Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification

The magnetohydrodynamics(MHD) convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of thermal stratification are examined.The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations,i.e.,a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gillbased shooting method.It is concluded that the flow field,temperature,and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.     

Local nonsimilarity solution for the impact of the buoyancy force on heat and mass transfer in a flow over a porous wedge with a heat source in the presence of suction/injection

Combined heat and mass transfer in free, forced and mixed convection flows along a porous wedge with internal heat generation in the presence of uniform suction or injection is investigated. The boundary-layer analysis is formulated in terms of the combined thermal and solute buoyancy effect. The flow field characteristics are analyzed using the Runge-Kutta-Gill method, the shooting method, and the local nonsimilarity method. Due to the effect of the buoyancy force, power law of temperature and concentration, and suction/injection on the wall of the wedge, the flow field is locally nonsimilar. Numerical calculations up to third-order level of truncation are carried out for different values of dimensionless parameters as a special case. The effects of the buoyancy force, suction, heat generation, and variable wall temperature and concentration on the dimensionless velocity, temperature, and concentration profiles are studied. The results obtained are found to be in good agreement with previously published works.     

Trapping Dimethyltin Cations by Bipyridine‐N,N′‐Dioxide Ligands

N,N′‐dioxide ligands such as 2, 2′‐bipyridine‐N,N‐dioxide (BPDO‐I) and 4, 4′‐bipyridine‐N,N‐dioxide (BPDO‐II) were used to trap the hydrated dimethyltin cations under controlled hydrolysis. The use of the chelating ligand BPDO‐I leads to the isolation of the discrete monocation [Me₂Sn(BPDO‐I)(OH₂)(NO₃)]⁺[NO₃]^– ( 2 ), whereas the linear ligand BPDO‐II directs the construction of cationic polymers, [{Me₂Sn(OH₂)₂(μ‐BPDO‐II)}²⁺{NO₃^–}₂ · 2H₂O]_n ( 3· 2H₂O) and [{Me₂Sn(μ‐OH)(BPDO‐II)}₂²⁺{NO₃^–}₂ · H₂O]_n ( 4· H₂O) under different reaction conditions.     

Lie group analysis for the effect of temperature-dependent fluid viscosity and thermophoresis particle deposition on free convective heat and mass transfer under variable stream conditions

This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equa- tions. The system remains invariant due to some relations among the transformation parameters. 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 decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases but the temperature increases with the decreasing viscosity. The impact of the thermophoresis particle deposition plays an important role in the concentration boundary layer. The obtained results are presented graphically and discussed.     

(1R,2S)‐2‐[N‐Methyl‐N‐(4‐toluene­sulfonyl)amino]‐1‐phenylpropan‐1‐ol

In the title compound, C₁₇H₂₁NO₃S, the S atom is in a distorted tetrahedral geometry and the N atom exhibits sp² character. The antiperiplanar conformation is observed for the N and hydroxyl‐O atoms and the torsion angle around the N—C linkage is ?136.3 (2)°. The mol­ecules are linked by O—H?O intermolecular hydrogen bonds to form an infinite one‐dimensional chains along the c axis.     

A class of non-Moufang Bol loops isomorphic to all their loop isotopes

For any two primes, , such that< and divides–1, it is shown that there exists a non-Moufang Bol loop of order ² which is isomorphic to each of its loop isotopes.     

4‐(3,17‐Dioxoandrost‐4‐en‐16‐ylidenemethyl)benzonitrile

The title compound, C₂₇H₂₉NO₂, has the outer six‐membered ring in a sofa conformation, while the central rings are in chair conformations. The five‐membered ring adopts a slightly distorted 13β,14α‐half‐chair conformation. The cyano­benzyl­idene moiety has an E configuration with respect to the carbonyl group at position 17.     

Aerobic oxidation of benzyl alcohols by MoVI compounds

Selective and controlled aerobic oxidation of activated benzyl alcohols to the corresponding aldehydes is achieved in refluxing CH₃CN using catalytic amounts of MoO₂Cl₂(L)₂ where L is DMSO, DMF or THF. The catalysis reactions are possible under open air in the absence of any other external co‐oxidants. However, bubbling of oxygen to the reaction mixture is useful in making the catalysis reaction sustained. Both activated and deactivated varieties of α‐substituted benzyl alcohols (secondary alcohols) give ketones in the same reaction conditions. The inexpensive catalyst is selective towards activated primary benzyl alcohols and also, being mild, stops the oxidation at the aldehyde stage, making it synthetically useful. Copyright © 2006 John Wiley & Sons, Ltd.