An analytical solution to non-axisymmetric heat transfer with viscous dissipation for non-Newtonian fluids in laminar forced flow

Forced convection heat transfer in a non-Newtonian fluid flow inside a pipe whose external surface is subjected to non-axisymmetric heat loads is investigated analytically. Fully developed laminar velocity distributions obtained by a power-law fluid rheology model are used, and viscous dissipation is taken into account. The effect of axial heat conduction is considered negligible. The physical properties are assumed to be constant. We consider that the smooth change in the velocity distribution inside the pipe is piecewise constant. The theoretical analysis of the heat transfer is performed by using an integral transform technique – Vodicka’s method. An important feature of this approach is that it permits an arbitrary distribution of the surrounding medium temperature and an arbitrary velocity distribution of the fluid. This technique is verified by a comparison with the existing results. The effects of the Brinkman number and rheological properties on the distribution of the local Nusselt number are shown.     

Experimental study on effect of relative humidity on heat transfer of an evaporating water droplet in air flow

Dispersed water droplets are often seen in environmental air flows in rain, cloud, mist, sea spray and so on. It is therefore of great importance to precisely estimate heat transfer between water droplets and atmospheric air in developing a reliable climate model. The purpose of this study is to fabricate the measurement system for the temperature of a small water droplet in air flow under the controlled relative humidity condition and to investigate the effect of relative humidity on heat transfer across the surface of an evaporating water droplet in air flow. The results show that the droplet temperature decreases in the low-relative-humidity condition, whereas it increases in the high-relative-humidity condition. Nusselt number on the droplet surface is not affected by the relative humidity.     

Formation of 1,2,4-trioxolanes via 9,10-dicyanoanthracene(DCA)-sensitized photo-oxygenation of 2,2-diaryl-3-(2,2-diarylvinyl)oxiranes

9,10-Dicyanoanthracene-sensitized photo-oxygenation of 2,2-diaryl-3-(2,2-diarylvinyl)oxiranes 3 in acetonitrile did not afford the corresponding 1,2,4-trioxepines 4, but 1,2,4-trioxolanes 7. The structural assignment of 7 was reported, and the mechanism of the formation of 7 was proposed.     

Efficient Simulations of Charged Colloidal Dispersions: A Density Functional Approach

Summary: A numerical method is presented for simulating charged colloidal dispersions in electrolyte solutions. Utilizing a smoothed profile for colloid‐solvent boundaries, efficient mesoscopic simulations are enabled for modeling dispersions of many colloidal particles exhibiting many‐body electrostatic interactions. The validity of the method was examined for simple colloid geometries, and the efficiency was demonstrated by calculating stable structures of two‐dimensional dispersions, which resulted in the formation of colloidal crystals.

Formation of a charged colloidal crystal.     

Statistical mechanics of thermal diffusion

Expressions of the flows of atoms A and B of a binary system in a crystal are derived as the response to the imposed gradients of temperature and chemical potentials. The formulation is done using the pair approximation of the Path Probability Method of irreversible statistical mechanics and atomic migration is assumed to be via the vacancy mechanism. The energy carried by photons (and electrons) under the temperature gradient is assumed to be independent of the atomic flux. For the case near equilibrium, linear relations are derived among the atomic fluxes, the energy flux (associated with atomic flux) and the gradients. The Onsager reciprocal relations are proved to hold among the coefficients, including those related to energy flows. The heat of transport (energy carried by a diffusing atom) and the heat conduction due to atomic flux are thus unambigously derived.     

Cross-coupling of benzylic acetates with arylboronic acids: one-pot transformation of benzylic alcohols to diarylmethanes

Benzylic acetates reacted with arylboronic acids in the presence of a DPEphos-[Pd(eta3-C3H5)Cl]2 catalyst when tert-amyl alcohol was used as a solvent, and the catalytic cross-couplings produced diarylmethanes in high yields (up to 94% isolated yield).     

Determination of 1-hydroxypyrene in human urine by high-performance liquid chromatography with fluorescence detection using a deuterated internal standard

A high-performance liquid chromatographic method has been developed for the quantification of 1-hydroxypyrene (1-OHP) in human urine using deuterated 1-hydroxypyrene ([2H9]1-OHP) as an internal standard with fluorescence detection. [2H9]1-OHP was prepared enzymatically from deuterated pyrene ([2H10]Pyr) with cytochrome P450 1A1. It eluted immediately prior to non-deuterated 1-OHP on alkylamide-type reversed-phase columns and had nearly the same fluorescence characteristics as non-deuterated 1-OHP. The detection limit was 0.1 microg/L and the calibration range was from 1 to 100 nmol/L. Urine sample treatment involved enzymatic hydrolysis followed by solid-phase extraction using Sep-Pak C18 cartridges. The proposed method was used to determine urinary 1-OHP in smokers and non-smokers.     

Inequalities for a distribution with monotone hazard rate

Summary LetX be a positive random variable with the survival function and the densityf. LetX have the moments μ=E(X) and μ₂=E(X ²) and put ε=|1-μ₂/2μ²|. Put and . It is proved that the following inequalities hold: , for allx>0, ifq(x) is monotone and that , ifq ₁ (x) is monotone. It is also shown that Brown's inequality which holds wheneverq ₁ (x) is increasing is not valid in general whenq ₁ is decreasing. The Institute of Statistical Mathematics