Hybrid finite element/volume method for 3D incompressible flows with heat transfer

An implicit hybrid finite element (FE)/volume solver has been extended to incompressible flows coupled with the energy equation. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centred finite volume (FV) method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centres and the auxiliary variable at vertices. The Generalized Minimal Residual (GMRES) matrix-free strategy is adapted to solve the governing equations in both FE and FV methods. The presented 2D and 3D numerical examples show the robustness and accuracy of the numerical method.     

Statistical regression and artificial neural network analyses of impinging jet experiments

The purpose of this paper is to focus on the experimentally obtained results of impinging jet applications by the help of two different analysis methods. Circular round pipes (D = 7.9, 10.8, 13.8 and 23.1 mm) have been used as the impinging jets. The heat transfer is calculated with Nusselt number (Nu). The variable parameters are the dimensionless jet-to-impingement plate distance (z/D), Reynolds number (Re) and dimensionless temperature measurement points on the heated surface (x/L, y/L). Some important analysis methods such as artificial neural network (ANN), statistical regression, and uncertainty analysis are applied to the obtained data. It is shown that the ANN application is not simply a classification analysis; it is actually an application of the convergence of functions. As a result, by considering random data, 4.57% convergence level is obtained regarding the pipe diameter. The software STATISTICA 5.0 is used to estimate new empirical correlations nonlinearly. The smallest regression coefficient for the correlations is 0.87, while the highest value is 0.99. The result of the uncertainty analyses showed that the total uncertainties are in the agreeable range; 8% for Nu, and 2.89% for Re. Dr. Nevin Celik is a Post Doctoral Fellowship in University of Minnesota since August 2007.     

Mehmet Nadir: An amateur mathematician in Ottoman Turkey

This note summarizes the results of a recent survey of all the mathematical work of Mehmet Nadir, a Turkish amateur mathematician and professional educator who lived from 1856 to 1927 during the last years of the Ottoman Empire and the first years of the Turkish Republic. It is shown that, although working in isolated and adverse conditions, Nadir was able to establish a continuous correspondence with mathematicians in western Europe and, through his studies in number theory, obtained some results of lasting value.     

Hydrogen sulfide determination by solid surface luminescence

In the analytical system suggested, atmospheric hydrogen sulfide reacts with the surface of a filter paper treated with aqueous cadmium chloride and yields a luminescent species whose intensity can be correlated with the analyte concentration in ambient air. It was shown that the luminescent species are CdS solid particles which were formed in a well defined size. The paper luminescence was also tried on polymeric surfaces; polyethyleneoxide, polyvinyl alcohol, ethylcellulose and carboxymethylcellulose were found to give a similar luminescence signal. The system can be used on the tip of an optical fiber for an irreversible, cumulative type of analytical device for hydrogen sulfide determination. The 3s detection limit for the paper luminescence detection system was 7.8 ppb H₂S.     

Fixed points for cyclic orbital generalized contractions on complete metric spaces

We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303]. Our results generalize some theorems of Kirk, Srinavasan and Veeramani, and of Karpagam and Agrawal.     

Effect of boron containing materials on flammability and thermal degradation of polyamide‐6 composites containing melamine cyanurate

Three different boron containing materials, zinc borate (ZnB), borophosphate (BPO₄), and boron and silicon containing oligomer (BSi), were used to improve the flame retardancy of melamine cyanurate (MC) in a polyamide‐6 (PA‐6) matrix. The combustion and thermal degradation characteristics were investigated using limiting oxygen index (LOI), UL‐94 standard, thermogravimetric analysis‐Fourier transform infrared spectroscopy (TGA‐FTIR), differential scanning calorimeter (DSC), and scanning electron microscopy (SEM). All the three boron compounds showed no synergistic effect with MC, and only BPO₄ at high loadings showed comparable LOI values by increasing the dripping rate. For ZnB and BSi glassy film and char formation decreases the dripping rate and sublimation of melamine and give rise to low LOI. According to TGA‐FTIR results, addition of boron compounds does not alter the gaseous product distribution of both MC and PA‐6. The addition of boron compounds affects flame retardancy through physical means. It was noted from the TGA data that boron compounds reduced the decomposition temperature of both MC and PA‐6, also affecting the flame retardancy negatively by premature degradation of MC at low temperatures. Copyright © 2009 John Wiley & Sons, Ltd.     

