Numerical optimization of a conical cavity as a radiation-focused concentrator

Conical enclosures rely on the conical cavity and can be used as radiation concentrators. Two circular cross-section baffles were used to improve the heat transfer of this geometry. By changing the rigid fins to porous, it could improve the heat transfer. Al₂O₃/water nanofluid was also employed to enhance the heat transfer performance of the cavity. For this purpose, numerical analysis of three-dimensional natural convection heat transfer was performed in a conical cavity with two types of fins. The best combination of fins arrangement for the next step was selected using the differential evolutionary optimization method (D.E). In this case study, a new combination of laminar and turbulence methods was employed for the first time to increase the accuracy of the natural convection solution. This combination is based on the laminar solution by suppressing the perturbation parameter in the turbulence method which led to more accurate results. The analysis results showed that a conical cavity with optimized fin geometry can lead to a 23% increase in Nu. The best porosity for the inner fin was calculated 40% in the case of constant porosity. Ascending porosity along the fin, whose increase was more intense near the base and slower near the cone's tip, was the best variable porosity for the inner fin.

     

Implicit constitutive relations in thermoelasticity

In this paper, after a brief discussion on the implicit constitutive relations used in thermoelasticity, based on Fox’s [1] work, we derive a general implicit relation for the heat flux vector. In the section following that we use the methodology suggested by Rajagopal [2] and [69] whereby we derive a class of implicit constitutive relations for q and we show that by selecting appropriate functions appearing in the formulation, we can obtain as special cases the Fourier heat conduction and the Maxwell-Cattaneo-Fox model. We do not discuss the implications of the second law of thermodynamics.     

Different cyclic motifs in phosphoric triamides containing a C(O)NHP(O)(NH)2 skeleton and an R22(10) graph set in three new compounds: a database analysis of hydrogen‐bond strengths based on motifs

In the crystal networks of N,N′‐bis(2‐chlorobenzyl)‐N′′‐(2,6‐difluorobenzoyl)phosphoric triamide, C₂₁H₁₈Cl₂F₂N₃O₂P, (I), N‐(2,6‐difluorobenzoyl)‐N′,N′′‐bis(4‐methoxybenzyl)phosphoric triamide, C₂₃H₂₄F₂N₃O₄P, (II), and N‐(2‐chloro‐2,2‐difluoroacetyl)‐N′,N′′‐bis(4‐methylphenyl)phosphoric triamide, C₁₆H₁₇ClF₂N₃O₂P, (III), C=O...H—N_C(O)NHP(O) and P=O...H—N_amide hydrogen bonds are responsible for the aggregation of the molecules. This is the opposite result from that commonly observed for carbacylamidophosphates, which show a tendency for the phosphoryl group, rather than the carbonyl counterpart, to form hydrogen bonds with the NH group of the C(O)NHP(O) skeleton. This hydrogen‐bond pattern leads to cyclic R₂²(10) motifs in (I)–(III), different from those found for all previously reported compounds of the general formula RC(O)NHP(O)[NR¹R²]₂ with the syn orientation of P=O versus NH [R₂²(8)], and also from those commonly observed for RC(O)NHP(O)[NHR¹]₂ [a sequence of alternate R₂²(8) and R₂²(12) motifs]. In these cases, the R₂²(8) and R₂²(12) graph sets are formed through similar kinds of hydrogen bond, i.e. a pair of P=O...H—N_C(O)NHP(O) hydrogen bonds for the former and two C=O...H—N_amide hydrogen bonds for the latter. This article also reviews 102 similar structures deposited in the Cambridge Structural Database and with the International Union of Crystallography, with the aim of comparing hydrogen‐bond strengths in the above‐mentioned cyclic motifs. This analysis shows that the strongest N—H...O hydrogen bonds exist in the R₂²(8) rings of some molecules. The phosphoryl and carbonyl groups in each of compounds (I)–(III) are anti with respect to each other and the P atoms are in a tetrahedral coordination environment. In the crystal structures, adjacent molecules are linked via the above‐mentioned hydrogen bonds in a linear arrangement, parallel to [010] for (I) and (III) and parallel to [100] for (II). Formation of the N_C(O)NHP(O)—H...O=C instead of the N_C(O)NHP(O)—H...O=P hydrogen bond is reflected in the higher N_C(O)NHP(O)—H vibrational frequencies for these molecules compared with previously reported analogous compounds.     

