepared by using the co-precipitation method. The prepared nanoparticles were characterized using X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, Raman spectroscopy, field emission scanning electron microscopy (FE-SEM) and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. The XRD results infer that Ni-doped CeO₂ nanoparticles have single phase nature similar to that of pure CeO₂ nanoparticles. We have calculated lattice parameters using Powder-X software, particle size using Scherer’s formula and strain using the Williamson-Hall method for all the synthesized samples. We have observed a systematic decrease in the lattice parameters, particle size and strain with an increase in Ni doping in CeO₂. The FE-SEM micrographs also confirm that Ni-doped CeO₂ have nanocrystalline behavior and particles are spherical shaped. From the Raman spectra, it is observed that the intensity of classical CeO₂ vibration modes first increases then decreases with Ni doping. The NEXAFS spectra measured at Ce M_4,5 and Ni L_3,2 edges clearly indicate that Ce ions are in the +4 valence state and Ni ions are in the +2 valence state.     

Analysis of multiple reflections in hybrid photonic crystal multimode interference coupler

In this paper the analysis of multiple reflections in photonic crystal (PhC) multimode interference (MMI) couplers using eigen-mode expansion method is presented. The analysis is conducted on a hybrid PhC structure which consisted of 1-D PhC multimode waveguide sandwiched between 2-D PhC input/output waveguides. In PhC multimode waveguide, where the mechanism of wave confinement is not due to total internal reflection but due to photonic bandgap properties, the reflectivity at 2-D PhC facet wall would be very large for all the guided modes in the waveguide when ever the image formed due to MMI effect does not coincides with the output access waveguide.     

Thermoanalytical investigations on heterocyclic organic compounds. Part II. Thermal decomposition of substituted 1,4-dihydro-2,4-dioxo-2H-3,1-benzoxazine

The thermal decomposition of substituted 1,4-dihydro-2,4-dioxo-2H-3,1-benzoxazine involves a decarboxylation reaction and the formation of dimeric products that arise by a Diels—Alder reaction involving the ketenimine as diene and dienophile. Significant destabilization of the oxazinedione ring was manifested in the thermal decomposition of 3,4-dihydro-1,3-dioxo-1H-pyrido (3,2-d)(1,3) oxazine (V). The shape of the thermogram is dependent on the experimental conditions. Further decomposition of the dimers leads to dark glassy materials of polymeric nature.     

Carbonic acid: an important intermediate in the surface chemistry of calcium carbonate

Calcium carbonate is an important and ubiquitous component of biological and geochemical systems. In this study, the surface chemistry of calcium carbonate with several trace atmospheric gases including HNO3, SO2, HCOOH, and CH3COOH is investigated with infrared spectroscopy. Adsorbed carbonic acid, H2CO3, is found to be an intermediate in these reactions. In the absence of adsorbed water, carbonic acid is stable on the surface at room temperature. However, upon water adsorption, carbonic acid dissociates as indicated by the evolution of gaseous CO2 and the disappearance of infrared absorption bands associated with adsorbed carbonic acid. Thus, it is postulated that under ambient conditions, carbonic acid may be an important albeit short-lived intermediate in the surface chemistry of calcium carbonate.     

Numerical solution of sine-Gordon equation by variational iteration method

In this Letter, variational iteration method (VIM) is applied to obtain approximate analytical solution of the sine-Gordon equation without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.