THERMOSOLUTAL CONVECTION WITH COUPLED HEAT AND MASS TRANSFER PROCESS IN A SQUARE ENCLOSURE

Thermosolutal convection flow and its effect on the heat and the mass transfer in a square enclosure is studied experimentally. Both thermal and solute diffusion are induced from the sides, and natural convection is initiated by the combined thermal and solutal buoyancies, which either augment or oppose to each other. The solute diffusion is initiated in an electrochemical system that uses copper sulfate-sulfuric acid solution as an electrolyte. Depending on the magnitude of buoyancy ratio, three different kinds of flow regimes and structures can occur, which lead to different distributions of concentration in the enclosure. The formation and growth of layered flow structure is attributed to the solutal boundary-layer flow that can intrude and accumulate along the horizontal wall. The nearly stagnant layer that occurs can reduce the heat transfer rate. The Nusselt numbers at different flow regimes are measured and correlated in terms of relevant nondimensional parameters. This suggests the correlation of Sherwood number in different ranges of buoyancy ratio. The visualization of flow structures and measurements of both heat and mass transfer allow better understanding of the complicated system.     

Anderson's theorem for compact operators

It is shown that if is a compact operator on a Hilbert space with its numerical range contained in the closed unit disc and with intersecting the unit circle at infinitely many points, then is equal to . This is an infinite-dimensional analogue of a result of Anderson for finite matrices.

     

Defect indices of powers of a contraction

Let A be a contraction on a Hilbert space H. The defect index d_A of A is, by definition, the dimension of the closure of the range of I-A^∗A. We prove that (1) d_Aⁿ?nd_A for all n?0, (2) if, in addition, Aⁿ converges to 0 in the strong operator topology and d_A=1, then d_Aⁿ=n for all finite n,0?n?dimH, and (3) d_A=d_A^∗ implies d_Aⁿ=d_A^n∗ for all n?0. The norm-one index k_A of A is defined as sup{n?0:‖Aⁿ‖=1}. When dimH=m<∞, a lower bound for k_A was obtained before: k_A?(m/d_A)-1. We show that the equality holds if and only if either A is unitary or the eigenvalues of A are all in the open unit disc, d_A divides m and d_Aⁿ=nd_A for all n, 1?n?m/d_A. We also consider the defect index of f(A) for a finite Blaschke product f and show that d_f(A)=d_Aⁿ, where n is the number of zeros of f.     

Ripening of ordered breath figures

We have investigated the ripening of breath figures with variable initial order. A dramatic impact of the degree of order on the coalescence behavior is observed. As opposed to the two-droplet coalescence events common to the usual disordered droplet arrays, four-droplet coalescence cascades predominate in a perfectly hexagonal breath figure. Upon introduction of disorder, a gradual transition to a regime dominated by three-droplet cascades is observed. The statistics of coalescence cascades allows for detailed conclusions on the microscopic droplet dynamics.     

Asymmetric addition of phenylacetylene to aldehydes catalyzed by complex of O‐sulfonyl camphor derivatives and titanium

Several novel ligands that are based on the camphor skeleton or contain the O‐sulfonyl group were synthesized and used in the asymmetric addition of phenylacetylene to aldehydes. This enantioselective reaction afforded chiral propargylic alcohols in high yields and with good to excellent levels of enantiopurity (up to 99% enantiomeric excess). Copyright © 2016 John Wiley & Sons, Ltd.     

Sulfone–Metal Exchange and Alkylation of Sulfonylnitriles

The first general sulfone–metal exchange is described. Treating substituted 2-pyridylsulfonylacetonitriles with either BuLi or Bu₃MgLi generates metalated nitriles that efficiently intercept a variety of electrophiles to afford quaternary nitriles. The 2-pyridylsulfone is critical for the sulfone–metal exchange because chelation anchors the organometallic proximal to the electrophilic, tetrasubstituted sulfone to override complex-induced deprotonation. Alkylating commercial 2-pyridinesulfonylacetonitrile with mild bases, either K₂CO₃ or DBU, and subsequent sulfone–metal exchange and alkylation rapidly assembles quaternary nitriles by three alkylations, only one of which requires an organometallic reagent.     

Experimental study of pre-swirl flow effect on the heat transfer process in the entry region of a convergent pipe

Experiments have been performed to study the heat transfer process of swirling flow issued into a heated convergent pipe with a convergent angle of 5° with respect to the pipe axis. A flat vane swirler situated at the entrance of the pipe is used to generate the swirling flow. During the experiments, the Reynolds number ranges from 7970 to 47,820, and the swirl number from 0 to 1.2. It is found that the convergence of the pipe can accelerate the flow which has an effect to suppress the turbulence generated in the flow and reduce the heat transfer. However, in the region of weak swirl (S = 0-0.65), the Nusselt numbers increase with increasing swirl numbers until S = 0.65, where turbulence intensity is expected to be large enough and not suppressible. In the region of strong swirl (S > 0.65), where recirculation flow is expected to be generated in the core of the swirling flow, the heat transfer characteristic can be altered significantly. At very high swirl (S ? 1.0), the accelerated flow in the circumferential direction is expected to be dominant, which leads to suppress the turbulence and reduce the heat transfer. The Nusselt number is found proportional to the swirl number. Correlations of the Nusselt numbers in terms of the swirl number, the Reynolds number and the dimensionless distance are attempted and are very successful in both the weak and the strong swirl regions.