Numerical solution of nth‐order integro‐differential equations using trigonometric wavelets

The main aim of this paper is to apply the trigonometric wavelets for the solution of the Fredholm integro‐differential equations of nth‐order. The operational matrices of derivative for trigonometric scaling functions and wavelets are presented and are utilized to reduce the solution of the Fredholm integro‐differential equations to the solution of algebraic equations. Furthermore, we get an estimation of error bound for this method. Copyright © 2011 John Wiley & Sons, Ltd.     

FRW cosmology from five dimensional vacuum Brans–Dicke theory

We follow the approach of induced-matter theory for a five-dimensional (5D) vacuum Brans–Dicke theory and introduce induced-matter and induced potential in four dimensional (4D) hypersurfaces, and then employ a generalized FRW type solution. We confine ourselves to the scalar field and scale factors be functions of the cosmic time. This makes the induced potential, by its definition, vanishes, but the model is capable to expose variety of states for the universe. In general situations, in which the scale factor of the fifth dimension and scalar field are not constants, the 5D equations, for any kind of geometry, admit a power–law relation between the scalar field and scale factor of the fifth dimension. Hence, the procedure exhibits that 5D vacuum FRW-like equations are equivalent, in general, to the corresponding 4D vacuum ones with the same spatial scale factor but a new scalar field and a new coupling constant, [(w)\tilde]{\tilde{\omega}} . We show that the 5D vacuum FRW-like equations, or its equivalent 4D vacuum ones, admit accelerated solutions. For a constant scalar field, the equations reduce to the usual FRW equations with a typical radiation dominated universe. For this situation, we obtain dynamics of scale factors of the ordinary and extra dimensions for any kind of geometry without any priori assumption among them. For non-constant scalar fields and spatially flat geometries, solutions are found to be in the form of power–law and exponential ones. We also employ the weak energy condition for the induced-matter, that gives two constraints with negative or positive pressures. All types of solutions fulfill the weak energy condition in different ranges. The power–law solutions with either negative or positive pressures admit both decelerating and accelerating ones. Some solutions accept a shrinking extra dimension. By considering non-ghost scalar fields and appealing the recent observational measurements, the solutions are more restricted. We illustrate that the accelerating power–law solutions, which satisfy the weak energy condition and have non-ghost scalar fields, are compatible with the recent observations in ranges −4/3 < ω ≤ −1.3151 for the coupling constant and 1.5208 ≤ n < 1.9583 for dependence of the fifth dimension scale factor with the usual scale factor. These ranges also fulfill the condition ${\tilde{\omega} > -3/2}${\tilde{\omega} > -3/2} which prevents ghost scalar fields in the equivalent 4D vacuum Brans–Dicke equations. The results are presented in a few tables and figures.     

Collocation method for the numerical solutions of Lane–Emden type equations using cubic Hermite spline functions

Three numerical techniques based on cubic Hermite spline functions are presented for the solution of Lane–Emden equation. Some properties of Hermite splines are presented and are utilized to reduce the solution of Lane–Emden equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of these techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

Synthesis and crystal structure of a new N-(2,6-dichlorobenzoyl)-N′,N″-bis(pyrrolidinyl)-phosphoric triamide as a carrier and competitive bulk liquid membrane transport of six metal cations

The competitive metal ion transport experiments of Co⁺², Cd⁺², Ag⁺, Pb⁺², Ni⁺², and Cu⁺² were carried out by N-(2,6-dichlorobenzoyl)-N′,N″-bis(pyrrolidinyl)-phosphoric triamide as a carrier in organic membrane phase. 2,6-Cl₂C₆H₃C(O)NHP(O)[NC₄H₈]₂ has been synthesized and characterized by mass spectrometry IR spectroscopy and single crystal X-ray diffraction. The asymmetric unit of title phosphoric triamide contains one symmetrically independent molecule. The source phase contained equimolar concentrations of metal ions at pH 5 and the receiving phase being buffered at pH 3. The following solvents were examined as membrane: chloroform (CHCl₃), nitrobenzene (NB), 1,2-dichloroethane (1,2-DCE), dichloromethane (DCM), dichloromethane/1,2-dichloroethane (DCM/1,2-DCE). The obtained results show that the selectivity and efficiency of transport for these heavy metal cations change with the nature of the ligand and also the organic solvents, which were used as liquid membrane in these experiments. A good selectivity was observed for Pb⁺² cation by this ligand in all membrane systems. Moreover, the selectivity of metal cations in DCM is higher than other solvents. A non-linear relationship was found between the percent of transport of Pb⁺² cation by this ligand and the compositions of DCM/1,2-DCE and binary solution by this ligand. The effect of several factors such as the nature of carboxylic acids (stearic, fumaric and maleic acid) as surfactant in the membrane phase and the time of transport on transport efficiency of Pb⁺² cation were investigated.     

