Scaling group transformation for the effect of temperature-dependent nanofluid viscosity on an mhd boundary layer past a porous stretching surface

This paper deals with a steady two-dimensional flow of an electrically conducting incompressible fluid over a porous vertical stretching sheet. The flow is permeated by a uniform transverse magnetic field. The fluid viscosity is assumed to vary as a linear function of temperature. The partial differential equations governing the problem under consideration are transformed by a special form of Lie group transformations, namely, scaling group of transformations, into a system of ordinary differential equations, which are solved numerically using the Runge-Kutta-Gill algorithm and the shooting method. The conclusion is drawn that the flow field and temperature profiles are significantly influenced by the Lewis number, Brownian motion number, and thermophoresis number.     

2-(Trimethylsilyl)ethanol as a new alcohol equivalent for copper-catalyzed coupling of aryl iodides

2-(Trimethylsilyl)ethanol as a new alcohol equivalent has been employed for copper-catalyzed coupling of aryl iodides. Using mild reaction conditions, it has been observed that substituted phenols and phenols with sensitive functional groups can be readily prepared.     

子半理想环

本文提出了环论中的一个新概念：子半理想，得到了群环为子半理想环的一个充要条件。     

Scaling Transformation for the Effect of Temperature-Dependent Fluid Viscosity with Thermophoresis Particle Deposition on MHD-Free Convective Heat and Mass Transfer Over a Porous Stretching Surface

This article concerns with a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching sheet. The flow is permeated by a uniform transverse magnetic field. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation, and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity to decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases with the decreasing viscosity but the temperature increases in this case. Impact of thermophoresis particle deposition in the presence of temperature-dependent fluid viscosity plays an important role on the concentration boundary layer. The results, thus, obtained are presented graphically and discussed.     

传热传质对有抽吸的收缩薄片上的非线性磁流体动力学边界层流动的影响

This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

Lubrication of a rotating circular thrust bearing with a casson lubricant

Lubricants today are subjected to increasing mechanical shearing forces. This has resulted in an increasing interest in materials having variable viscosity. The problem of rotating circular thrust bearing is investigated with Casson fluid as a shear thinning lubricant. The pressure and load capacity of the thrust bearing is calculated when the feeding is done from the centre of the plates to the periphery. Also, moment of friction acting on the plates is calculated for different values of Casson number and for various values of ratio of inside to outside radius. It has been found that there is a decrease in the value of load capacity of the Casson lubricant. Also, it has been observed that there is an appreciable increase in the values of moment of friction for Casson fluid.     

Structure and conformation of a nickel complex: {2‐Hydroxo‐3‐piperidine‐1‐yl‐methyl‐N,N′(bis‐5‐bromobenzylpropylenediimine)nickel(II)perchlorate}

The title compound, a nickel complex [C₂₃H₂₆N₃O₂Br₂Ni.(ClO₄)] (CCDC 199520) crystallizes in triclinic space group P with the cell parameters a = 10.2560(4), b = 10.8231(4), c = 12.0888(5)Å, α = 99.404(1), β = 99.780(1), γ = 92.252(1)° and V = 1301.49(9)ų. The structure was solved by Patterson method and refined by full‐matrix least‐squares procedures to a final R = 0.0497 using 6287 observed reflections. In the complex, the piperidine ring takes chair conformation and the geometry around the Ni ion is slightly distorted square planar. The dihedral angle between the planes [N‐Ni‐N and O‐Ni‐O] is 9.4(1)°. The chelate ring containing both the nitrogen atoms adopts twisted boat conformation. The molecules in the crystal are stabilized by N‐H…O and C‐H…O types of hydrogen bonds in addition to a C‐H…π interaction. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chlor­amine‐B sesquihydrate

In the title compound, sodium N‐chloro­benzene­sulfon­amide sesquihydrate, Na⁺·C₆H₅ClNO₂S^?·1.5H₂O, the sodium ion exhibits octahedral coordination by O atoms from three water mol­ecules and by three sulfonyl O atoms of three different N‐­chloro­benzene­sulfon­amide anions. A two‐dimensional polymeric layer consists of units, each comprising two face‐sharing octahedra which share four corners with four other such units, the layer running parallel to the ab plane. The water mol­ecules participate in hydrogen bonds of the types O—H?O, O—H?N and O—H?Cl.     

(E)‐N′‐(4‐Chlorobenzylidene)‐, (E)‐N′‐(4‐bromobenzylidene)‐ and (E)‐N′‐[4‐(diethylamino)benzylidene]‐ derivatives of 4‐hydroxybenzohydrazide

The 4‐chloro‐ [C₁₄H₁₁ClN₂O₂, (I)], 4‐bromo‐ [C₁₄H₁₀BrN₂O₂, (II)] and 4‐diethylamino‐ [C₁₈H₂₁N₃O₂, (III)] derivatives of benzylidene‐4‐hydroxybenzohydrazide, all crystallize in the same space group (P2₁/c), (I) and (II) also being isomorphous. In all three compounds, the conformation about the C=N bond is E. The molecules of (I) and (II) are relatively planar, with dihedral angles between the two benzene rings of 5.75 (12) and 9.81 (17)°, respectively. In (III), however, the same angle is 77.27 (9)°. In the crystal structures of (I) and (II), two‐dimensional slab‐like networks extending in the a and c directions are formed via N—H...O and O—H...O hydrogen bonds. The molecules stack head‐to‐tail viaπ–π interactions involving the aromatic rings [centroid–centroid distance = 3.7622 (14) Å in (I) and 3.8021 (19) Å in (II)]. In (III), undulating two‐dimensional networks extending in the b and c directions are formed via N—H...O and O—H...O hydrogen bonds. The molecules stack head‐to‐head viaπ–π interactions involving inversion‐related benzene rings [centroid–centroid distances = 3.6977 (12) and 3.8368 (11) Å].