Solving systems of ODEs by homotopy analysis method

This paper applies the homotopy analysis method (HAM) to systems of ordinary differential equations (ODEs). The systems investigated include stiff systems, the chaotic Genesio system and the matrix Riccati-type differential equation. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge–Kutta method (RK78).     

Solution of fully developed free convection of a micropolar fluid in a vertical channel by homotopy analysis method

In this paper, we reconsider the problem of fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations. The resulting boundary‐value problem is solved analytically by the homotopy analysis method. The accuracy of the present solution is found to be in excellent agreement with the solutions of Cheng (Int. Commun. Heat Mass Transfer 2006; 33 :627–635). Copyright © 2008 John Wiley & Sons, Ltd.     

Synthesis,magnetic properties and microstructure of Ni–Zn ferrite by sol–gel technique

In the study, the Ni–Zn ferrite powder of a Ni_0.3Zn_0.7Fe₂O₄ composition was synthesized by sol–gel route using metal acetates at low temperatures. Both the scanning electron microscope and X-ray diffraction analyses of various gel samples heated at different temperatures were used to identify the reaction stages where the amorphous-gel-to-crystalline phase transition occurred. The electrical, magnetic and microstructural properties of the toroidal cores were studied. It was found that the initial permeability increased with a large frequency band (0.1–31.39 MHz) and the magnetic loss was small. The electrical resistivity was higher as compared to the ones which were obtained by the conventional process. Therefore, well–defined polycrystalline microstructure nickel–zinc ferrite and a short processing time of gel preparation have become the major achievements of this study.     

Series Solution for Unsteady Boundary-Layer Flows Due to Impulsively Stretching Plate

The third-order nonlinear partial differential equation modelling the unsteady boundary-layer flows caused by an impulsively stretching fiat plate is solved by using the Adomian decomposition method （ADM）. The ADM yields analytic solution in the form of a rapidly convergent infinite series with easily computable terms. The series solution using the ADM for the unsteady flows is presented for the first time.     

Thermoanalytical investigations on heterocyclic organic compounds. Part I. Thermal decomposition of pyrazolinoimides

Pyrazolinoimides undergo denitrogenation reaction upon heating to form the cyclopropane derivatives and the corresponding olefins. They are studied by dynamic TG, DTG, DTA and DSC techniques. The enthalpies and kinetic parameters are evaluated. Further decomposition of the compounds led to carbon, and in some cases, polymeric products are suspected to be formed. The fluorene derivatives behave differently and undergo irreversible isomerization in the melt prior to decomposition. Practical mechanistic steps are postulated in order to explain the formation of the decomposition, rearrangement and isomerization products during thermal treatment.     

The optical properties of trivalent rare earth ions (Er3+) doped borotellurite glass

Erbium doped borotellurite glass has been fabricated by using conventional melting method. The density and molar volume have been calculated and analyzed while their optical properties were studied by measuring the optical absorption and luminescence spectra at room temperature. From the XRD results, since the patterns do not exhibit any diffraction line thus it confirms their amorphous nature. It is found that the density of the glass samples increased and the molar volume decreased with respect to Er ions content. Meanwhile, the upconversion emissions centered at 487, 523, 558, 642, 695 and 782 nm have been observed under the 650 nm excitation in the ⁴ F _9/2 level. Some other results will be analysed and discussed in details.     

Synthesis,optimization, characterization,and potential agricultural application of polymer hydrogel composites based on cotton microfiber

The optimum content of cotton microfiber, initiator, cross-linker, and sodium hydroxide were determined using the central composite design method. Polymer hydrogels (PHGs) were characterized using Fourier-transform infrared (FT-IR), scanning electron microscopy, and thermal gravimetric analysis. A comparison between plain PHG and the polymer hydrogel composite (PHGC) in terms of biodegradation, swelling rate, and re-swelling capacity was carried out. The effect of PHGC on the sandy soil holding capacity, urea leaching loss rate (ULLR), and okra plant growth were evaluated. The highest water absorption capacity was obtained at 1.30 mass %, 0.15 mass %, 13.00 mass %, and 13.50 mass % of the initiator, cross-linker, sodium hydroxide, and cotton microfiber, respectively. Cotton microfiber has a prominent effect on the swelling rate, re-swelling capacity, and biodegradability of PHG. Okra plant growth and ULLR were positively affected by PHGC and the best leaching loss rate of 33.3 mass % was observed for the lowest urea loaded sample.