Influence of Dispersing Agents on the Solubility of Perovskites in Water

In this study, solubility behavior of lead magnesium niobate (PMN) powders in water was investigated in the presence of pure polyacrylic acid and polyacrylic acid/polyethylene oxide comb polymers. Experiments were performed by measuring the solubility of PMN in terms of the concentration of Pb⁺² and Mg⁺² ions in supernatant as a function of pH and dispersing agent dosage. The concentrations of the metal ions in supernatant were found to be affected by the dispersant concentration, stirring time and the suspension pH. Results revealed that both dispersing agents enhance the cation dissolution from PMN surface at pH 9 due to weak (reversible) adsorption and complexation of Pb⁺² and Mg⁺² by carboxylate groups. On the other hand, under acidic conditions cation dissolution from PMN is inhibited and this was attributed to the strong adsorption of dispersing agents onto the powder surface and formation of a dense polymer layer.     

Electroinitiated Cationic Copolymerization of Styrene and 4-Methoxystyrene

The copolymerization of styrene and 4-methoxystyrene by constant potential electrolysis in 1,2-dichloroethane was achieved at three different potentials. Amounts of the monomers in the resulting copolymers were found to be potential-dependent. The effect of polymerization potential on copolymer composition was also found to be related to anodic peak potentials (E_p,a) of the monomers.

Monomer reactivity ratios were found with the integrated Lewis-Mayo equation.     

Performance of birnessite-type manganese oxide in the thermal-catalytic degradation of polyamide 6

Birnessite-type manganese oxide (BMO) was prepared by oxidation of Mn(NO₃)₂ with H₂O₂ in KOH solution. The nature and the extent of degradation of polyamide 6 (PA6) in the presence of samples were analysed by thermogravimetric analysis under static air atmosphere at several heating rates between 5 and 30 °C min^?1. The surface and structure of BMO were characterized using infrared (IR) spectroscopy, X-ray diffraction, and thermal analysis techniques. The acid sites of BMO were investigated by IR using pyridine as a molecular probe. The activation energy for degradation estimated by Kissinger method for PA6 and BMO/PA6 system containing 10 mass% of BMO was found to be 212 and 144 kJ mol^?1 under air, respectively. The catalytic activity observed in BMP catalyst was associated to a high lattice oxygen mobility.     

Two‐way and three‐way approaches to ultra high performance liquid chromatography–photodiode array dataset for the quantitative resolution of a two‐component mixture containing ciprofloxacin and ornidazole

Two‐way and three‐way calibration models were applied to ultra high performance liquid chromatography with photodiode array data with coeluted peaks in the same wavelength and time regions for the simultaneous quantitation of ciprofloxacin and ornidazole in tablets. The chromatographic data cube (tensor) was obtained by recording chromatographic spectra of the standard and sample solutions containing ciprofloxacin and ornidazole with sulfadiazine as an internal standard as a function of time and wavelength. Parallel factor analysis and trilinear partial least squares were used as three‐way calibrations for the decomposition of the tensor, whereas three‐way unfolded partial least squares was applied as a two‐way calibration to the unfolded dataset obtained from the data array of ultra high performance liquid chromatography with photodiode array detection. The validity and ability of two‐way and three‐way analysis methods were tested by analyzing validation samples: synthetic mixture, interday and intraday samples, and standard addition samples. Results obtained from two‐way and three‐way calibrations were compared to those provided by traditional ultra high performance liquid chromatography. The proposed methods, parallel factor analysis, trilinear partial least squares, unfolded partial least squares, and traditional ultra high performance liquid chromatography were successfully applied to the quantitative estimation of the solid dosage form containing ciprofloxacin and ornidazole.