Numerical Study of Heat Transfer in a Rectangular Channel with Porous Covering Obstacles

A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered. The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with the increase of Reynolds number.     

Hydrogen-bonding versus van der Waals interactions in self-assembled monolayers of substituted isophthalic acids

Self-assembled monolayers of a series of isophthalic acids (5-octadecyloxyisophthalic acid, 5-decyloxyisophthalic acid, 5-hexyloxyisophthalic acid, and 5-pentyloxyisophthalic acid) formed on highly ordered pyrolytic graphite (HOPG) at the solid-liquid interface were studied using scanning tunneling microscopy (STM). Although these molecules have the same dicarboxyl headgroup, their hydrocarbon tails are of different lengths. Hydrogen-bonding between headgroups and van der Waals interactions between the hydrocarbon tails control the final morphology of the monolayer. The STM images show that both van der Waals interactions (vdWs) and hydrogen-bonding (H-B) compete to control the structure, but the final structure of the monolayer is determined by balance between the two interactions.     

Holditch Theorem and Steiner Formula for the Planar Hyperbolic Motions

The Steiner formula and the Holditch Theorem for one-parameter closed planar Euclidean motions [1, 5] were expressed by Müller, under the one-parameter closed planar motions in the complex sense. Also, Müller had given Holditch theorem in the complex sense, [6].     

Coherent states for Smorodinsky-Winternitz potentials

In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.      

Operator time‐splitting techniques combined with quintic B‐spline collocation method for the generalized Rosenau–KdV equation

In this article, the generalized Rosenau–KdV equation is split into two subequations such that one is linear and the other is nonlinear. The resulting subequations with the prescribed initial and boundary conditions are numerically solved by the first order Lie–Trotter and the second‐order Strang time‐splitting techniques combined with the quintic B‐spline collocation by the help of the fourth order Runge–Kutta (RK‐4) method. To show the accuracy and reliability of the proposed techniques, two test problems having exact solutions are considered. The computed error norms L₂ and L_∞ with the conservative properties of the discrete mass Q(t) and energy E(t) are compared with those available in the literature. The convergence orders of both techniques have also been calculated. Moreover, the stability analyses of the numerical schemes are investigated.     

Synthesis and crystal structure of bis[N-(2-fluoro-3-methoxy)-salicylideneaminato]copper(II)

The title compound, bis[N-(2-fluoro-3-methoxy)-salicylideneaminato]copper(II) [Cu(C₁₄H₁₂O₂FN)₂] was synthesized and its crystal structure was determined. The title compound is triclinic, space group P with a = 8.552(1), b = 9.645(1), c = 7.871(1) Å, = 108.708(1), = 93.769(1), = 79.429(1), V = 1208.98(1) ų, Z = 2, D _c = 1.696 gcm_–3, (Mo K) = 1.815 mm^–1, R = 0.0369 for 2963 reflections [I>2(I)]. The title compound has crystallographic inversion symmetry with two bidentate Schiff base ligand coordinated to the Cu atom in a square-planar arrangement. The Cu–N1 and Cu–O2 distances are 1.995(1) and 1.885(1) Å, respectively.     

D-dimensional Smorodinsky-Winternitz potential: Coherent state approach

In this study, we construct the coherent states for a particle in the D-dimensional maximally superintegrable Smorodinsky-Winternitz potential. We, first, map the system into 2D harmonic oscillators, second, construct the coherent states of them by evaluating the transition amplitudes. Third, in the Cartesian and the hyperspherical coordinates, we find the coherent states and the stationary states of the original sytem by reduction.     

Adsorption of Cr(VI) from Aqueous Solutions Onto Raw and Acid-Activated Reşadiye and Hançılı Clays

ABSTRACT

The adsorption of Cr(VI) from aqueous solutions onto raw and acid-activated clays—namely, Re?adiye region clay (R, raw Re?adiye region clay; R-H₂SO₄, acid-activated with H₂SO₄ Re?adiye region clay; R-HCl, acid-activated with HCl Re?adiye region clay) and Hanç?l? region clay (H, raw Hanç?l? region clay; H-H₂SO₄, acid-activated with H₂SO₄ Hanç?l? region clay; H-HCl, acid-activated with HCl Hanç?l? region clay)—was studied in a batch system. For optimization of the Cr(VI) adsorption on raw clays and acid-activated clays, the effect of pH, temperature, initial Cr(VI) concentration, time, and adsorbent dosage were investigated. X-ray diffraction analyses of raw and acid-activated clays were used to determine the effects of acid-activating on the layer structure of the clays. The surface characterizations of clays and modified clays were performed by using FT-IR spectroscopy. The Langmuir and Freundlich adsorption models were employed to describe the equilibrium isotherms, and thus the isotherm constants were determined. The data obtained from our investigations were well described by the Langmuir model. The adsorption capacity of the adsorbents Re?adiye and Hanç?l? clays were found to be 0.0269, 0.0144, and 0.0170 mmol/g for H, H-HCl, and H-H₂SO₄ and 0.0356, 0.0276, and 0.0422 mmol/g for R, R-HCl, and R-H₂SO₄, respectively. The results show that the adsorption was strongly dependent on pH of the medium, initial Cr(VI) concentration and temperature. The removal of Cr(VI) reached saturation in about 120 min, and the adsorption process of Cr(VI) was observed as exothermic. A maximum removal of 73% was noted at 1.0 × 10^?4 M concentration of Cr(VI) in solution for H-HCl. Furthermore the enhancement of removal of Cr(VI) was observed from pH 3 to 4. The results are discussed to highlight the influence of acid activation on Cr(VI) adsorption characteristics of the clays.     

Transient response of a moving spherical shell in an acoustic medium

A ring-stiffened spherical shell is submerged in an acoustic medium. The shell is thin and elastic. The acoustic medium is inviscid, irrotational and compressible. The center of mass of the shell is subjected to a translational acceleration which is an arbitrary function of time. The absolute displacements of the shell are expressed in terms of the relative displacements and the displacement of the base of the shell, base being defined as the rigid ring placed at the equator. The motion of the acoustic medium is governed by the wave equation. The transient response of the shell is investigated numerically. The results are compared with the results of the in-vacuo response. The effects of the plane wave approximation and the base velocity on the transient response of the shell are studied. The numerical results show that the plane wave approximation accurately predicts the response of the shell in the acoustic medium for short times after excitation. The displacements of the shell in fluid are larger than those in vacuo. But when the base of the shell is restrained from translating, the displacements in fluid are smaller than those in vacuo. Therefore, base translation has a very significant effect on the transient response of the shells submerged in an acoustic medium.