Preparation of Magnetic-Activated Carbon Nanocomposite and Its Application for Dye Removal from Aqueous Solution

A nanocomposite of activated carbon and iron oxide was prepared and characterized by x-ray diffraction and scanning electron microscopy methods. The prepared magnetic nanocomposite can be separated easily from water by an external magnet. The prepared magnetic nanocomposite was used as adsorbent for removal of Bismarck Brown (B.B.) as a dye pollutant from water. The adsorption studies include both equilibrium and kinetic aspects, and the results were modeled with different equations. The obtained results indicate that the prepared magnetic nanocomposite of iron oxide and activated carbon is one of the best adsorbents for the removal of B.B. from aqueous solution.     

Two new thiophosphoramide structures: N,N′,N′′‐tricyclohexylphosphorothioic triamide and O,O′‐diethyl (2‐phenylhydrazin‐1‐yl)thiophosphonate

The compound N,N′,N′′‐tricyclohexylphosphorothioic triamide, C₁₈H₃₆N₃PS or P(S)[NHC₆H₁₁]₃, (I), crystallizes in the space group Pnma with the molecule lying across a mirror plane; one N atom lies on the mirror plane, whereas the bond‐angle sum at the other N atom has a deviation of some 8° from the ideal value of 360° for a planar configuration. The orientation of the atoms attached to this nonplanar N atom corresponds to an anti orientation of the corresponding lone electron pair (LEP) with respect to the P=S group. The P=S bond length of 1.9785 (6) Å is within the expected range for compounds with a P(S)[N]₃ skeleton; however, it is in the region of the longest bond lengths found for analogous structures. This may be due to the involvement of the P=S group in N—H...S=P hydrogen bonds. In O,O′‐diethyl (2‐phenylhydrazin‐1‐yl)thiophosphonate, C₁₀H₁₇N₂O₂PS or P(S)[OC₂H₅]₂[NHNHC₆H₅], (II), the bond‐angle sum at the N atom attached to the phenyl ring is 345.1°, whereas, for the N atom bonded to the P atom, a practically planar environment is observed, with a bond‐angle sum of 359.1°. A Cambridge Structural Database [CSD; Allen (2002). Acta Cryst. B 58 , 380–388] analysis shows a shift of the maximum population of P=S bond lengths in compounds with a P(S)[O]₂[N] skeleton to the shorter bond lengths relative to compounds with a P(S)[N]₃ skeleton. The influence of this difference on the collective tendencies of N...S distances in N—H...S hydrogen bonds for structures with P(S)[N]₃ and P(S)[O]₂[N] segments were studied through a CSD analysis.     

Evaluation of lithium separation by dispersive liquid–liquid microextraction using benzo-15-crown-5

In this article a dispersive liquid?Cliquid microextraction method was applied for evaluation of lithium separation from aqueous solution. Benzo-15-crown-5 (B15C5) was used as a chelating agent prior to extraction. An appropriate mixture of disperser solvent and extraction solvent were added rapidly into the aqueous sample containing lithium ion; as a result, a cloudy solution was formed which consisted of fine droplets of extraction solvent dispersed entirely into aqueous phase. The mixture was centrifuged and the lithium complex with B15C5 was sedimented at the bottom of the conical sample holder. Then, 2.0?mL of enriched phase containing lithium complex was used for determination of lithium ion by flame atomic absorption spectrometry. The conditions for the microextraction performance were investigated. Under the best optimized conditions, the accepted recovery factors for the lithium obtained, ranged from 37.24 to 99.63?%. Furthermore, high preconcentration factors (7.46?C19.93) were also achieved. The relative standard deviation for three replicate measurements of 0.127?mg?L^?1 of lithium was 2.83?%.